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| Name | Type | Description | Created | Examples |
|---|---|---|---|---|
| amazon-braket-qpe-tutorial | webpage | Amazon Braket QPE tutorial notebook. 129 ket expressions with 13 explicit multi-qubit kets. Step-by-step derivation of Quantum Phase Estimation algorithm: eigenstate |ψ⟩ with U|ψ⟩=e^{2πiφ}|ψ⟩, controlled-U^{2^k} application to produce (|0⟩+e^{2πi·2^k·φ}|1⟩)|ψ⟩, binary fraction notation [0.φ1...φn], inverse QFT extraction of phase bits. Full circuit diagram. Amazon Braket SDK implementation. Concrete T gate examples: QPE for T gate phase φ=1/8 with 4 precision qubits, 2x2 CNOT Bell state examples, T†T=I verification. Circuit subroutine functionality demonstration. | 3/22/2026 | 0 |
| automating-equational-proofs-dirac | research_paper | POPL 2025 paper by Yingte Xu, Gilles Barthe, Li Zhou. Proves decidability of Dirac notation first-order theory and efficient validity checking via term rewriting. Implements DiracDec in Mathematica, evaluating over 100 worked Dirac notation examples from the literature including entanglement, teleportation, and operator identities. Foundational literature for Fanal. | 3/21/2026 | 102 |
| avveduti-bologna-teleportation-networks-2019 | research_paper | Analysis of multi-hop Teleportation Protocols for Quantum Networks by Silvia Avveduti, University of Bologna, 2019. English Master's thesis (Telecommunications Engineering) covering quantum teleportation protocols for quantum networks. Covers Bell states with step-by-step derivations (|00>, |01>, |10>, |11>), CNOT gate circuit applications, Hadamard gate, entanglement swapping, multi-hop teleportation chains, quantum repeaters, and network topology analysis. 149 multi-qubit kets with dense Bell state measurement circuits. | 3/23/2026 | 0 |
| bandini-bologna-shor-algorithm-2018 | research_paper | Undergraduate mathematics thesis 'Crittografia quantistica e algoritmo di Shor' (Quantum cryptography and Shor's algorithm) by Michele Bandini (Univ. Bologna, Math degree, 2017/2018). 56 multi-qubit kets, 8 3-qubit+, 312 total kets, 63K chars. Italian language. Covers qubits, quantum gates (Hadamard, CNOT), multi-qubit systems, quantum Fourier transform (QFT) derivation, Shor's factoring algorithm (period finding via QFT, modular exponentiation), quantum cryptography (BB84), RSA-QFT connection. Step-by-step Shor algorithm derivation with computational basis states. Italian-language mathematics undergraduate thesis focused on Shor's algorithm and quantum cryptography. | 3/23/2026 | 0 |
| baroncini-bologna-computazione-quantistica-2015 | lecture_notes | Alex Baroncini, University of Bologna (UNIBO) physics undergraduate thesis (2015). Italian. 95 multi-qubit kets. Covers: multi-qubit states, 4 Bell states derivation (|00⟩+|11⟩, |01⟩+|10⟩, |00⟩-|11⟩, |01⟩-|10⟩), Bell state creation circuit (H+CNOT on |00⟩), quantum teleportation (step-by-step: 3-qubit state expansion α|0⟩⊗(|00⟩+|11⟩)+β|1⟩⊗... showing all 4 measurement outcomes), Toffoli gate (|110⟩→|111⟩), Hadamard transform H⊗2 on |00⟩, quantum error correction with logical qubits |00⟩L/|01⟩L/|10⟩L/|11⟩L, Deutsch/Deutsch-Jozsa algorithms, QFT algorithms, Grover search. | 3/23/2026 | 0 |
| basic-quantum-algorithms-portugal | research_paper | Basic Quantum Algorithms by Renato Portugal (LNCC, Brazil, arXiv:2201.10574, v9 March 2026). Comprehensive circuit-model tutorial covering: quantum circuits and Dirac notation review, single/two-qubit/multi-qubit gates, entanglement analysis, Deutsch's algorithm, Deutsch-Jozsa, Bernstein-Vazirani, Simon's problem, Shor's factoring algorithm (with modular exponentiation oracle circuits), QPE via Kitaev, Grover's search, HHL quantum linear systems. Each algorithm includes problem formulation, quantum circuit walkthrough, state analysis, entanglement analysis, and oracle circuit construction. 159 multi-qubit kets, 364 total ket patterns. Updated March 2026. | 3/22/2026 | 0 |
| basics-quantum-computation-vedral-plenio | research_paper | Basics of Quantum Computation by Vlatko Vedral and Martin Plenio (Imperial College London, 1998). Review article introducing quantum computation covering: qubit basics, Hadamard gate with ket derivation (|0>->|0>+|1>, |1>->|0>-|1>), two-qubit systems (a|00>+b|01>+c|10>+d|11>), EPR pairs, quantum gates and circuits, Deutsch algorithm, Shor's algorithm with QFT step (measuring |2>+|6>+|10>+...|4> periodicity), Grover search, quantum error correction. 381 total kets, 63 multi-qubit kets. Classic pedagogical reference with clear derivations for CS/physics audience. | 3/22/2026 | 0 |
| benjumea-us-elementos-computacion-cuantica-2018 | research_paper | TFG (Universidad de Sevilla, 2018) covering quantum computing fundamentals in Spanish. Dirac notation, qubits, Bloch sphere, tensor products, Bell states, superdense coding, quantum teleportation, gates (NOT, Hadamard, CNOT, SWAP), and Shor's algorithm with detailed QFT circuit derivation and worked example. 100 multi-qubit kets. | 3/23/2026 | 0 |
| bernstein-vazirani-ccnot-oracle | research_paper | Bernstein-Vazirani algorithm with CCNOT-based oracle by Annaby. Introduces two Toffoli-gate oracles for BV problem. Contains step-by-step ket-state derivation of circuit evolution showing |psi0> through |psi4> with explicit tensor product computations. Covers oracle definition with ket notation, phase kickback analysis, and a second algorithm for related Problem PI. 278 ket angle-bracket expressions. | 3/21/2026 | 0 |
| bodin-exo7-mathematiques-informatique-quantique | lecture_notes | Un peu de mathématiques pour l'informatique quantique by Arnaud Bodin (Exo7, Version 1.01, April 2024). Free French-language quantum computing textbook covering: Part I - qubits, quantum gates, complex numbers, vectors/matrices, quantum physics, quantum teleportation; Part II - quantum algorithms (Deutsch-Jozsa, Grover with proofs); Part III - Shor's algorithm with full number theory, discrete Fourier transform; Part IV - BB84 cryptography, quantum error correction, quantum advantage. Uses |x.y〉 notation for multi-qubit states: 666 two-qubit kets (|0.0〉, |0.1〉, |1.0〉, |1.1〉), 212 three-qubit kets, 3312 total ket expressions. Complete step-by-step circuit derivations in French. Includes Qiskit programming examples. 389K chars. | 3/23/2026 | 0 |
| callisesi-bologna-quantum-teleportation-2016 | research_paper | Il teletrasporto quantistico: principi quantomeccanici ed esperimenti (Quantum Teleportation: quantum mechanical principles and experiments) by Giulia Callisesi, University of Bologna, 2016. Italian thesis covering quantum computing foundations (qubits, multi-qubit systems, single and multi-qubit gates, quantum circuits), quantum entanglement, EPR paradox, Bell states and their measurement, quantum teleportation protocol (full step-by-step state evolution through CNOT and Hadamard gates), superdense coding, and experimental verification of teleportation. 114 multi-qubit kets including |00>, |01>, |10>, |11> Bell state derivations and CNOT applications. Strong on Bell state generation and teleportation circuit walkthroughs. | 3/23/2026 | 0 |
| cambridge-cst-quantum-computing-2526 | lecture_notes | Cambridge University CST Part II Quantum Computing lecture notes 2025-26 by Dr. Steven Herbert and Dr. Prakash Murali. 15 lectures covering qubits, quantum circuits, quantum algorithms (Grover, QFT, Shor, QPE), teleportation, superdense coding, BB84, and quantum error correction. 440 multi-qubit kets, 1729 total kets across all lectures. Brand-new 2026 material. | 3/22/2026 | 0 |
| carlesso-trieste-quantum-algorithms-open-systems | lecture_notes | Lecture notes on quantum algorithms for open quantum systems by Matteo Carlesso (Univ. Trieste, June 2024). 252 multi-qubit kets, 1183 total kets. Chapter 1: gate model (qubit gates, Hadamard test, teleportation, dense coding, QPE, HHL). Chapter 2: variational algorithms (QAOA, VQE, adiabatic). Covers both circuit-based algorithms and open system extensions. | 3/22/2026 | 0 |
| carpio-ucm-computacion-cuantica-2022 | research_paper | TFG (UCM 2022) Introduction to quantum computing for Mathematical Engineering. Covers qubits, gates (X,Y,Z,H), circuits, Deutsch-Jozsa, Grover, qubit addition with Qiskit. In Spanish. 69 multi-qubit kets. | 3/23/2026 | 0 |
| castellani-quantum-computation-lecture-notes | lecture_notes | Lecture Notes on Quantum Computation by Leonardo Castellani (University of Eastern Piedmont/INFN Torino, Italy, December 2021). 24 lectures covering: qubits, Bloch sphere, quantum gates, multi-qubit systems (tensor products, entanglement), superdense coding, teleportation, Deutsch's algorithm, Deutsch-Jozsa algorithm, quantum parallelism, density operators, Bell inequalities, BB84/Ekert quantum cryptography, classical/quantum complexity, controlled gates, universal gate sets, Quantum Fourier Transform, phase estimation (with Kitaev variant), order finding, Shor's factoring algorithm (including N=91 worked example), Grover search algorithm (2-bit example). 119 multi-qubit kets, 791 total ket expressions. | 3/22/2026 | 0 |
| cleve-qic710-lecture-notes-2025 | lecture_notes | Quantum Information Processing lecture notes by Richard Cleve (IQC/Waterloo, QIC 710, Fall 2025, V6, 327 pages). Three-part combined notes: Part I (Primer for Beginners): qubits, gates, circuits, measurements, teleportation, superdense coding; Part II (Quantum Algorithms): black-box query algorithms (Deutsch-Jozsa, Bernstein-Vazirani, Simon), QFT, Shor's order-finding and factoring, Grover search, amplitude amplification; Part III (Quantum Information Theory): density matrices, quantum operations, error-correcting codes, non-locality. 357 multi-qubit kets, 1514 total ket expressions. Updated September 2025 with extensive revisions. By co-inventor of quantum algorithms at IQC Waterloo. | 3/22/2026 | 0 |
| cortese-bologna-entanglement-protocol-2021 | lecture_notes | Quantificare l'entanglement: un protocollo su computer quantistico - Bachelor thesis by Chiara Cortese (University of Bologna, Physics, 2021). 228 multi-qubit kets, 1063 total kets. Covers: qubit mechanics, multi-qubit systems (|00>,|01>,|10>,|11> computational basis), tensor products, quantum gates (Hadamard, CNOT, Pauli), Bell states (all 4 Bell states with explicit derivations), quantum circuits, Schmidt decomposition, entanglement definition and measures (von Neumann entropy, geometric measure), 4-qubit entanglement protocol (Kuzmak-Tkachuk), IBM Qiskit implementation on ibmq_santiago. Italian language. Strong on Bell state derivations and multi-qubit circuit implementations. | 3/23/2026 | 0 |
| cortese-bologna-entanglement-qc-2021 | research_paper | Quantificare l'entanglement: un protocollo su computer quantistico (Quantifying entanglement: a protocol on quantum computers) by Chiara Cortese, University of Bologna, Physics, 2020/2021. Italian thesis covering Dirac notation fundamentals, qubits, multi-qubit systems and tensor products, quantum gates (CNOT, Hadamard, Toffoli, Fredkin), Bell states with step-by-step derivations, quantum teleportation protocol, density operator formalism, partial trace, entropy measures (Shannon, Von Neumann), quantum channel capacity, and IBM Q implementation. 219 multi-qubit kets including 137 3-qubit+ kets covering |000⟩ through |011⟩ in teleportation state evolution. | 3/23/2026 | 0 |
| czegel-uni-szeged-kvantum-programozas | lecture_notes | Kvantum programozás Jegyzet (Quantum Programming Lecture Notes) by Czégel András (University of Szeged, 2021). Hungarian-language quantum computing lecture notes covering: basic quantum mechanics and qubits (Chapters 1-4), multi-qubit systems and CNOT gates (Chapter 5), entanglement and Bell states (Chapter 5.4), quantum algorithm design and IBM Quantum Experience (Chapter 7), Deutsch-Jozsa algorithm (Chapter 8.5), quantum teleportation and superdense coding (Chapter 9), Quantum Fourier Transform (Chapter 10), Grover's search algorithm with phase estimation (Chapter 11), Shor's factoring algorithm with Qiskit implementation examples (Chapter 12). 93 multi-qubit kets, 353 total ket expressions. Unique Hungarian-language pedagogical resource with step-by-step gate and circuit derivations. | 3/23/2026 | 0 |
| d-hammer-labelled-dirac-reasoning | research_paper | D-Hammer paper by Yingte Xu, Li Zhou, Gilles Barthe. First tool for automated equational proof for labelled Dirac notation. Features expressive higher-order dependently-typed language for labelled Dirac notation, efficient normalization algorithm, and C++ implementation. Evaluates on representative examples from plain and labelled Dirac notation. Direct successor to DiracDec (2411.11617). Directly relevant to Fanal's labelled Dirac layer. | 3/21/2026 | 3 |
| deutsch-jozsa-elementary-derivation | research_paper | Pedagogical undergraduate-level paper presenting an elementary derivation of the Deutsch-Jozsa algorithm by Amin and Labelle. Shows how students can derive the algorithm from first principles using only basic quantum mechanics and linear algebra. 190 ket expressions with explicit tensor product oracle applications, phase kickback analysis, and step-by-step state evolution. Covers both standard presentation and the novel elementary approach. 15 pages. Ideal for formalization of Deutsch-Jozsa algorithm circuit in Fanal. | 3/21/2026 | 0 |
| dias-ufpe-grover-multiple-solutions-2019 | lecture_notes | Débora Fortunato Dias, UFPE undergraduate thesis (2019): step-by-step derivation of Grover's algorithm with multiple solutions. 142 multi-qubit kets. Brazilian Portuguese. Covers CNOT truth table, 3-qubit Grover iteration (H⊗n|000⟩, oracle phase flip, inversion-about-average), amplitude analysis, and IBM/Microsoft/Amazon quantum hardware benchmarking. | 3/23/2026 | 0 |
| diaz-caro-unr-computacion-cuantica-2018 | lecture_notes | Introducción a la computación cuántica y fundamentos de lenguajes de programación by Alejandro Díaz-Caro (CONICET/Universidad Nacional de Rosario/Universidad Nacional de Quilmes, Argentina, 2018). Spanish-language course notes for CS students with mathematical focus. Covers: bra-ket notation, Hilbert space, tensor products, qubits, quantum operators (Hadamard, CNOT, Toffoli), Bell states, superdense coding, quantum teleportation, no-cloning theorem, quantum algorithms (Deutsch, Deutsch-Jozsa, Grover search, Shor factoring), BB84 quantum cryptography. 122 multi-qubit kets, 1116 total kets. Step-by-step derivations with explicit computational-basis state expansions. Creative Commons licensed. | 3/23/2026 | 0 |
| dipierro-verona-informatica-quantistica | lecture_notes | Italian lecture notes on quantum computing (Informatica Quantistica) by Alessandra Di Pierro (University of Verona). Covers Dirac notation (notazione di Dirac), qubits, CNOT gate with explicit computational-basis transformations (|00>→|00>, |01>→|01>, |10>→|11>, |11>→|10>), quantum circuits, Deutsch/Grover/Fourier/Shor algorithms. 91 multi-qubit kets, 1059 total kets. Italian. | 3/23/2026 | 0 |
| dittel-freiburg-quantum-information-theory | lecture_notes | Quantum information theory lecture notes from Universität Freiburg (Dittel, 2022). 98 multi-qubit kets, 1543 total kets. Covers Bell states, CNOT, Grover, QFT, Shor, phase estimation, and quantum error correction. | 3/22/2026 | 0 |
| equivalent-quantum-circuits | research_paper | Tutorial on quantum circuit equivalence rules with extensive Dirac notation. Covers gate identities for X, Z, Hadamard, CNOT, CZ gates, and derives quantum teleportation and superdense coding from circuit equivalences. | 3/21/2026 | 13 |
| faigle-uni-koeln-mathematische-grundlagen-quantenrechnens | lecture_notes | Mathematische Grundlagen des Quantenrechnens (Mathematical Foundations of Quantum Computing) by Ulrich Faigle (Universität zu Köln, ZAIK, Sommersemester 2003). German-language mathematical lecture notes covering: classical bits and Boolean circuits (Chapter 1), stobits and qubits (Chapter 2), quantum circuits and unitary transformations (Chapter 3), Hilbert spaces and Fourier transform including tensor products and discrete Fourier transform (Chapter 4), Shor's algorithm with quantum period-finding (Chapter 5). 82 multi-qubit kets, 309 total ket expressions. Mathematical treatment emphasizing circuit model foundations, QFT derivation, and Shor's algorithm analysis. | 3/23/2026 | 0 |
| faist-quantum-error-correction-lecture-notes | lecture_notes | Comprehensive quantum error correction lecture notes by Philippe Faist (updated March 2026), covering stabilizer codes, CSS codes, surface codes, fault-tolerant computation, and approximate QEC with 62 multi-qubit kets; graduate-level treatment | 3/23/2026 | 0 |
| freitas-ufmg-shor-algorithm-factorization | lecture_notes | Adriana Xavier Freitas, UFMG (Universidade Federal de Minas Gerais) master's dissertation on Shor's algorithm (2010). Brazilian Portuguese. 54 multi-qubit kets, 646 total kets. Dedicated study of Shor's algorithm covering: modular arithmetic, algorithms (Euclidean GCD, continued fractions), quantum computing foundations (qubits, quantum gates, quantum circuits), quantum Fourier transform (QFT) with complexity analysis, Shor's algorithm derivation (order-finding, period-finding for factorization), and special case (order equal to power of 2). Includes quantum oracle for computing x^j mod N. Complete circuit-level derivations with Dirac notation for register states throughout. | 3/23/2026 | 0 |
| galvao-hhl-algorithm-tutorial | research_paper | Solving Linear Systems of Equations with the Quantum HHL Algorithm: A Tutorial on Physical and Mathematical Foundations for Undergraduate Students by Galvao et al. (SENAI CIMATEC Brazil, arXiv:2509.16640, September 2025). Comprehensive tutorial explaining HHL algorithm theory and Qiskit implementation. State preparation (|b>=|1>), QPE circuit derivation with 2-qubit clock register (|00>+|01>+|10>+|11> superposition), ancilla quantum encoding, inverse QPE. Includes numerical 2x2 matrix example showing full circuit state evolution phi0->phi1->phi2->phi3. Noise analysis and IBM quantum device demonstrations. 304 total ket expressions, 70 multi-qubit kets. Step-by-step HHL circuit derivation with tensor product state evolution. | 3/22/2026 | 0 |
| garcia-lacalle-upm-computacion-cuantica-2016 | lecture_notes | Master's textbook on quantum computing (UPM ETSISI, 2016) by Garcia Lopez de Lacalle et al. In Spanish. Covers quantum computing model, entanglement, teleportation, basic gates (X,H,CNOT,CCNOT), Deutsch, Deutsch-Jozsa, Simon, Grover, QFT, Shor, BB84/B92 crypto. With exercises. 90 multi-qubit kets. | 3/23/2026 | 0 |
| gaspari-bologna-qec-toric-code-2020 | research_paper | Quantum Error Correction and the Toric Code by Andrea Gaspari, University of Bologna, Physics, 2020. English thesis covering quantum error correction fundamentals: quantum bit flip and phase flip codes, stabilizer formalism, stabilizer states, Shor code, toric code construction with syndrome extraction circuits. Covers CNOT applications, stabilizer measurements, logical qubits, anyonic excitations. 95 multi-qubit kets including |000>, |111>, Bell states |00>, |01>, |10>, |11> in error syndrome circuits. | 3/23/2026 | 0 |
| gharibian-paderborn-intro-quantum-computation-2021 | lecture_notes | Introduction to Quantum Computation by Sevag Gharibian (Paderborn University, Germany, July 2021). Comprehensive 280-page lecture notes covering: linear algebra review, quantum mechanics basics, qubits, quantum gates (X, Z, H, CNOT), multi-qubit systems, Bell states (|00>+|11>), quantum teleportation (full derivation), Deutsch/Deutsch-Jozsa algorithm, Bernstein-Vazirani, Simon's algorithm, quantum Fourier transform, Shor's factoring algorithm, Grover's search, quantum error correction, quantum complexity (BQP/QMA). 138 multi-qubit kets with 45 instances of |00>, 41 of |11>, and concrete basis-state circuit derivations. 1962 total ket expressions. | 3/23/2026 | 0 |
| ghz-w-states-algorithms-ibm-quantum | research_paper | Efficient quantum algorithms for GHZ and W states with IBM implementation by Cruz et al. (2018). Step-by-step algorithms for generating GHZ (|000...>+|111...>) and W states on n qubits. W state generation: starts with |1000>, uses beam-splitter gate B(p) to progressively distribute weight giving |1000>->|0100>+... -> |W4>=|1000>+|0100>+|0010>+|0001>. Six-qubit W state (|100000>+|010000>+...) generation shown step-by-step. 87 multi-qubit kets with 50 distinct states including 4 and 6 qubit states. IBM Quantum circuit implementations with circuit diagrams and noise analysis. | 3/22/2026 | 0 |
| gopalan-vtu-quantum-gates-module | lecture_notes | Module 3: Quantum Computing & Quantum Gates for VTU (Visvesvaraya Technological University) CSE 2022 scheme, from Gopalan College of Engineering and Management. Indian undergraduate course module covering: qubit definition (|0> and |1> basis, superposition α|0>+β|1>), Bloch sphere, Dirac notation (bra-ket), single-qubit gates (Pauli X/Y/Z, Hadamard, S, T), multi-qubit gates (CNOT truth table on |00>|01>|10>|11>, SWAP, CZ, Toffoli), Bell states and entanglement. 96 multi-qubit kets, 324 total kets. Step-by-step gate matrix representations with explicit basis state actions. Official course module aligned with VTU 2022 scheme syllabus. | 3/23/2026 | 0 |
| gottesman-cmsc657-quantum-info-fall2024 | lecture_notes | CMSC 657: Introduction to Quantum Information Processing (Fall 2024) by Daniel Gottesman at University of Maryland. 29 lectures covering: pure states, unitary operators, no-cloning, tensor products, measurements, density matrices, reversible computation, quantum circuits, Bell measurement, quantum teleportation, superdense coding, Deutsch-Jozsa, Shor's algorithm, Grover's algorithm (single and multiple elements), Hamiltonian simulation, QEC (3-qubit code, 9-qubit code, stabilizer codes, 5-qubit code, 7-qubit code, toric code), fault-tolerant error correction, entropy, quantum channel capacity, quantum key distribution (BB84, Ekert91). Individual PDF lectures with explicit ket derivations. 172 multi-qubit kets across 29 lectures (34 mq kets in Lec 5 on quantum circuits alone), covering |00>, |01>, |10>, |11>, |000>, |001>, |111> states. Step-by-step Toffoli gate truth table, CNOT circuit identities, Bell state generation from |0>|0> inputs. | 3/23/2026 | 0 |
| grover-algorithm-database-search-tutorial | research_paper | Grover's Algorithm: Quantum Database Search by Lavor, Manssur, Portugal (2003, arXiv:quant-ph/0301079). 28-page introductory review with detailed geometric interpretation and worked 3-qubit example searching for |101⟩. Covers quantum circuit basics (H, CNOT, Toffoli), superposition, quantum parallelism, oracle construction, Grover operator, amplitude amplification. Step-by-step 3-qubit state evolution: |000⟩ initial state, Hadamard applied, oracle marks |101⟩ (flips sign), Grover diffusion, measurement. 67 multi-qubit kets, 133 total ket patterns. Geometric interpretation of Grover rotation in 2D subspace. | 3/22/2026 | 0 |
| grover-search-algorithm-derivation | research_paper | Derivation of Grover quantum search algorithm from Schrodinger's equation by Lov Grover. Step-by-step construction of the algorithm using state vectors, superposition, and unitary transformations. | 3/21/2026 | 0 |
| hervas-uva-circuitos-cuanticos-entrelazados-2021 | research_paper | TFG (UVA Valladolid, Physics, 2021) on quantum circuits for entangled photonic states. In Spanish. Covers entanglement, Bell states, GHZ states, quantum circuits (Hadamard, CNOT, Toffoli), teleportation protocol with explicit circuit derivation, no-cloning, Holevo theorem. 90 multi-qubit kets. | 3/23/2026 | 0 |
| hhl-quantum-linear-systems-algorithm | research_paper | Original Harrow-Hassidim-Lloyd (HHL) quantum algorithm for solving linear systems of equations. Presents step-by-step algorithm derivation using Dirac ket state vectors. Covers phase estimation, Hamiltonian simulation, and the quantum state preparation and measurement steps. | 3/21/2026 | 0 |
| hhl-step-by-step-walkthrough | research_paper | A Step-by-Step HHL Algorithm Walkthrough by Zaman, Morrell, Wong (San Jose State, IEEE Access 2022). Explains HHL analytically with explicit |Psi0> through |Psi9> state evolution in bra-ket notation covering QPE (phase kickback, QFT, inverse QFT), controlled rotation ancilla, and uncompute steps. Includes 4-qubit numerical example with explicit tensor product computations. 636 ket expressions. Also includes Matlab and Qiskit implementations. Ideal for encoding the complete HHL algorithm with all intermediate ket states in Fanal. | 3/21/2026 | 0 |
| hoever-fh-aachen-quanten-computing-skript | lecture_notes | Skript zur Vorlesung Quanten Computing (Version 3.3) by Georg Hoever (FH Aachen, Fachbereich Elektrotechnik und Informationstechnik). German-language comprehensive quantum computing lecture script covering: qubits, quantum gates (Hadamard, CNOT, Toffoli), multi-qubit systems, quantum circuits, Deutsch and Deutsch-Jozsa algorithm (Chapter 4), quantum circuits and universality (Chapter 5), Grover's search algorithm (Chapter 6), quantum teleportation and superdense coding (Chapter 7), Shor's algorithm and Quantum Fourier Transform (Chapter 10). 587 multi-qubit kets, 2224 total ket expressions with step-by-step circuit derivations in German. Unique German-language pedagogical resource with detailed gate-by-gate state evolution. | 3/23/2026 | 0 |
| intro-classical-quantum-computing-wong | book | Thomas Wong's comprehensive undergraduate textbook covering both classical and quantum computing (430+ pages). Quantum chapters cover qubits, quantum gates, multi-qubit states, entanglement, Bell states, quantum teleportation, quantum error correction, and quantum algorithms (Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon's, Grover's, QFT, Phase Estimation, Period Finding, Shor's). 4617 ket expressions, 1056 multi-qubit kets. Step-by-step Dirac notation derivations throughout. Free textbook available at thomaswong.net. | 3/22/2026 | 6 |
| intro-coding-quantum-algorithms-pyquil | research_paper | Introduction to Coding Quantum Algorithms: A Tutorial Series Using Pyquil, by Koch, Wessing, Alsing (AFRL). Tutorial for beginners covering single-qubit gates (Hadamard, Pauli X/Y/Z), multi-qubit circuits (CNOT, Toffoli), Bell states, quantum entanglement, Deutsch's algorithm, Bernstein-Vazirani algorithm, Grover's search algorithm, and QFT basics. 203 multi-qubit kets with explicit computational-basis state derivations and PyQuil/Rigetti quantum circuit implementations. Companion to the Qiskit tutorial series (arXiv:1903.04359) using the same pedagogical approach for the Rigetti platform. | 3/22/2026 | 0 |
| intro-coding-quantum-algorithms-qiskit | research_paper | Introduction to Coding Quantum Algorithms: A Tutorial Series Using Qiskit, by Koch, Wessing, Alsing (AFRL). Part 1 of tutorial series for beginners covering: single-qubit gates (Hadamard, Pauli X/Y/Z), multi-qubit circuits, Bell states, Deutsch's algorithm, Bernstein-Vazirani algorithm, Grover's search algorithm. 1107 ket expressions with explicit computational-basis state derivations, Qiskit implementations. Written for minimal background in quantum physics. Pairs with 2008.10647 (Part 2). | 3/21/2026 | 0 |
| intro-quantum-information-science-ekert-2025 | lecture_notes | Introduction to Quantum Information Science by Artur Ekert, Timothy Hosgood, Alastair Kay, Chiara Macchiavello (qubit.guide, last updated July 2025). Comprehensive free online textbook covering quantum mechanics foundations, qubits, quantum gates, quantum circuits, entanglement, Bell states, teleportation, superdense coding, quantum algorithms (Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, Grover, QFT, Shor, QPE), quantum error correction, quantum cryptography (BB84). 428 multi-qubit kets, 2891 total ket expressions with step-by-step Dirac notation derivations throughout. High-quality pedagogical textbook from Oxford/CQT authors. | 3/22/2026 | 0 |
| introduction-qc-non-physicists-rieffel | research_paper | An Introduction to Quantum Computing for Non-Physicists by Eleanor Rieffel and Wolfgang Polak (FX Palo Alto Lab, ACM Computing Surveys 2000). Classic comprehensive survey introducing quantum computing to computer scientists. Covers quantum mechanics basics, tensor products, entanglement, quantum gates, quantum teleportation (full step-by-step derivation: |000>+|011>+|100>+|111> state evolution through CNOT and Hadamard), dense coding, Deutsch-Jozsa, Simon's algorithm, Shor's algorithm (QFT derivation), Grover's search, and quantum error correction. 715 total kets, 217 multi-qubit kets. Written for CS audience, accessible without physics background. | 3/22/2026 | 0 |
| jesus-etal-qiskit-computacao-quantica-graduacao-2021 | research_paper | Jesus et al., Federal University of Oeste da Bahia, arXiv:2101.11388 (2021): Brazilian Portuguese undergraduate quantum computing tutorial using Qiskit. 113 multi-qubit kets. Published in Revista Brasileira de Ensino de Física. Covers CNOT (complete truth table), Bell states (all 4 states derived), 3-qubit Grover algorithm (oracle construction, amplitude amplification with explicit state evolution from |000⟩ to |111⟩), quantum teleportation, AND/OR quantum gate implementations. Includes Qiskit code for real IBM quantum hardware. | 3/23/2026 | 0 |
| jha-notes-quantum-computation-information | lecture_notes | Notes on Quantum Computation and Information by Raghav Jha (Jefferson Lab/Perimeter Institute, 2023). Comprehensive notes covering quantum gates, circuits, algorithms, error correction, and Qiskit programs. Topics: multi-qubit states (|00>, |01>, |10>, |11> basis), tensor products, CNOT outer product (|00><00|+|01><01|+|10><11|+|11><10|), Toffoli gate action (|110>->|111>, |111>->|110>), Bell state derivation, GHZ state (|000>+|111>), quantum teleportation, Bernstein-Vazirani, Simon, Grover, Shor algorithms, QEC, density matrices. 110 multi-qubit kets with explicit circuit derivations and Qiskit implementations. | 3/22/2026 | 0 |
| joffe-qec-introductory-guide | research_paper | Quantum Error Correction: An Introductory Guide by Joschka Roffe (University of Sheffield, 2019, updated March 2025). Comprehensive QEC introduction covering: classical error correction (3-bit repetition code), quantum error correction basics, 2-qubit code, 3-qubit bit-flip code with syndrome extraction circuit (|0⟩_L=|00⟩, |1⟩_L=|11⟩), 3-qubit phase-flip code, [[4,2,2]] code, Shor [[9,1,3]] code construction via concatenation with explicit codespace derivation (|0⟩_L=|+++⟩, |1⟩_L=|---⟩ expanded in computational basis), general stabilizer codes, fault-tolerant QEC, surface codes and topological codes. 75 multi-qubit kets, 224 total ket expressions. Circuit diagrams for syndrome extraction. | 3/22/2026 | 0 |
| katabira-vut-brno-grover-algorithm-2021 | research_paper | Grover's Algorithm in Quantum Computing and Its Applications by Joseph Katabira (VUT Brno, Master's Thesis, Mathematical Engineering, 2021). English-language comprehensive treatment of Grover's algorithm covering: quantum computing foundations, single/multi-qubit systems, quantum gates (Hadamard, CNOT, Pauli, Toffoli), Deutsch and Deutsch-Jozsa algorithms, Simon's algorithm, quantum teleportation, Bell states, Grover search (oracle, diffusion operator, amplitude amplification), generalized Grover with multiple solutions, and practical implementations in Python. 212 multi-qubit kets including Bell states and step-by-step Grover algorithm state evolution. Covers applications and complexity analysis. | 3/23/2026 | 0 |
| kaye-laflamme-mosca-intro-quantum-computing | book | An Introduction to Quantum Computing by Phillip Kaye, Raymond Laflamme, Michele Mosca (Oxford University Press, 2007). Comprehensive undergraduate textbook. Chapter 2: Linear Algebra and Dirac Notation (bras, kets, dual vectors, tensor products, Schmidt decomposition). Chapter 3: Qubits and Quantum Mechanics framework (composite systems, measurement, mixed states). Chapter 4: Quantum Circuit Model (1-qubit gates including X, Y, Z, H, S, T with matrix forms and ket actions; controlled-U gates, CNOT truth tables). Chapter 5: Superdense Coding and Teleportation with full ket derivations. Chapter 6: Introductory algorithms (Deutsch, Deutsch-Jozsa, Simon's algorithm with step-by-step state evolution). Chapter 7: Algorithms with superpolynomial speedup (QFT, phase estimation, order-finding, Shor's algorithm). Chapter 8: Grover's search algorithm. Chapter 9: Quantum error correction. 255 multi-qubit kets, 2864 total ket expressions. Explicit gate truth tables for all 2-qubit computational basis states. | 3/23/2026 | 2 |
| kempe-approaches-quantum-error-correction | lecture_notes | Approaches to Quantum Error Correction by Julia Kempe (2006, Seminaire Poincare). Comprehensive 29-page survey covering repetition codes, quantum error correction fundamentals, stabilizer codes, CSS codes, syndrome extraction, and fault-tolerant quantum computation. Includes step-by-step ket derivations showing how quantum repetition codes correct bit-flip errors, phase-flip errors, and the 9-qubit Shor code. 98 multi-qubit kets with circuit derivations. | 3/22/2026 | 0 |
| koch-qiskit-quantum-algorithms-tutorial-2019 | research_paper | Introduction to Coding Quantum Algorithms: A Tutorial Series Using Qiskit by Daniel Koch, Laura Wessing, Paul Alsing (Air Force Research Lab, arXiv:1903.04359, March 2019). Multi-lesson tutorial teaching quantum algorithms from scratch using Qiskit. Covers: qubit basics with Dirac notation, single-qubit gates (H, X, Y, Z, S, T), multi-qubit systems (|000⟩ through |111⟩ basis), CNOT and controlled gates, Bell states generation (H+CNOT circuits), quantum teleportation, Deutsch-Jozsa algorithm, Bernstein-Vazirani, Simon's algorithm, Grover's search with oracle construction, QFT, and Shor's algorithm. 215 multi-qubit kets with 96 3-qubit+ kets including full 3-qubit basis {|000⟩,...,|111⟩} in algorithm walkthroughs. Each algorithm includes mathematical derivation with ket notation plus Qiskit code implementation. | 3/23/2026 | 0 |
| kockum-chalmers-quantum-computing-lecture-notes | lecture_notes | Comprehensive lecture notes on quantum computing from Chalmers University of Technology (Kockum et al., 2025). 109 multi-qubit kets, 1672 total kets. Covers quantum algorithms (Grover, QFT, Shor, QPE), variational algorithms (VQE, QAOA), and quantum error correction across 12 chapters. | 3/22/2026 | 0 |
| kofler-jku-quantum-information-2025 | lecture_notes | Quantum Information lecture notes by Johannes Kofler, Johannes Kepler University Linz, Austria, Summer Term 2025. 165 pages covering qubits, multi-qubit states and gates, superdense coding, quantum teleportation, QKD, density matrices, and quantum channels. Strong Dirac notation throughout chapters 2-6 with step-by-step circuit and protocol derivations. | 3/23/2026 | 0 |
| kumar-quantum-internet-technologies-2025 | research_paper | Quantum Internet: Technologies, Protocols, and Research Challenges by Kumar et al. (Univ. Pisa/CNR, 2025). Comprehensive guide to quantum internet covering: qubit and quantum gate fundamentals, Bell states (all 4: |Φ+>=|00>+|11>, etc.), entanglement swapping protocol (step-by-step Bell state measurement on qubits 2&3 to transfer entanglement 1→4), quantum teleportation, quantum key distribution, quantum repeaters and purification circuits. 76 multi-qubit kets (|00⟩,|01⟩,|10⟩,|11⟩,|000⟩,|011⟩,|100⟩,|111⟩ states). Covers network protocol layers, entanglement generation schemes, and current quantum internet infrastructure. | 3/23/2026 | 0 |
| leroyer-senizergues-enseirb-info-quantique-2017 | lecture_notes | Introduction à l'information quantique (Introduction to Quantum Information) by Y. Leroyer and G. Sénizergues (ENSEIRB-MATMECA, Bordeaux, updated April 2017). French-language course notes covering: qubits and quantum postulates, BB84 quantum cryptography, single-qubit gates (Hadamard, Pauli, phase), two-qubit states and entanglement, CNOT operations, quantum teleportation circuit derivation, quantum computation model (registers, gates), Deutsch algorithm, Grover search algorithm, Shor factoring algorithm with QFT, quantum information theory. 217 multi-qubit kets including Bell states |00⟩+|11⟩, |01⟩+|10⟩ and step-by-step teleportation protocol. 202K characters with exercises. | 3/23/2026 | 0 |
| li-cklixx-wm-quantum-invitation-2021 | lecture_notes | An Invitation to Quantum Information and Quantum Computing lecture series (Nov-Dec 2021) by Chi-Kwong Li (College of William & Mary) and Ray-Kuang Lee (National Tsinghua University). Elementary matrix theory approach covering quantum mechanics, quantum information, and quantum computing. 5 chapters + supplementary notes. Chapter 5 (Quantum Gates, Circuits, and Computation): 138 mq kets covering CNOT truth tables, Toffoli gate, universal gate sets, quantum circuit model. Chapters 2 and notes add 145 more mq kets covering Bell states, teleportation, BB84. Total: 290 multi-qubit kets, 2722 total ket expressions across all PDFs. | 3/23/2026 | 0 |
| magnani-bologna-qec-quantum-networks-2021 | research_paper | Syndrome-based Piggybacking for Quantum Networks by Lorenzo Domenico Magnani, University of Bologna, 2021. English Master's thesis covering quantum error correction for quantum networks: Bell state generation (|00>, |01>, |10>, |11>), CNOT and Hadamard gate derivations, teleportation protocol, stabilizer formalism, syndrome extraction, and quantum repeater networks. 96 multi-qubit kets with step-by-step Bell state measurement and teleportation circuit walkthroughs. | 3/23/2026 | 0 |
| mahmud-goldsmith-minimal-qc-intro-2025 | research_paper | Tutorial introduction to quantum computing for computing professionals by M M Hassan Mahmud and Daniel Goldsmith (Digital Catapult, arXiv:2504.00995v2, May 2025). Covers quantum states, basis states, gates (Identity, NOT/X, Hadamard with explicit ket actions H|0>=1/sqrt(2)(|0>+|1>), CNOT with all 4 basis states), tensor products, and Deutsch-Jozsa algorithm. 64 multi-qubit kets, 277 total kets. English. Framed as a model-of-computation perspective, abstracting quantum physics. | 3/23/2026 | 0 |
| malagoli-bologna-qec-ibm-2022 | research_paper | Quantum error correction with the IBM quantum experience by Pietro Malagoli, University of Bologna, Physics, 2022. Italian/English thesis covering quantum error correction algorithms: bit flip codes, phase flip codes, Shor code, stabilizer formalism with syndrome extraction circuits. Implements QEC on IBM Quantum hardware. 128 multi-qubit kets including |00>, |01>, |10>, |11>, |000>, |111> in CNOT and Hadamard gate error syndrome circuits. Strong on circuit-level QEC with explicit basis state computations. | 3/23/2026 | 0 |
| malagoli-bologna-qec-ibm-2023 | research_paper | Experimental analysis of quantum error correction through IBM Quantum by Pietro Malagoli, University of Bologna, 2023. Italian thesis covering quantum error correction theory and implementation: 3-bit repetition code (|000⟩ and |111⟩ encoding), syndrome extraction with ancilla qubits, CNOT circuits for parity checks, Shor QEC code, and Steane code. Step-by-step state evolution through encoding and decoding circuits on IBM Q hardware. 183 multi-qubit kets with 133 3-qubit+ kets including |100⟩, |011⟩, |010⟩, |101⟩, |001⟩, |110⟩ for all error syndrome cases. | 3/23/2026 | 0 |
| marzi-shor-qc-tor-vergata-2020 | lecture_notes | Italian undergraduate thesis on quantum computing and Shor's algorithm by Mattia Marzi (University of Rome Tor Vergata, 2020). Covers quantum postulates, CNOT gate, teleportation (including Bell state |beta_00> creation circuit), QFT circuit implementation, Shor's algorithm with quantum phase estimation, and Qiskit implementation. 55 multi-qubit kets including 4-qubit oracle states (|0111>, |0100>, etc.), 476 total kets. Italian. | 3/23/2026 | 0 |
| meyer-bell-states-superdense-teleportation | lecture_notes | Step-by-step derivations of Bell state generation, superdense coding (all 4 cases), and quantum teleportation. 146 multi-qubit kets with gate-by-gate ket evolution: H+CNOT creating Bell states, reverse Bell circuit for measurement, 3-qubit teleportation protocol with all outcomes. Clear circuit notation with Dirac bra-ket formalism. | 3/23/2026 | 0 |
| mielgo-uam-quantum-computing-linear-algebra-2024 | research_paper | TFG (UAM 2023-2024) on quantum computing fundamentals through linear algebra. Covers qubits, gates, entanglement, Deutsch-Jozsa, Grover, Shor, QFT in Spanish. 87 multi-qubit kets. | 3/23/2026 | 0 |
| minimal-intro-quantum-computing-mahmud | research_paper | A Minimal Introduction to Quantum Computing by Mahmud and Goldsmith (Digital Catapult, 2025). Tutorial for computing professionals abstracting away physics. Covers: qubit state representation with 6-qubit register examples (|010010>, |110010>, |011010>), superposition states, tensor products (tensor product expansion a1b1|00>+a1b2|01>+a2b1|10>+a2b2|11>), CNOT gate action on all basis states (CNOT|00>=|00>, CNOT|01>=|01>, CNOT|10>=|11>, CNOT|11>=|10>), CNOT outer product form, circuit examples, Deutsch-Jozsa algorithm. 64 multi-qubit kets with explicit computational-basis demonstrations. | 3/22/2026 | 0 |
| miroglio-bologna-qec-codes-2024 | research_paper | I codici di correzione degli errori quantistici (Quantum Error Correction Codes) by Virginio Miroglio, University of Bologna, 2024. Italian master's thesis covering QEC theory: error channels (depolarizing, phase damping, amplitude damping), first QEC codes (3-qubit bit-flip, phase-flip, Shor 9-qubit code), CSS codes, stabilizer codes (symplectic notation, 5-qubit code), quantum surface codes, and LDPC codes. 73 multi-qubit kets including Bell state generation circuits, CNOT applications, stabilizer syndrome extraction. Comprehensive coverage of quantum error correction with explicit circuit derivations. | 3/23/2026 | 0 |
| mondal-parhi-stabilizer-qec-tutorial-2023 | research_paper | Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial by Arijit Mondal and Keshab K. Parhi (University of Minnesota, arXiv:2309.11793, September 2023). IEEE journal article serving as tutorial on designing and simulating quantum encoder/decoder circuits for stabilizer codes. Covers: 3-qubit repetition code circuit (|000⟩,|111⟩ encoding), 5-qubit code encoder/decoder with syndrome detection circuits, Steane [7,1,3] code encoder/decoder with CNOT ladder structures, nearest-neighbor compliant circuit transformations, and IBM Qiskit verification. 338 multi-qubit kets, 300 3-qubit+ kets including syndrome measurement patterns across all error types. Step-by-step circuit gate sequences with explicit ket state evolution. | 3/23/2026 | 0 |
| monzali-bologna-quantum-perceptron-2023 | research_paper | Simulations of a quantum perceptron on IBM-Qiskit by Valentina Monzali, University of Bologna, Physics, 2023. English thesis implementing a quantum perceptron (quantum neural network) on IBM Quantum using Qiskit. Covers quantum gates (CNOT, Hadamard, Toffoli), Bell state preparation with step-by-step circuit derivations, multi-qubit measurement, and quantum perceptron learning algorithm. 80 multi-qubit kets including Bell state derivations |00>, |01>, |10>, |11> and 3-qubit computational states. | 3/23/2026 | 0 |
| multi-controlled-su2-decomposition | research_paper | Decomposition of n-qubit multi-controlled SU(2) gates with improved CNOT count. Includes concrete circuit constructions and gate identity derivations. | 3/21/2026 | 0 |
| murolo-bologna-qc-postquantum-crypto-2022 | research_paper | Quantum Computing and Post-Quantum Cryptography by Giuseppe Murolo (University of Bologna, Mathematics, 2022). English. Covers: quantum mechanics foundations, qubits, quantum gates (X/Y/Z/H/CNOT), 2-qubit computational basis states |00>,|01>,|10>,|11>, quantum circuits, Bell states, Shor's algorithm (order finding, QFT), and post-quantum cryptography (NIST standardization, lattice-based crypto, digital signatures). 50 multi-qubit kets, 451 total kets. Step-by-step circuit derivations using Dirac notation for CNOT gate actions and Bell state generation. Focus on quantum computing foundations with Shor algorithm impact on RSA/cryptography. | 3/23/2026 | 0 |
| nannicini-ibm-intro-quantum-computing-2017 | research_paper | An Introduction to Quantum Computing, Without the Physics by Giacomo Nannicini (IBM T.J. Watson, arXiv:1708.03684, 2017, updated 2020). Rigorous introduction for discrete mathematicians covering: quantum gates (Hadamard, CNOT, Toffoli), tensor products, quantum states and measurements, quantum algorithms (Deutsch-Jozsa, Simon's algorithm, quantum search, Shor's algorithm), quantum error correction, and circuit complexity. 90 multi-qubit kets with concrete basis-state derivations (23 instances each of |00>, |01>, |11>, 18 of |10>). 657 total ket expressions. Accessible to readers without physics background via axiomatic approach. | 3/23/2026 | 0 |
| notation-general-quantum-teleportation | research_paper | Introduces notation for quantum teleportation of finite-dimensional states through generally entangled channels. Presents mathematical criterion for faithful teleportation using Dirac notation. | 3/21/2026 | 0 |
| olivares-milan-qc-lecture-notes-2021 | lecture_notes | Comprehensive lecture notes on quantum computing by Stefano Olivares (University of Milan, ver. 5.0, 2021). Covers qubits, single/multi-qubit gates including CNOT, Bell states, teleportation, circuit identities, Deutsch/Deutsch-Jozsa/Bernstein-Vazirani algorithms, Toffoli/Fredkin gates, universality, QFT, Grover, Shor. 102 multi-qubit kets, 2329 total kets. English. | 3/23/2026 | 0 |
| ozhigov-quantum-computations-course-msu | lecture_notes | Quantum computations course of lectures by Yuri Ozhigov (Moscow State University Lomonosov, 2021). Lecture series taught at MSU for several years covering quantum computing theory. Topics include: qubit basics and Bloch sphere, multi-qubit systems (EPR pairs, Bell states |00>+|11>), quantum entanglement and entropy, teleportation protocol with explicit state derivation (3-step λ|000>+λ|110>+μ|001>+μ|111> evolution), quantum error correction (|000>→|000>, |100>→|111> encoding), Grover's algorithm, quantum communication. 78 multi-qubit kets across 317K char text with step-by-step circuit derivations. | 3/22/2026 | 0 |
| pakin-rieffel-sc21-intro-quantum-computing-2021 | lecture_notes | Introduction to Quantum Computing tutorial slides (SC21/Supercomputing 2021) by Scott Pakin (LANL) and Eleanor Rieffel (NASA Ames). Covers qubits, multi-qubit states, CNOT, Hadamard, SWAP, Bell states, Grover, Shor, QFT. Slides format with explicit gate matrices and state examples. 98 multi-qubit kets. | 3/23/2026 | 0 |
| peconi-bologna-deutsch-jozsa-qscript-2017 | research_paper | L'Algoritmo di Deutsch-Jozsa in QScript by Federico Peconi, University of Bologna, 2017. Italian thesis implementing the Deutsch-Jozsa algorithm in QScript quantum programming language. Covers qubit formalism, multi-qubit systems, quantum gates (CNOT, Hadamard), the original Deutsch algorithm and its generalization, and full step-by-step derivation of Deutsch-Jozsa including oracle construction and quantum parallelism. 52 multi-qubit kets with computational basis states |00>, |01>, |10>, |11> in circuit derivations. | 3/23/2026 | 0 |
| pennylane-quantum-teleportation-tutorial | webpage | PennyLane tutorial on quantum teleportation by Matthew Silverman (2023). Step-by-step protocol walkthrough with explicit Dirac notation: no-cloning theorem proof, Bell state preparation (|00⟩+|11⟩)/√2, 3-qubit state expansion α|000⟩+β|100⟩+α|011⟩+β|111⟩, CNOT and Hadamard application giving (1/2)|00⟩(α|0⟩+β|1⟩)+(1/2)|01⟩(β|0⟩+α|1⟩)+(1/2)|10⟩(α|0⟩-β|1⟩)+(1/2)|11⟩(-β|0⟩+α|1⟩), measurement outcomes and Bob's corrections. Includes PennyLane Python code. 122 ket expressions with computational-basis multi-qubit kets. | 3/22/2026 | 0 |
| perry-fermilab-quantum-hs-module-2020 | lecture_notes | Pedagogical high school quantum computing module (Fermilab, 2020): superposition, qubit math, Bell states, entanglement, CNOT circuits. 137 multi-qubit kets, structured problem sets. | 3/23/2026 | 0 |
| pollachini-computacao-quantica-ufsc-2018 | lecture_notes | Comprehensive Brazilian Portuguese undergraduate thesis on quantum computing by Giovani Goraiebe Pollachini (UFSC, 2018). Covers linear algebra prerequisites, multi-qubit systems (tensor products), single/multi-qubit gates (X, Y, Z, H, S, T, CNOT, CZ, SWAP, Toffoli, Fredkin) with explicit basis-state action tables, circuit identities (CZ symmetry, CNOT=HZH, SWAP via 3 CNOTs), Pauli algebra, Deutsch-Jozsa algorithm, Simon's algorithm, Grover's algorithm, and IBM Quantum Experience implementation. 289 multi-qubit kets, 2352 total kets. Brazilian Portuguese. | 3/23/2026 | 0 |
| poremba-bu-cs599-quantum-computation-fall2025 | lecture_notes | CS 599 P1: Introduction to Quantum Computation (Fall 2025) by Alexander Poremba (Boston University). 24 scribed lecture notes covering quantum computing from scratch. Lecture 6 (Quantum Entanglement and Teleportation): step-by-step Bell state derivation from |00>, H applied to get (|00>+|10>)/sqrt(2), CNOT to get (|00>+|11>)/sqrt(2), all 4 Bell states (|00>+|11>, |01>+|10>, |00>-|11>, |01>-|10>), quantum teleportation with explicit 3-qubit state evolution through 12 steps. Lecture 13 (Grover's Algorithm): oracle phase flip, diffusion operator, amplitude analysis. Lecture 18-20: QFT, Shor's algorithm. Covers superdense coding, Deutsch-Jozsa, Bernstein-Vazirani, Simon's algorithm. 98 multi-qubit kets across 24 lectures, 1843 total ket expressions. September-December 2025. Scribe notes in LaTeX format. | 3/23/2026 | 0 |
| portugal-lncc-basic-quantum-algorithms-2022 | research_paper | Renato Portugal (LNCC/MCTI Brazil), arXiv:2201.10574 (2022, updated March 2026): Basic Quantum Algorithms. Comprehensive English-language textbook-style treatment. 159 multi-qubit kets, 2382 total kets. Chapter 2 covers quantum circuits: single-qubit gates, 2-qubit states with entanglement, CNOT truth table, Toffoli/CCNOT, universal gate decomposition. Chapters 3-9: Deutsch's algorithm (circuit analysis + oracle construction), Deutsch-Jozsa, Bernstein-Vazirani (BV oracle circuit), Simon's problem (quantum analysis + classical part), Shor's factoring algorithm (QFT circuit, modular exponentiation circuit), Shor's discrete logarithm, Grover's algorithm. Step-by-step state evolution with explicit basis states throughout. | 3/23/2026 | 0 |
| portugal-sbmac-computacao-quantica-2012 | book | Livro introdutório de computação quântica por Renato Portugal, SBMAC Vol. 8 (2ª ed. 2012). Cobre estados quânticos, portas universais, algoritmo de Grover, QFT e algoritmo de Shor. 1245 kets em notação de Dirac. Base matemática rigorosa com derivações passo a passo. | 3/23/2026 | 0 |
| preskill-caltech-ph219-quantum-lecture-notes | lecture_notes | Physics 219/Computer Science 219: Quantum Computation lecture notes by John Preskill (Caltech). Seven chapters of comprehensive quantum computing notes used for Caltech's flagship quantum computing course since 1997. Chapter 1 (Introduction, 30pp): overview of quantum computing, superposition, interference, entanglement with 40 multi-qubit kets including |01>, |10>, |11> examples. Chapter 2 (Foundations I, 52pp): quantum states and density matrices. Chapter 3 (Foundations II, 66pp): measurement and evolution. Chapter 5 (Classical and Quantum Circuits, 54pp): CNOT truth tables, universal gate sets, Bell state creation circuits, Toffoli gate, 26 multi-qubit kets. Chapter 6 (Quantum Algorithms, 64pp): Deutsch-Jozsa, Shor, Grover, phase kickback, Bernstein-Vazirani, Simon's algorithm, QFT, period finding. Chapter 7 (Quantum Error Correction, 92pp): 3-qubit repetition code, Shor's 9-qubit code, stabilizer codes with 39 multi-qubit kets (|000>, |111> codewords and syndrome extraction). Total: 130 multi-qubit kets, 2680 total ket expressions. Most recent update: Chapter 10 (Quantum Shannon Theory) updated June 2025. | 3/23/2026 | 0 |
| programming-quantum-computers-lecture-notes | research_paper | Lecture notes on programming quantum computers using Qiskit. Covers single-qubit and multi-qubit gates with ket state descriptions, quantum circuit diagrams, quantum adder using QFT, Bell state preparation, and QAOA. Includes annotated Python/Qiskit code examples. | 3/21/2026 | 0 |
| qas2023-quantum-programming-tutorial-2 | webpage | Quantum Autumn School 2023 (ENCCS/WACQT/NordIQuEst) Tutorial - Quantum Programming II. 105 ket expressions with 60 multi-qubit kets. Covers: n-qubit state vector as 2^n complex amplitudes, computational basis states |00...0⟩ through |11...1⟩, tensor product notation |0⟩⊗|0⟩=|00⟩, CNOT gate action (X⊗X⊗X)|000⟩=|111⟩, Hadamard on multi-qubit systems creating uniform superposition, Bell state (|00⟩+|11⟩)/√2 via H+CNOT circuit, quantum entanglement (no separable decomposition), GHZ state (|000⟩+|111⟩)/√2. Qiskit implementations with mathematical explanations. Part of Nordic quantum school series. | 3/22/2026 | 0 |
| qas2023-quantum-programming-tutorial-3 | webpage | Quantum Autumn School 2023 (ENCCS/WACQT/NordIQuEst) Tutorial - Quantum Programming III on quantum teleportation. 101 ket expressions with 37 multi-qubit kets. Step-by-step teleportation protocol: Alice's qubit |ψ⟩=α|0⟩+β|1⟩, shared Bell state |β00⟩=(|00⟩+|11⟩)/√2, combined 3-qubit state expansion showing α(|000⟩+|011⟩)+β(|100⟩+|111⟩), CNOT application, Hadamard on Alice's qubit, measurement-based corrections (X and Z gates). Full state evolution through all circuit steps. Qiskit implementation of teleportation circuit with verification. No-cloning theorem discussion. | 3/22/2026 | 0 |
| qec-stabilizer-circuits-tutorial | lecture_notes | Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial by Mondal and Parhi (University of Minnesota, 2023). Tutorial on designing and simulating quantum encoder/decoder circuits for stabilizer codes. Covers: five-qubit code and Steane code with explicit circuit construction, syndrome detection, nearest-neighbor compliant circuits, and IBM Qiskit verification. Step-by-step encoding/decoding with explicit multi-qubit computational-basis states showing syndrome extraction. 338 multi-qubit kets covering |000>, |111>, |00100>, |11000>, |0101>, |0111> and full syndrome tables. | 3/22/2026 | 0 |
| qec-stabilizer-codes-intro-bradshaw | lecture_notes | Introduction to Quantum Error Correction with Stabilizer Codes by Bradshaw, Dale, Evans (QodeX Quantum, 2025). Tutorial for computer scientists and mathematicians. Covers: quantum computation basics, simple QEC codes (bit-flip repetition, phase-flip codes, Shor nine-qubit code), stabilizer formalism, CSS codes, Steane code, five-qubit perfect code, fault-tolerant operations. 335 multi-qubit kets with 44 distinct computational-basis states including 5-qubit codewords (|00000>, |11100>, |10011>, |01111>). Step-by-step error correction circuits with explicit syndrome measurement. | 3/22/2026 | 0 |
| qiskit-textbook-bernstein-vazirani | webpage | Qiskit Textbook chapter on Bernstein-Vazirani Algorithm (archived Qiskit/textbook GitHub, 2021-2023). Jupyter notebook with 68 ket expressions covering: problem formulation with oracle f(x)=s·x mod 2, classical n-query approach vs 1-query quantum solution, step-by-step state derivation through H⊗n|0...0⟩, oracle application, measurement. Multi-qubit kets |00⟩, |01⟩, |10⟩, |11⟩ throughout. Includes Qiskit implementation and simulation on IBM device. | 3/22/2026 | 0 |
| qiskit-textbook-deutsch-jozsa | webpage | Qiskit Textbook chapter on Deutsch-Jozsa Algorithm (archived Qiskit/textbook GitHub, 2021-2023). Jupyter notebook with 92 ket expressions covering: problem formulation with oracle f({x0,x1,...}), classical vs quantum comparison, step-by-step DJ quantum algorithm derivation, Hadamard transform analysis, constant vs balanced oracle circuit examples, Qiskit implementation and simulation. | 3/22/2026 | 0 |
| qiskit-textbook-grover-algorithm | webpage | Qiskit Textbook chapter on Grover's Algorithm (archived Qiskit/textbook GitHub, 2021-2023). Jupyter notebook with 238 ket expressions covering: oracle construction U_ω|x⟩=-|x⟩, diffusion operator, state preparation for search spaces, 2-qubit and 3-qubit concrete examples with computational-basis states |000⟩ through |111⟩, oracle matrix for ω=101, applications to Sudoku and triangle problems. Includes Qiskit circuit implementations and simulation results. | 3/22/2026 | 0 |
| qiskit-textbook-multiple-qubits | webpage | Qiskit Textbook chapter on Multiple Qubits and Entangled States (archived Qiskit/textbook GitHub, 2021-2023). Jupyter notebook with 72 ket expressions covering: multi-qubit state representation with 4D vectors (a00|00⟩+a01|01⟩+a10|10⟩+a11|11⟩), tensor product Kronecker construction, CNOT gate action, Bell state creation (|00⟩+|11⟩)/√2, entanglement analysis and measurement correlation. Foundational multi-qubit circuit material with step-by-step derivations. | 3/22/2026 | 0 |
| qiskit-textbook-phase-kickback | webpage | Qiskit Textbook chapter on Phase Kickback (archived Qiskit/textbook GitHub, 2021-2023). Jupyter notebook with 79 ket expressions covering: phase kickback mechanism where controlled-U on eigenstate |u⟩ kicks phase to control qubit, CNOT phase kickback derivation (|+⟩|1⟩ → e^{iπ/2}|-⟩|1⟩), Hadamard-CNOT-Hadamard = CZ circuit equivalence with explicit ket analysis, T-gate and phase gate kickback. Essential for understanding oracle phase marking in Grover and BV algorithms. | 3/22/2026 | 0 |
| qiskit-textbook-quantum-fourier-transform | webpage | Qiskit Textbook chapter on Quantum Fourier Transform (archived Qiskit/textbook GitHub, 2021-2023). Jupyter notebook with 145 ket expressions covering: QFT definition QFT|j⟩=(1/√N)Σω^{jk}|k⟩, product representation formula QFT|x⟩=⊗_k(|0⟩+e^{2πix/2^k}|1⟩), 1-qubit QFT as Hadamard, circuit construction with Hadamard and controlled phase gates, counting in Fourier basis, inverse QFT. Includes Qiskit implementation. | 3/22/2026 | 0 |
| qiskit-textbook-superdense-coding | webpage | Qiskit Textbook chapter on Superdense Coding (archived Qiskit/textbook GitHub, 2021-2023). Jupyter notebook with 41 ket expressions covering: superdense coding vs teleportation comparison, Bell pair preparation, Alice Pauli gate operations (I, X, Z, XZ) to encode 2 classical bits, Bob CNOT and Hadamard decoding circuit with explicit |Φ+⟩, |Ψ+⟩, |Φ-⟩, |Ψ-⟩ Bell state derivations. Includes Qiskit implementation and IBM device results. | 3/22/2026 | 0 |
| qiskit-textbook-teleportation | webpage | Qiskit Textbook chapter on Quantum Teleportation (archived Qiskit/textbook GitHub, 2021-2023). Jupyter notebook with 116 ket expressions covering: no-cloning theorem, Bell pair preparation (|00⟩+|11⟩)/√2, 3-qubit state expansion α|000⟩+β|100⟩, Alice CNOT and Hadamard application yielding 4 measurement outcomes, Bob corrections based on 2-bit classical message. Full protocol derivation with explicit tensor product expansions. Includes Qiskit implementation and IBM quantum device execution. | 3/22/2026 | 0 |
| qlmn-expqcqec-grover-qft-qpe-2026 | lecture_notes | Lecture 6 from Master M2 QLMN Experimental Quantum Computing and Error Correction course (PASQAL/Institut d'Optique, February 2026) by Le Régent. Covers Grover's search algorithm, quantum Fourier transform, quantum phase estimation, and resource estimates for fault-tolerant computing. 54 multi-qubit kets, 263 total ket expressions. | 3/22/2026 | 0 |
| qsharp-katas-multi-qubit-gates | webpage | Microsoft Q# Katas multi-qubit gates tutorial (new qsharp repo, 2024). Interactive kata covering: tensor products of gates (X⊗I, X⊗H), CNOT gate with explicit |00>→|00>, |01>→|01>, |10>→|11>, |11>→|10> action, SWAP, CZ gates, controlled gates, Toffoli (CCNOT), and Fredkin (CSWAP). Uses LaTeX ket macros (\ket{}) with 205 multi-qubit ket instances (|00>, |01>, |10>, |11>, |000>, |111>) and 256 total ket expressions. Step-by-step matrix derivations and Q# implementations. Part of new microsoft/qsharp katas replacing old QuantumKatas repo. | 3/23/2026 | 0 |
| qsharp-katas-qec-shor | webpage | Microsoft Q# Katas QEC tutorial - Shor's 9-qubit error correction code (new qsharp repo, 2024). Covers: classical repetition code, quantum bit flip code (3-qubit: |0>→|000>, |1>→|111>), syndrome measurement, phase flip code, and Shor's full 9-qubit code combining both. Uses LaTeX ket macros with 72 multi-qubit kets (|00>, |11>, |000>, |111>, |100>, |010>, |001>) and 143 total. Step-by-step QEC circuit derivations from bit flip to full 9-qubit Shor code. Part of new microsoft/qsharp katas. | 3/23/2026 | 0 |
| quantum-algorithm-implementations-beginners | research_paper | Quantum Algorithm Implementations for Beginners by Abhijith J. et al. (LANL, arXiv:1804.03719, 2022). Comprehensive tutorial covering quantum computing programming model, then step-by-step implementations on IBM Q: Grover search, Bernstein-Vazirani, Linear Systems (HHL), Shor factoring, Matrix Elements, Group Isomorphism, Quantum Random Walks, QAOA, VQE, Quantum Simulation, and QEC tests. 684 total kets, 110 multi-qubit kets covering |000>-|111> and larger computational basis states. Each algorithm includes problem formulation, algorithm description with ket derivations, and Qiskit/IBM Q implementation. Ideal for encoding a wide range of algorithm examples. | 3/22/2026 | 0 |
| quantum-algorithms-beginners-implementations | research_paper | Comprehensive tutorial on quantum algorithm implementations by Abhijith J. et al. (LANL). Covers Grover's algorithm, Bernstein-Vazirani, Shor's algorithm, HHL (linear systems), quantum Fourier transform, and Variational Quantum Eigensolver with step-by-step ket state derivations. Includes IBM 5-qubit computer implementations. 683 ket expressions with tensor product expansions and oracle state derivations. | 3/21/2026 | 0 |
| quantum-algorithms-fourier-transform-jozsa | research_paper | Richard Jozsa's survey on quantum algorithms and the Fourier transform. Covers Deutsch's, Simon's, and Shor's algorithms with step-by-step ket-state derivations. Shows unified Fourier transform structure underlying all three algorithms. 245 ket expressions. Includes Kitaev's formalism for factoring. Clear pedagogical derivations of oracle application and superposition analysis. | 3/21/2026 | 0 |
| quantum-algorithms-lecture-notes-berta-rwth | lecture_notes | Quantum Algorithms lecture notes by Prof. Mario Berta, RWTH Aachen University (2025). 463 ket expressions covering: quantum circuit model (2-qubit basis |00⟩,|01⟩,|10⟩,|11⟩), Deutsch's problem with step-by-step state evolution showing |0⟩⊗|1⟩→(1/√2)(|0⟩+|1⟩)⊗(1/√2)(|0⟩-|1⟩)→(-1)^f(0)|0⟩+(-1)^f(1)|1⟩, Deutsch-Jozsa n-qubit derivation, Simon's problem, QFT product formula FN|k⟩ with binary fraction notation 0.k1...kn, QPE circuit derivation. Also covers Hamiltonian simulation (Trotter), QSVT, HHL, QRAM. Step-by-step circuit state evolution with numbered equations. | 3/22/2026 | 0 |
| quantum-algorithms-lecture-notes-faryad | lecture_notes | Comprehensive lecture notes on quantum algorithms by Muhammad Faryad (2025). 8 chapters covering: linear algebra review and single/multi-qubit gates, oracle circuit construction, foundational algorithms (entanglement, teleportation, Deutsch-Jozsa, Bernstein-Vazirani, Simon's), QFT-based algorithms (phase estimation, period finding, Shor's factoring), Grover's search and amplitude amplification, Hamiltonian simulation (Lie-Trotter, sparse, LCU), and HHL quantum linear systems algorithm. 2804 ket expressions with 361 multi-qubit computational-basis kets. Step-by-step state derivations (|psi0>, |psi1>, |psi2>...) with tensor product expansions, oracle constructions, and detailed circuit walkthroughs. Covers comprehensive algorithm coverage from Grover to HHL. | 3/22/2026 | 2 |
| quantum-algorithms-lecture-notes-quillen-rochester | lecture_notes | PHY265 Lecture notes on Introducing Quantum Algorithms by A.C. Quillen (University of Rochester, April 2025). 151 multi-qubit kets, 934 total kets. Comprehensive coverage: black-box algorithms (Deutsch, N-bit Hadamard transform, Deutsch-Jozsa, Bernstein-Vazirani), Quantum Fourier Transform (DFT, 3-qubit QFT step-by-step in Section 3.3 with |000⟩ through |111⟩ state evolution, product representation, efficient circuit), algorithms using QFT (Simon's, phase estimation, Shor's factoring with period finding), hidden subgroup problem, Grover's search, quantum counting, HHL linear systems, adiabatic algorithms, QAOA. Section 3.3 derives the 3-qubit QFT gate-by-gate on all basis states. Updated April 22, 2025. | 3/22/2026 | 0 |
| quantum-algorithms-revisited-cleve | research_paper | Quantum Algorithms Revisited by Cleve, Ekert, Macchiavello, Mosca (1997). Unifies quantum algorithms via multi-particle interference and phase estimation. Covers Deutsch's problem, Bernstein-Vazirani, Deutsch-Jozsa, Simon's algorithm, and Shor's order-finding algorithm with explicit ket-state derivations. Introduces phase kickback formalism. 496 ket expressions with step-by-step state evolution through Hadamard, oracle, and controlled-U operations. | 3/21/2026 | 0 |
| quantum-algorithms-tutorial-qiskit-fundamentals | research_paper | Fundamentals In Quantum Algorithms: A Tutorial Series Using Qiskit Continued, by Koch, Patel, Wessing, Alsing (AFRL). Part 2 of tutorial series covering: Quantum Fourier Transform (QFT), Quantum Phase Estimation (QPE), Quantum Counting, Shor's Algorithm, Q-Means, QAOA, and Variational Quantum Eigensolver. 1590 ket angle-bracket expressions with step-by-step state vector derivations including explicit QFT circuit walkthroughs. Accompanies each algorithm with Qiskit implementations. Ideal for encoding QFT and QPE circuits in Fanal. | 3/21/2026 | 0 |
| quantum-circuit-identities | research_paper | Constructs all quantum circuit identities from 3 or fewer operations from common one-qubit gates. Directly relevant for Dirac notation gate identity formalization. | 3/21/2026 | 2 |
| quantum-computation-lecture-notes-shor-mit | lecture_notes | Quantum Computation lecture notes by Peter Shor (MIT 8.370/18.435, Fall 2022). 31 lectures covering joint systems, tensor products, quantum gates (Hadamard, CNOT, T), quantum teleportation with EPR pair (|00>+|11> Bell pair), Deutsch-Jozsa algorithm with H^n Hadamard transform derivation (H^n|j> = sum (-1)^{j.k}|k>), Simon's algorithm with oracle Of|x>|z>=|x>|z+f(x)> step-by-step, QFT, Shor's factoring algorithm, Grover's search, and quantum error correcting codes. ~795 kets with 144 multi-qubit computational-basis kets across 22 individual PDFs. Notation: |xy denotes |x⟩ (LaTeX rendering). Features back-action analysis (CNOT on |->|->, circuit equivalences), oracle computation, phase kickback. Files available individually at Lecture_01.pdf through Lecture_31.pdf. | 3/22/2026 | 3 |
| quantum-computation-lecture-notes-watrous | lecture_notes | Comprehensive quantum computing lecture notes by John Watrous (University of Calgary, 2006). 22 lectures, 139 pages covering all major quantum algorithms: Deutsch, Deutsch-Jozsa, Simon's algorithm, phase estimation, QFT, order-finding and Shor's factoring algorithm, Grover's search algorithm, quantum teleportation, superdense coding, quantum error correction, QKD, and quantum complexity. 1656 ket expressions with 342 multi-qubit kets. Features step-by-step state derivations using black-box oracle notation Zf|x> = (-1)^f(x)|x>, phase kickback analysis, and explicit circuit walkthroughs. Includes detailed Grover analysis with geometric (reflection/rotation) proof and complete Shor's algorithm derivation via phase estimation. | 3/22/2026 | 1 |
| quantum-computation-review-aharonov | research_paper | Quantum Computation review by Dorit Aharonov (Hebrew University, 1998). Comprehensive 53-page introduction covering: quantum gates and universality, Deutsch's problem, Shor's factorization algorithm (full period-finding derivation with modular exponentiation oracle), Grover's search algorithm, quantum error correction, and quantum complexity theory. 515 ket expressions with computational-basis oracle applications |i⟩|j⊕f(i)⟩, QFT derivations, and state evolution through multi-qubit circuits. Written for computer scientists with theoretical CS background. | 3/21/2026 | 0 |
| quantum-computation-watrous-calgary-2006 | lecture_notes | CPSC 519/619 Quantum Computation lecture notes by John Watrous, University of Calgary, 2006. 19-lecture course covering quantum information basics, superdense coding, quantum circuits, teleportation (step-by-step |000>, |011>, |100>, |111> state derivations with CNOT and Hadamard), Deutsch algorithm, Deutsch-Jozsa algorithm, Simon's algorithm, phase estimation, quantum Fourier transform, order finding, Shor's factoring algorithm, Grover's search algorithm, quantum error correction (CSS codes), and quantum key distribution. 1683 ket expressions with 342 multi-qubit computational-basis kets. Archival version predating the UQIC.pdf course; provides alternative pedagogical derivations especially for teleportation, Bell states, and quantum circuit introduction sections. Referenced by Watrous as basis for his later comprehensive UQIC course. | 3/22/2026 | 4 |
| quantum-computing-error-correction-steane | research_paper | Andrew Steane's introduction to quantum error correction. Covers encoding, syndrome extraction, error operators, and code construction. 158 ket expressions with concrete ket-state walkthroughs of 3-qubit bit-flip code, phase-flip code, and 7-qubit Steane code. Shows general noise as Pauli operators, explains hierarchical fault-tolerant quantum computing architecture. | 3/21/2026 | 0 |
| quantum-computing-high-school-module | lecture_notes | Comprehensive 123-page quantum computing educational module by Perry, Sun, Hughes, Isaacson, and Turner (Fermilab/IMSA). Covers superposition, qubits, quantum measurement, entanglement, quantum gates (X, Hadamard, Z, CNOT), quantum teleportation, and Deutsch-Jozsa algorithm. Includes problem sets and simulation labs. 777 ket expressions. Excellent for foundational formalization of qubit gates, Bell states, teleportation circuit, and Deutsch-Jozsa algorithm step-by-step in Dirac notation. | 3/21/2026 | 0 |
| quantum-computing-lecture-notes-aaronson | lecture_notes | Quantum Computing lecture notes by Scott Aaronson (UT Austin, Fall 2018). Comprehensive 232-page introduction covering quantum gates, circuits, quantum teleportation, Deutsch/Deutsch-Jozsa, Bernstein-Vazirani, Simon's algorithm, Shor's factoring algorithm (RSA, QFT, period finding), Grover's search algorithm, and quantum error correction (9-qubit and 7-qubit Hamming codes). 1512 ket expressions with 166 multi-qubit computational-basis kets. Contains step-by-step oracle application derivations (|x,y>→|x,y⊕f(x)>), phase kickback analysis, Hadamard transform on bit strings (H^n|j> formula), and Bell state circuit walkthroughs. Written for advanced CS undergraduates. Complements Watrous 2006 and de Wolf 2023 notes. | 3/22/2026 | 1 |
| quantum-computing-lecture-notes-cambridge-1819 | lecture_notes | Quantum Computing lecture notes by Anuj Dawar (Cambridge University Computer Lab, Part II CST, 2018-19). Slide-style lecture notes covering: quantum bits and superposition, quantum gates and circuits, entanglement and Bell states, quantum teleportation (3-slide step-by-step derivation), Deutsch-Jozsa algorithm, Grover search algorithm (geometric analysis of Grover iterate, rotation in amplitude space), quantum Fourier transform, Shor's factoring algorithm. 62 multi-qubit kets, 351 total ket expressions. Clear pedagogical treatment with circuit diagrams. | 3/22/2026 | 0 |
| quantum-computing-lecture-notes-cambridge-2026 | lecture_notes | Quantum Computing lecture notes by Dr. Steven Herbert (Cambridge University CST Part II, 2025-26). 15 lecture PDFs plus supplementary materials. Total ~1958 ket expressions, ~495 multi-qubit kets. Covers: qubits and Hilbert space (L1-4), Bell states and entanglement (L5), teleportation and superdense coding with step-by-step derivations (L6: 56 mq kets), Deutsch-Jozsa and Bernstein-Vazirani algorithms (L7: 25 mq kets), Simon's algorithm (L8), QFT and phase estimation (L9-10), Grover's search algorithm (L11-12), quantum error correction with 3-qubit bit-flip code and 9-qubit Shor code derivations (L13: 273 mq kets), fault-tolerant quantum computing (L14: 32 mq kets), quantum complexity (L15). Supplementary materials (55 mq kets) cover Bell's theorem, universal gate sets, implicit measurement. Brand-new 2026 course with fresh pedagogical derivations. | 3/22/2026 | 0 |
| quantum-computing-lecture-notes-chalmers | research_paper | Comprehensive quantum computing lecture notes from Chalmers University (master's course). Covers Grover's algorithm, QFT, phase estimation, Shor's algorithm, VQE, QAOA, and quantum error correction with extensive Dirac notation (1100+ ket expressions). Includes exercises and tutorials. | 3/21/2026 | 0 |
| quantum-computing-lecture-notes-dewolf | lecture_notes | Comprehensive quantum computing lecture notes by Ronald de Wolf (CWI/University of Amsterdam, v5 Jan 2023). Covers Deutsch-Jozsa, Bernstein-Vazirani, Simon's algorithm, quantum Fourier transform, phase estimation, Shor's factoring algorithm, Grover's search, quantum error correction, and quantum complexity. 1935 ket expressions with 107 multi-qubit kets. Features explicit step-by-step derivations: DJ algorithm state evolution (uniform superposition, oracle application, Hadamard, measurement), teleportation with Alice-Bob 3-qubit state decomposition (|00>, |01>, |10>, |11> tensor products), phase estimation circuit derivation. Written for computer science students with focus on algorithmic analysis. | 3/22/2026 | 2 |
| quantum-computing-lecture-notes-grier-2025 | lecture_notes | Introduction to Quantum Computing lecture notes by Daniel Grier (UC San Diego, Spring 2025). Covers foundations of quantum mechanics, quantum circuits, query complexity, Shor's algorithm. Includes Deutsch-Jozsa, Bernstein-Vazirani, Simon's problem, Grover's algorithm with step-by-step Dirac notation derivations. 56 multi-qubit kets, 95 total ket patterns. Systematic treatment of CNOT, Hadamard, Toffoli gates with explicit ket action formulas. | 3/22/2026 | 0 |
| quantum-computing-lecture-notes-odonnell-cmu | lecture_notes | Quantum Computation lecture notes by Ryan O'Donnell and John Wright (CMU 15-859BB, Fall 2015). Scribe notes for 26 lectures covering: quantum circuit model with CNOT, Toffoli, quantum math basics (complex amplitudes, measurement, unitary matrices), power of entanglement (Bell states, teleportation, superdense coding), Grover's algorithm, quantum query model, Simon's problem with Fourier analysis, QFT over Z_N, period finding, Shor's algorithm, and hidden subgroup problem. Lectures 1-9 contain 783 ket lines with 243 multi-qubit computational-basis kets. Individual lecture PDFs at lecture01.pdf through lecture26.pdf. | 3/22/2026 | 0 |
| quantum-computing-textbook-gruska | book | Quantum Computing textbook by Jozef Gruska (Masaryk University, MUNI). 361 multi-qubit kets, 3406 total kets. Comprehensive textbook covering: Hilbert space basics, quantum circuits and gates (Chapter 2), quantum algorithms (Chapter 3): Shor's factoring algorithm (QFT-based period finding), Grover's search algorithm with amplitude amplification, quantum teleportation and superdense coding (Chapter 6), quantum error correction and stabilizer codes (Chapter 7), quantum automata (Chapter 4), quantum information theory (Chapter 8). Covers Bell states, quantum cryptography (BB84), and fundamental quantum protocols with explicit ket derivations. Bell state analysis, teleportation with |00⟩|01⟩|10⟩|11⟩ basis states. Available free online from MUNI. | 3/22/2026 | 0 |
| quantum-computing-undergraduate-qiskit | lecture_notes | Undergraduate-level quantum computing course using Qiskit by Gleydson et al. (UFOB, Brazil). Written in Portuguese with full mathematical notation. Covers single-qubit gates (Hadamard, Pauli, phase gates) with ket state derivations, CNOT, Bell state preparation (|Φ+⟩, |Φ-⟩, |Ψ+⟩, |Ψ-⟩), quantum teleportation, and Grover's algorithm. 228 ket expressions. Mathematical content (equations, Dirac notation) is universally readable despite Portuguese text. | 3/21/2026 | 0 |
| quantum-error-correction-beginners-devitt | research_paper | Quantum Error Correction for Beginners by Devitt, Munro, Nemoto. Comprehensive 50-page introduction covering single-qubit noise model, 3-qubit bit-flip code, 3-qubit phase-flip code, Shor 9-qubit code, 7-qubit Steane code, CSS codes, and fault-tolerant computation. 572 ket expressions with computational-basis derivations (|000⟩, α|000⟩+β|111⟩ encoding, CNOT syndrome extraction). Logical qubit definitions |0⟩_L = |000⟩, |1⟩_L = |111⟩. Covers error types, stabilizer formalism, and topological surface codes. Ideal for encoding logical qubit encoding circuits and QEC syndrome measurement in Fanal. | 3/21/2026 | 0 |
| quantum-error-correction-khalid-methods-guide | book | A Methods Focused Guide to Quantum Error Correction and Fault-Tolerant Quantum Computation by Abdullah Khalid (online interactive Jupyter book). 154 multi-qubit ket macros, 470 total ket macros across 10 notebooks. Uses LaTeX \ket{} macros. Step-by-step derivations: quantum repetition code for bit-flips (|000⟩, |111⟩ encoding with syndrome extraction, 63 mq kets), Shor 9-qubit code via code concatenation (|000⟩+|111⟩ building blocks for both |0⟩_L and |1⟩_L, 64 mq kets), phase-flip code, syndrome measurement circuits, stabilizer formalism with Pauli group. Covers encoding/decoding/syndrome circuits for stabilizer codes algorithmically. Source: github.com/abdullahkhalids/qecft. Last updated 2024. | 3/22/2026 | 0 |
| quantum-error-correction-stabilizer-circuits-tutorial | research_paper | Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial by Mondal and Parhi (U. Minnesota). Designs and verifies quantum encoder/decoder circuits for 3-qubit bit-flip code, 3-qubit phase-flip code, 5-qubit perfect code, and 7-qubit Steane code. 630 ket expressions using computational-basis ket notation. Step-by-step syndrome state derivations with explicit tensor product expansions (e.g. |000>+|111>, |001>, |010>). Includes IBM Qiskit circuit verification and nearest-neighbour compliant implementations. Covers CSS codes and stabilizer formalism with circuit diagrams. | 3/21/2026 | 0 |
| quantum-error-correction-stabilizer-codes-intro | research_paper | Introduction to Quantum Error Correction with Stabilizer Codes by Bradshaw, Dale, Evans (QodeX Quantum, 2025). Comprehensive 147-page introduction geared toward computer scientists and mathematicians. Section 2 reviews Dirac notation and quantum gates with teleportation circuit walkthrough (explicit |000⟩, |011⟩, |100⟩, |111⟩ state derivations). Section 3 covers basic QEC codes with step-by-step syndrome extraction: bit-flip code with 5-qubit state derivations (|00000⟩ through |11100⟩), phase-flip code. Section 4 covers stabilizer formalism with Pauli group generators and syndrome table. Section 5 introduces topological codes. Section 6 covers ML decoders. Includes OpenQASM 3.0 code examples. 1348 ket expressions, 335 multi-qubit kets (58 4+ qubit kets). More comprehensive than existing QEC database entries. | 3/22/2026 | 2 |
| quantum-information-computation-course-watrous | lecture_notes | Understanding Quantum Information and Computation by John Watrous (IBM/Waterloo, 2022-2025). Comprehensive 16-lesson course originally created for IBM Quantum Learning platform. 4 units: (I) Basics of quantum information — single/multiple systems, quantum circuits, entanglement in action with teleportation derivation (|pi0>->|pi1>->|pi2> circuit states, 3-qubit computations); (II) Fundamentals of quantum algorithms — query model, Deutsch, DJ, Simon's, BV, phase estimation, factoring, Grover's algorithm; (III) General formulation — density matrices, channels, measurements, purifications; (IV) QEC — error correction, stabilizer formalism, code constructions, fault-tolerant computation. 4196 ket expressions, 334 multi-qubit computational-basis kets (|000>, |001>, |110>, |111> etc). Step-by-step state derivations for teleportation, algorithm analysis. Free PDF at jhwatrous.github.io. | 3/22/2026 | 6 |
| quantum-information-computation-jozsa-cambridge | lecture_notes | Quantum Information and Computation lecture notes by Richard Jozsa (Cambridge University, Part IIC, 2019). Comprehensive notes covering: Dirac bra-ket notation, quantum states and operations, measurements, no-cloning theorem, quantum dense coding, quantum teleportation, BB84 QKD, Deutsch-Jozsa algorithm, Simon's algorithm, QFT and periodicity determination, Grover's search algorithm, Shor's factoring algorithm. 79 multi-qubit kets, 215 total ket patterns. Written by a co-inventor of the Deutsch-Jozsa algorithm. Clear pedagogical derivations with phase kickback analysis and oracle application formulas. | 3/22/2026 | 0 |
| quantum-information-processing-essential-primer | research_paper | Quantum Information Processing: An Essential Primer by Emina Soljanin (IEEE JSAIT 2020). Primer on quantum information science covering: qubit states, Bloch sphere, unitary operations, measurement, entanglement (Bell states |00>+|11>, |000>+|111> GHZ states), quantum teleportation, superdense coding, quantum error correction (three-qubit repetition code, syndrome detection), and quantum key distribution. 78 multi-qubit computational-basis kets with step-by-step state derivations. Well-structured IEEE journal paper for interdisciplinary readers. | 3/22/2026 | 0 |
| quantum-information-theory-lecture-notes | research_paper | Quantum information theory lecture notes from University of Freiburg. Dedicated chapter on Hilbert space and Dirac notation (kets, bras, inner products, outer products), operators, composite systems, tensor products, Bell states, Schmidt decomposition, quantum circuits, and quantum algorithms. ~960 ket notation expressions. | 3/21/2026 | 0 |
| quantum-introduction-lecture-notes-girvin-yale | lecture_notes | Introduction to Quantum Information, Computation and Communication by Steven M. Girvin (Yale University, PHYS 345, Spring 2024). Comprehensive undergraduate textbook covering qubits, Hilbert space, two-qubit gates (CNOT, Toffoli, SWAP), Bell states, Bell inequalities, quantum dense coding, no-cloning theorem, quantum teleportation, Deutsch-Jozsa algorithm, Grover search algorithm, QFT, phase estimation, Shor's algorithm. 157 multi-qubit kets (|00⟩,|01⟩,|10⟩,|11⟩,|000⟩...|111⟩), 171 total ket patterns. Step-by-step derivations with explicit two-qubit state expansions, CNOT truth tables, and Bell state circuit walkthroughs. | 3/22/2026 | 0 |
| quantum-katas-basic-gates | webpage | Microsoft Quantum Katas Basic Gates kata (Q# jupyter notebook). 176 ket expressions with 74 multi-qubit kets. Exercises covering: single-qubit gate applications (X, Z, H, S, T, Ry), two-qubit gates (CNOT, SWAP), multi-qubit gates (Toffoli/CCNOT, Controlled-H), adjoint and controlled gate variants. Each task specifies input state and target transformation with ket notation: |0⟩→|1⟩, |+⟩→|-⟩, |00⟩→|10⟩, Bell state preparation (|00⟩+|11⟩)/√2. Covers standard gate library with circuit exercises. | 3/22/2026 | 0 |
| quantum-katas-basic-gates-workbook | webpage | Microsoft Quantum Katas Basic Gates Workbook with explained solutions (Q# jupyter notebook). 341 ket expressions with 138 multi-qubit kets. Step-by-step derivations for gate transformations: X flips |0⟩↔|1⟩, Z maps |+⟩→|-⟩, H creates (|0⟩±|1⟩)/√2, CNOT maps |00⟩→|00⟩/|01⟩→|01⟩/|10⟩→|11⟩/|11⟩→|10⟩, SWAP maps |01⟩→|10⟩, Toffoli/CCNOT maps |110⟩→|111⟩, controlled gates, Bell state preparation (|00⟩+|11⟩)/√2. Comprehensive quantum gate action derivations. | 3/22/2026 | 0 |
| quantum-katas-distinguish-unitaries-workbook | webpage | Microsoft Quantum Katas Distinguish Unitaries Workbook with explained solutions (Q# jupyter notebook). 142 ket expressions with 62 multi-qubit kets. Step-by-step derivations for distinguishing quantum gates/unitaries by their action on basis states: identifying I vs X vs Y vs Z by applying to |0> and |1>, identifying H vs HX by action on computational basis, distinguishing CNOT variants by applying to |00>,|01>,|10>,|11>. Uses quantum state discrimination via controlled operations and measurement. Covers single-qubit and multi-qubit unitary identification tasks. | 3/22/2026 | 0 |
| quantum-katas-ghz-game-workbook | webpage | Microsoft Quantum Katas GHZ Game Workbook with explained solutions (Q# jupyter notebook). 40 ket expressions with 30 multi-qubit kets. Step-by-step derivation of GHZ entangled state preparation: from |000⟩ through X gates to |110⟩, then H gates to (1/2)(|000⟩-|010⟩-|100⟩+|110⟩), then CZ to flip last term sign, then CNOT to flip third qubit producing (1/2)(|000⟩-|011⟩-|101⟩-|110⟩). Explains quantum GHZ game strategy showing why (|000⟩-|011⟩-|101⟩-|110⟩)/2 achieves 100% win rate via measurement-based protocol. Classical strategy comparison included. | 3/22/2026 | 0 |
| quantum-katas-joint-measurements-workbook | webpage | Microsoft Quantum Katas Joint Measurements Workbook with explained solutions (Q# jupyter notebook). 224 ket expressions with 143 multi-qubit kets. Step-by-step derivations for joint measurement tasks: distinguishing (|00⟩+|11⟩)/√2 from (|01⟩+|10⟩)/√2 using parity measurement, quantum state discrimination using ancilla qubits, Bell state measurement with CNOT+H circuit, multi-qubit parity measurements and post-measurement state collapse. Explicit ket calculations showing state before/after measurement. | 3/22/2026 | 0 |
| quantum-katas-measurements | webpage | Microsoft Quantum Katas Measurements kata (Q# jupyter notebook). 164 ket expressions with 75 multi-qubit kets. Exercises on quantum measurement: distinguishing orthogonal states (|0⟩ vs |1⟩, |+⟩ vs |-⟩, Bell states), measuring in computational vs Hadamard basis, identifying multi-qubit states (|00⟩, |01⟩, |10⟩, |11⟩), partial measurements and post-measurement state collapse, POVM measurements. Each task provides target states and asks for Q# measurement circuit distinguishing them. | 3/22/2026 | 0 |
| quantum-katas-measurements-workbook | webpage | Microsoft Quantum Katas Measurements Workbook with explained solutions (Q# jupyter notebook). 297 ket expressions with 148 multi-qubit kets. Step-by-step measurement derivations: distinguishing |0⟩ vs |1⟩ (Z basis), |+⟩ vs |-⟩ (X basis via H), Bell state identification (measuring in Bell basis), partial measurement of 2-qubit system, multi-qubit state discrimination. Each solution explains which basis to measure in, with explicit ket calculation of post-measurement states and probabilities. | 3/22/2026 | 0 |
| quantum-katas-mq-measurements-workbook | webpage | Microsoft Quantum Katas Multi-Qubit System Measurements Workbook with explained solutions (Q# jupyter notebook). 101 ket expressions with 58 multi-qubit kets. Step-by-step derivations for multi-qubit measurement scenarios: partial measurement of Bell state (|00⟩+|11⟩)/√2 with post-measurement state collapse |00⟩ or |11⟩, measuring one qubit of GHZ state, joint measurement operators ZZ and ZI, distinguishing (|00⟩+|11⟩) from (|01⟩+|10⟩) via parity. Q# implementation with measurement-based state discrimination. | 3/22/2026 | 0 |
| quantum-katas-multi-qubit-gates | webpage | Microsoft Quantum Katas tutorial on Multi-Qubit Gates (Q# jupyter notebook). 255 ket expressions with 185 multi-qubit kets covering: applying single-qubit gates to multi-qubit systems (X⊗I, X⊗H tensor product matrices), CNOT gate with explicit |00⟩→|00⟩, |01⟩→|01⟩, |10⟩→|11⟩, |11⟩→|10⟩ action, SWAP gate, controlled gates (controlled-X, controlled-Z, controlled-H), multi-controlled gates (Toffoli/CCNOT, Fredkin/CSWAP). Step-by-step ket derivations with Q# implementation. Includes Bell state creation exercises. | 3/22/2026 | 0 |
| quantum-katas-multi-qubit-measurements | webpage | Microsoft Quantum Katas tutorial on Multi-Qubit System Measurements (Q# jupyter notebook). 94 ket expressions with 43 multi-qubit kets covering: multi-qubit measurement postulates, measuring one qubit of entangled pair (post-measurement state collapse), global measurement probability, partial measurements of Bell state ((|00⟩+|11⟩)/√2 → |00⟩ or |11⟩), measuring in different bases, joint measurements in Bell basis. Q# implementation of measurement protocols. | 3/22/2026 | 0 |
| quantum-katas-multi-qubit-systems | webpage | Microsoft Quantum Katas tutorial on Multi-Qubit Systems (Q# jupyter notebook). 96 ket expressions with 48 multi-qubit kets covering: multi-qubit state vector representation, computational basis for N-qubit systems (|00⟩, |01⟩, |10⟩, |11⟩ with explicit 4D vector representations), tensor product construction, Dirac notation for multi-qubit states, entangled vs separable states, Bell state (|00⟩+|11⟩)/√2, GHZ state. Step-by-step derivations with Q# code. | 3/22/2026 | 0 |
| quantum-katas-oracles-tutorial | webpage | Microsoft Quantum Katas tutorial on Quantum Oracles (Q# jupyter notebook). 425 ket expressions with 153 multi-qubit kets. Covers: classical vs quantum oracles, marking oracles (|x⟩|y⟩→|x⟩|y⊕f(x)⟩) with step-by-step ket derivations, phase oracles (|x⟩→(-1)^{f(x)}|x⟩), phase kickback mechanism with explicit CNOT on |+⟩|-⟩ derivation, oracle composition and combination rules, multi-qubit oracle construction for boolean functions AND/OR/XOR. Explicit computational-basis ket derivations showing oracle action on all basis states. | 3/22/2026 | 0 |
| quantum-katas-qec-bit-flip | webpage | Microsoft Quantum Katas Quantum Error Correction - Bit Flip Code kata (Q# jupyter notebook). 85 ket expressions with 38 multi-qubit kets. Covers: 3-qubit bit-flip error correcting code encoding (|0⟩→|000⟩, |1⟩→|111⟩), CNOT-based encoder circuit, syndrome measurement for error detection, error correction based on syndrome, decoding circuit. Step-by-step ket derivations of encoding, bit-flip error application, and syndrome-based correction. | 3/22/2026 | 0 |
| quantum-katas-qft-workbook | webpage | Microsoft Quantum Katas QFT Workbook with explained solutions (Q# jupyter notebook). 278 ket expressions with 44 multi-qubit kets. Step-by-step derivations for Quantum Fourier Transform: 1-qubit QFT (H gate as DFT), 2-qubit QFT circuit with controlled-R gates, n-qubit QFT using big-endian binary encoding |x1 x2..xn>, phase rotation gates R1Frac(2,k), QFT circuit decomposition into Hadamard + controlled-phase rotation layers. Includes binary fraction notation 0.j1j2...jn and product formula derivation. Covers implementation tasks from single-qubit to full n-qubit QFT with bit-reversal swap operations. | 3/22/2026 | 0 |
| quantum-katas-superposition | webpage | Microsoft Quantum Katas Superposition kata (Q# jupyter notebook). 123 ket expressions with 82 multi-qubit kets. Series of exercises for creating specific superposition states: |+⟩, |-⟩, (|00⟩+|01⟩+|10⟩+|11⟩)/2 uniform superposition, (|00⟩+|01⟩+|10⟩-|11⟩)/2, Bell states (|00⟩+|11⟩)/√2, (|00⟩-|11⟩)/√2, GHZ state (|000⟩+|111⟩)/√2, W state (|001⟩+|010⟩+|100⟩)/√3, and other multi-qubit superpositions. Each task states target ket expression and requires Q# circuit implementation. | 3/22/2026 | 0 |
| quantum-katas-superposition-workbook | webpage | Microsoft Quantum Katas Superposition Workbook with explained solutions (Q# jupyter notebook). 264 ket expressions with 94 multi-qubit kets. Provides step-by-step Q# circuit derivations for all superposition tasks: |+⟩ state (H gate), |-⟩ (HX), 2-qubit uniform superposition (|00⟩+|01⟩+|10⟩+|11⟩)/2, Bell states (|00⟩+|11⟩)/√2 and (|00⟩-|11⟩)/√2, GHZ state (|000⟩+|111⟩)/√2, W state (|001⟩+|010⟩+|100⟩)/√3, n-qubit superpositions. Each solution includes circuit explanation and ket state derivation. | 3/22/2026 | 0 |
| quantum-katas-superposition-workbook-2 | webpage | Microsoft Quantum Katas Superposition Workbook Part 2 with explained solutions (Q# jupyter notebook). 604 ket expressions with 253 multi-qubit kets. Comprehensive solutions for complex superposition states: N-qubit GHZ state (|000⟩+|111⟩)/√2 with circuit derivation showing H+CNOT chain, W state (|001⟩+|010⟩+|100⟩)/√3 construction, all-ones superposition state (|11...1⟩+...)/√N, arbitrary superpositions with controlled rotations, n-qubit uniform superposition H^n|0⟩, entangled superpositions. Step-by-step ket state transformations with circuit diagrams and explanations. | 3/22/2026 | 0 |
| quantum-native-dojo-multiqubit | webpage | Quantum Native Dojo tutorial on multi-qubit representation and operations (Qulacs framework). 99 ket expressions with 37 multi-qubit kets. Covers: n-qubit state vector as 2^n dimensional complex vector, computational basis |00...0⟩,|00...1⟩,...,|11...1⟩, tensor product construction |ψ1⟩⊗|ψ2⟩, CNOT gate action on |00⟩,|01⟩,|10⟩,|11⟩, Bell state (|00⟩+|11⟩)/√2 creation circuit, qubit ordering conventions, tensor product of operators X⊗I and I⊗X. Includes Python/Qulacs code examples with mathematical explanations. | 3/22/2026 | 0 |
| quantum-native-dojo-qft | webpage | Quantum Native Dojo tutorial on Quantum Fourier Transform (Qulacs framework). 74 ket expressions. Step-by-step QFT derivation: definition as DFT on computational basis |x⟩=|i1...in⟩, product formula showing QFT|j⟩=(1/√2)(|0⟩+e^{2πij/2}|1⟩)⊗...⊗(1/√2)(|0⟩+e^{2πi0.j1...jn}|1⟩), QFT circuit with Hadamard + controlled-R_k phase rotation gates, circuit diagram showing gate sequence and qubit wiring, bit-reversal swap step. Python/Qulacs implementation. Comparison to classical DFT: O(N log N) classical vs O(n^2) quantum gate count. Explains notation 0.k_l...k_m = binary fraction. | 3/22/2026 | 0 |
| quic-seminar-quantum-teleportation | lecture_notes | QUIC Seminar 2: The Quantum Teleportation Algorithm by Ryan LaRose. Covers multi-qubit states, multi-qubit gates (CNOT, Hadamard), no-cloning theorem, and full quantum teleportation protocol derivation with step-by-step Dirac notation. Includes Bell state creation, Alice measurement, Bob correction operations. 87 multi-qubit kets (|00⟩,|01⟩,|10⟩,|11⟩ patterns) with 103 total ket expressions. Well-structured pedagogical treatment. | 3/22/2026 | 0 |
| quic-seminar-tensor-products-measurements | lecture_notes | QUIC Seminar 3: More on Tensor Products and Measurements by Ryan LaRose. Covers multi-particle quantum systems (tensor product postulate), tensor product properties, controlled operations (CNOT), tensor products in quantum circuits, entanglement, and quantum measurements (POVMs, projective measurements). 31 multi-qubit computational-basis kets (|00⟩, |01⟩, |10⟩, |11⟩) with step-by-step derivations. Includes Bell state preparation, CNOT action on computational basis, partial measurements and post-measurement state collapse. | 3/22/2026 | 0 |
| quillen-rochester-qec-lecture-notes | lecture_notes | PHY265 Lecture notes: Introducing Quantum Error Correction by A.C. Quillen (Univ. Rochester, March 2025). 416 multi-qubit kets, 778 total kets. Comprehensive QEC coverage: 3-qubit bit-flip code with explicit syndrome extraction circuits and ket derivations, phase-flip code, Shor 9-bit code, theory of quantum error correction, stabilizer codes with Pauli group, CSS codes (classical Hamming [7,4] code, Steane 7-bit code), fault-tolerant computing (fault-tolerant NOT/Z/CNOT gates for 9-bit code), topological codes. Section 2.1 shows explicit gate-by-gate encoding circuit and syndrome measurement with ket evolution through all error cases. | 3/23/2026 | 0 |
| quillen-rochester-quantum-computing-gates | lecture_notes | PHY265 Lecture notes: Introducing Quantum Computing by A.C. Quillen (Univ. Rochester, February 2026). 147 multi-qubit kets, 427 total kets. Covers: logical operations on quantum computers with explicit gate action tables (CNOT, Toffoli on all basis states |000⟩ through |111⟩), 1-bit adder with carry, quantum parallelism, deferred measurement, implementing measurements (measuring in |+⟩/|-⟩ basis with ket derivations), single qubit unitary transformations, controlled unitary transformations, universality proofs, universal gate sets (CNOT + 1-qubit rotations). Shows CNOT: |x,y⟩ -> |x,x+y⟩ and Toffoli gate table with all 8 basis states. | 3/23/2026 | 0 |
| quillen-rochester-quantum-systems-measurement-qubits | lecture_notes | PHY265 Lecture notes on Introducing Quantum Systems, Measurement and the Qubit by A.C. Quillen (University of Rochester, updated February 2026); covers basis vectors, linear operators, single-qubit gates, measurements, BB84, Bell pairs, CNOT gate, entanglement with 216 multi-qubit kets | 3/23/2026 | 0 |
| radkohl-quantum-teleportation-superdense-coding-graz | lecture_notes | Bachelor thesis from University of Graz presenting quantum teleportation and superdense coding with full mathematical derivations in Dirac notation (187 multi-qubit kets), plus IBM Quantum computer implementations using Qiskit circuits | 3/23/2026 | 0 |
| ragni-bologna-algoritmi-informazione-quantistica | lecture_notes | Stefano Ragni, University of Bologna (UNIBO) physics undergraduate thesis (2016/2017). Italian. 50 multi-qubit kets, 467 total kets. Covers: qubit states, CNOT gate, controlled operations, IBM Quantum Experience with QISKit code examples. Three main topics: (1) quantum teleportation - step-by-step 3-qubit state evolution using Bell states, CNOT, Hadamard, measurement; (2) quantum Fourier transform - DFT to QFT circuit construction with explicit basis state evolution; (3) phase estimation algorithm - circuit derivation with eigenstate analysis. All circuits accompanied by QISKit Python code. Italian language with full mathematical Dirac notation derivations. | 3/23/2026 | 0 |
| rice-comp458-quantum-algorithms-notes-sp25 | lecture_notes | COMP 458/558 Quantum Computing Algorithms notes by Micah Kepe (Rice University, Spring 2025). Comprehensive compiled notes covering: linear algebra for quantum computing, qubits, quantum gates, multi-qubit systems, entanglement, Bell states, quantum teleportation, quantum circuits, Deutsch-Jozsa algorithm, Bernstein-Vazirani algorithm, Simon's algorithm, Quantum Fourier Transform, Shor's algorithm (full derivation with circuit), Grover's search algorithm with geometric analysis, quantum error correction (repetition code, Shor 9-qubit code, stabilizer formalism), Hidden Subgroup Problem, Abelian group Fourier analysis. 179 multi-qubit kets, 538 total ket expressions. Spring 2025 course notes. | 3/22/2026 | 0 |
| rieffel-polak-quantum-computing-gentle-intro | book | Quantum Computing: A Gentle Introduction by Eleanor Rieffel and Wolfgang Polak (MIT Press, 2011). Comprehensive undergraduate textbook. Part I: Quantum Building Blocks - Chapter 2 (single-qubit systems, BB84 QKD), Chapter 3 (multiple-qubit systems, tensor products, entangled states |00>+|11>), Chapter 4 (Dirac bra-ket notation, projection operators, EPR), Chapter 5 (quantum gates: Pauli X/Y/Z, Hadamard, CNOT truth table CNOT|00>=|00>...CNOT|11>=|10>, dense coding, quantum teleportation step-by-step). Part II: Quantum Algorithms - Chapters 6-7 (overview, quantum search problem), Chapter 8 (Grover's algorithm with geometric analysis), Chapter 9 (quantum fourier transform), Chapter 10 (Shor's algorithm: order finding, QFT, period finding, factoring), Chapter 11 (more quantum algorithms), Chapter 12 (quantum error correction: 3-qubit bit flip code, phase flip code, Shor 9-qubit code, stabilizer formalism). 737 multi-qubit kets, 4897 total ket expressions. Full pedagogical textbook with exercises. | 3/23/2026 | 0 |
| romeral-ucm-computacion-cuantica-2023 | research_paper | TFG (UCM Mathematical Engineering, 2023) introducing quantum computing in Spanish. Covers QFT, teleportation, Deutsch-Jozsa, and quantum algorithms in Qiskit. 69 multi-qubit kets. | 3/23/2026 | 0 |
| rosetta-stone-quantum-mechanics | lecture_notes | AMS lecture notes by Lomonaco introducing quantum mechanics and quantum computation. Covers Dirac notation from scratch (kets, bras, inner products, operators), quantum measurement, EPR, quantum teleportation with full ket-state derivation, Shor's algorithm, and Grover's algorithm. 545 ket expressions. Written for mathematicians with no QM background. | 3/21/2026 | 0 |
| schomerus-lancaster-quantum-information-processing | lecture_notes | PHYS483: Quantum Information Processing lecture notes by Henning Schomerus (Lancaster University). Comprehensive physics-oriented introduction covering: quantum mechanics (states, operators, density matrices, composite systems), Bell inequalities, classical computation, quantum gates (Hadamard, CNOT/CCNOT truth tables: |00>->|00>, |01>->|01>, |10>->|11>, |11>->|10>), quantum teleportation (Bell pair sharing, CNOT+Hadamard operations), superdense coding (BB84 QKD), Deutsch-Jozsa algorithm, Grover's search algorithm (oracle, diffusion operator, geometric interpretation with 2-bit worked example), quantum Fourier transform, Shor's factoring algorithm (order finding, QFT-based period finding), and quantum error correction (Shor 9-qubit code, stabilizer formalism). 66 multi-qubit kets with computational-basis state manipulations, 488 total kets. Includes circuit diagrams for all major algorithms. | 3/23/2026 | 0 |
| shi-sjtu-symbolic-quantum-circuits-coq-2021 | research_paper | Symbolic Reasoning about Quantum Circuits in Coq by Shi, Cao, Deng, Jiang, Feng (SJTU/UTS, arXiv:2005.11023, 2021). Proposes symbolic approach to quantum circuit reasoning using Dirac notation laws in Coq. Key content: Dirac notation algebraic laws (ket/bra/outer-product operations), Bell state derivations (|00⟩+|11⟩), CNOT circuit symbolic rewriting, QFT symbolic proofs, Grover oracle circuit. Directly relevant to automated formalization of quantum circuit equivalences. 53 multi-qubit kets, 654 total ket expressions. Machine-verified proofs of quantum circuit properties using symbolic Dirac notation. | 3/23/2026 | 0 |
| shor-algorithm-modular-exponentiation-pedagogy | research_paper | Pedagogical presentation of Shor's factoring algorithm by Singleton. Covers quantum Fourier transform (QFT) and quantum phase estimation (QPE) from first principles, theory of modular exponentiation (ME) operators, and the period-finding circuit. Contains 1179 ket expressions with step-by-step state derivations including |psi0> initialization, Hadamard superposition, controlled-ME, and inverse-QFT stages. Includes worked examples: factoring N=15, N=21, N=33, N=35, N=143 with Qiskit simulations. Discusses both physics convention and OpenQASM/Qiskit bit ordering conventions. | 3/21/2026 | 0 |
| shor-factoring-algorithm-tutorial | research_paper | Tutorial-style explanation of Shor's factoring algorithm by Gerjuoy. Explains RSA encryption, quantum manipulations in Shor's algorithm, and how period-finding achieves factoring. 229 ket expressions with step-by-step state vector derivations of QFT and modular exponentiation circuits. Written for non-experts with careful analysis of success probability. | 3/21/2026 | 0 |
| shoshany-thinking-quantum-lectures | lecture_notes | Thinking Quantum: Lectures on Quantum Theory by Barak Shoshany (Brock University, last updated Apr 2025, arXiv:1803.07098). Comprehensive 355K-char undergraduate-to-graduate quantum theory textbook covering: Dirac notation, qubits, tensor products, Bell states, quantum gates (CNOT, Hadamard, Pauli), quantum teleportation (step-by-step), no-cloning theorem, quantum parallelism, Deutsch's algorithm, Deutsch-Jozsa algorithm, and quantum error correction. 87 multi-qubit computational-basis kets, 31 3-qubit+ kets, 1967 total ket expressions. Pedagogical style with exercises, covers both physics and computing perspectives. | 3/23/2026 | 0 |
| spadano-bologna-grover-search-2019 | research_paper | Implementazione di un algoritmo di ricerca quantistico (Implementation of a quantum search algorithm) by Stefano Spadano, University of Bologna, 2019. Italian thesis covering Grover's search algorithm with step-by-step circuit derivations, Bell state analysis, CNOT gate applications, and multi-qubit state evolution. 63 multi-qubit kets including |00>, |01>, |10>, |11>, |000>, |00000> states. Covers: Grover diffusion operator, oracle construction, amplitude amplification iterations with explicit ket calculations. Written for physics students with concrete computational basis examples. | 3/23/2026 | 0 |
| stabilizer-codes-qec-gottesman-thesis | research_paper | Stabilizer Codes and Quantum Error Correction PhD Thesis by Daniel Gottesman (Caltech, 1997). Foundational work on stabilizer codes and QEC. Covers: classical error correction, quantum error correction basics with Shor code derivation (|0>->|000>+|111>)^3, (|1>->|000>-|111>)^3), Calderbank-Shor-Steane (CSS) codes, stabilizer formalism with explicit multi-qubit code states, fault-tolerant quantum computation (cat state construction for gates). 669 total kets, 116 multi-qubit kets including 5-qubit codewords (|00000>), 7-qubit Steane code states, 9-qubit Shor code states. Classic QEC reference. | 3/22/2026 | 0 |
| steane-oxford-quantum-computing-review-1997 | research_paper | Quantum Computing review by Andrew Steane (Oxford, Reports on Progress in Physics, 1997, arXiv:quant-ph/9708022). Comprehensive 94-page review covering quantum information theory and quantum computing: qubit basics, quantum gates and circuits, quantum algorithms (Deutsch, Shor's factoring algorithm with period finding, Grover's search), quantum error correction (3-qubit codes, Steane 7-qubit code, CSS codes, stabilizer formalism), quantum communication (teleportation, dense coding, BB84). 66 multi-qubit kets including 2-qubit Bell states (|00>, |01>, |10>, |11>) and QEC codewords (|00101>, |0011010>). 417 total ket expressions. Classic Oxford review for physics and CS audiences. | 3/23/2026 | 0 |
| steane-quantum-computing-error-correction | research_paper | Tutorial on quantum error correction by Andrew Steane (Oxford, 2003). 68 multi-qubit kets with step-by-step derivations of encoding, syndrome extraction, repetition code, Shor 9-qubit code, and Steane 7-qubit code. Covers error operators, noise channel models, and fault-tolerant QEC principles. | 3/22/2026 | 0 |
| strubell-intro-quantum-algorithms-2011 | research_paper | An Introduction to Quantum Algorithms by Emma Strubell (Princeton COS498, Spring 2011). Pedagogical tutorial covering quantum computing foundations and two major algorithms. Dirac notation from scratch: Hilbert spaces, kets as column vectors, bras as row vectors, inner and outer products. Quantum registers: multi-qubit states as tensor products (|0>|0>=|00>, Hadamard superposition across registers). Quantum gates: Hadamard H|0>=(|0>+|1>)/sqrt(2) and H|1>=(|0>-|1>)/sqrt(2) with Bloch sphere; Pauli X, Y, Z with outer product forms; CNOT truth table (CNOT|00>=|00>, |01>=|01>, |10>=|11>, |11>=|10>); Toffoli and Fredkin gates. Grover's algorithm with worked 3-qubit example (N=8, marked |101>): oracle phase flip, diffusion operator inversion-about-average, state evolution |000>+|001>+|010>+...+|111>. Simon's algorithm with step-by-step derivation. 114 multi-qubit kets, 494 total ket expressions. | 3/23/2026 | 1 |
| tufts-cs150-qcs-lecture-notes-2025 | lecture_notes | Lecture Notes for CS 150 - Quantum Computer Science by Saeed Mehraban (Tufts University, Fall 2025, December 2025). Comprehensive notes covering: quantum vs classical bits, qubits, Bloch sphere, quantum gates and circuits, entanglement, quantum teleportation (with 3-qubit circuit derivation), Bell inequalities, Deutsch-Jozsa algorithm, Bernstein-Vazirani algorithm, Simon's algorithm, Quantum Fourier Transform, Shor's algorithm (full derivation), Grover's search algorithm, quantum error correcting codes (3-qubit repetition code, Shor 9-qubit code, stabilizer formalism). 103 multi-qubit kets, 617 total ket expressions. Full lecture notes through December 2025. | 3/22/2026 | 0 |
| tunon-uni-oviedo-computacion-cuantica-medidas | lecture_notes | Computación Cuántica Basada en Medidas (Measurement-Based Quantum Computing) by Nacho Tuñón Rubio (Universidad de Oviedo, Mathematics TFG, 2023-2024, supervised by Fernández-Combarro Álvarez and Fernández Rúa). Spanish-language undergraduate thesis covering: mathematical preliminaries (Hilbert spaces, linear algebra, quantum mechanics) (Chapter 1), quantum circuit model including Bell states, CNOT, Hadamard, 2-qubit gates, N-qubit gates, universality, and quantum algorithms (Deutsch-Jozsa, Grover, Shor) (Chapter 2), and Measurement-Based Quantum Computing (MBQC) including quantum teleportation, cluster states, and quantum algorithms in MBQC (Chapter 3). 73 multi-qubit kets, 647 total ket expressions. Unique coverage of both circuit model and measurement-based paradigm in Spanish. | 3/23/2026 | 0 |
| ufrb-conceicao-computacao-quantica-algoritmos | lecture_notes | Orlando dos Santos Conceição Júnior, UFRB (Universidade Federal do Recôncavo da Bahia) undergraduate TCC thesis (2016). Brazilian Portuguese. 45 multi-qubit kets, 685 total kets including 131 algorithm-specific variable kets (|x⟩, |y⟩, |f(x)⟩, |f(i)⟩). Covers: quantum mechanics postulates, qubit and Bloch sphere, tensor products, multi-qubit gates (Hadamard, CNOT), quantum circuits. Algorithms: (1) Deutsch algorithm - oracle circuit with phase kickback derivation; (2) quantum teleportation - Bell state preparation and measurement outcomes; (3) Shor algorithm - overview of period-finding with QFT; (4) Grover algorithm - detailed oracle inversion about average amplitude, geometric analysis. Comprehensive coverage of four canonical quantum algorithms in Brazilian Portuguese with Dirac notation derivations. | 3/23/2026 | 0 |
| umass-ece550-two-qubit-gates-lab | webpage | UMass ECE 550/650 Introduction to Quantum Computing Lab 06: Multi-Qubit Circuits (Robert Niffenegger). 40 ket expressions with 30 multi-qubit kets. Covers: 2-qubit state vector |Ψ⟩=a00|00⟩+a01|01⟩+a10|10⟩+a11|11⟩, CNOT gate as |0⟩⟨0|⊗I+|1⟩⟨1|⊗X with explicit 4x4 matrix, Bell state (|00⟩+|11⟩)/√2 creation via H+CNOT, tensor product of single-qubit states, SWAP gate, CZ gate, Toffoli/CCNOT gate. Qiskit implementation with circuit visualization and state tomography. Includes controlled-X, controlled-Y, controlled-Z variants. Ion trap hardware context. | 3/22/2026 | 0 |
| valiron-qdcs-quantum-algorithms-programming | lecture_notes | Introduction to Quantum Algorithms and Quantum Programming course notes by B. Valiron (Université Paris-Saclay, QDCS Master, v.2025.09.15). 327 multi-qubit kets, 2299 total kets. Covers: mathematical background (kets/bras, Kronecker product, unitary maps), qubit computation model, quantum gates, circuit synthesis, universality (CNOT + 1-qubit rotations), complexity theory, amplitude amplification, Quantum Fourier Transform (with step-by-step derivation), phase estimation, Shor's algorithm, HHL, oracle-based algorithms (Deutsch-Jozsa, Bernstein-Vazirani, Simon's), variational algorithms. Includes programming examples (Qiskit-style) alongside mathematical derivations. Comprehensive semester course covering foundations through advanced algorithms. | 3/23/2026 | 0 |
| vieira-albuquerque-grover-shor-passo-a-passo | research_paper | Luciano Alves Vieira and Clarice Dias de Albuquerque (UFCA - Universidade Federal do Cariri), Revista Eletrônica Paulista de Matemática (REPM), Volume 19, December 2020. Brazilian Portuguese. 248 multi-qubit kets, 526 total kets. Step-by-step study of Grover and Shor quantum algorithms showing explicit quantum state after each gate operation. Grover's algorithm: state evolution through H⊗n|0⟩^n, oracle application, inversion-about-average, multiple iterations with basis states |00⟩,|01⟩,|10⟩,|11⟩ and quantum entanglement analysis. Shor's algorithm: period-finding circuit with QFT, modular exponentiation oracle, explicit multi-qubit register states. Pedagogical focus on quantum state tracking step-by-step through circuits. | 3/23/2026 | 0 |
| vignatti-ufpr-intro-computacao-quantica-2004 | lecture_notes | Vignatti, Summa Netto & Bittencourt, UFPR undergraduate monograph (2004): comprehensive intro to quantum computing in Brazilian Portuguese. 119 multi-qubit kets. Covers: multiple qubits, tensor products, EPR pairs, gates (NOT/X, phase flip/Z, Hadamard, CNOT, Toffoli), reversible computation, dense coding (full step-by-step derivation of all 4 Bell state protocols), quantum teleportation (complete protocol), and Shor's algorithm with QFT. | 3/23/2026 | 0 |
| watrous-understanding-qic-2025 | lecture_notes | Understanding Quantum Information and Computation by John Watrous (arXiv:2507.11536, July 2025). Comprehensive 4-unit course on quantum computing theory with video and written components. Unit I (Basics): single systems, multiple systems (multi-qubit states, tensor products), quantum circuits, entanglement in action (teleportation, superdense coding). Unit II (Quantum Algorithms): query algorithms (Deutsch-Jozsa, Simon), algorithmic foundations (phase kickback, QFT), phase estimation and factoring (Shor's algorithm), Grover's algorithm. Unit III (General Formulation): density matrices, quantum channels, general measurements. Unit IV (Foundations): quantum error correction, stabilizer codes. 318 multi-qubit kets, 2353 total ket expressions with step-by-step circuit derivations. Fresh 2025 version by pioneering Watrous (IQC Waterloo). | 3/22/2026 | 0 |
| wei-stonybrook-quantum-information-science | lecture_notes | PHY568 Quantum Information Science combined lecture notes by Tzu-Chieh Wei (Stony Brook University / C.N. Yang ITPP, Fall 2024). 10 units covering: quantum phenomena (double-slit, interferometer), qubit formalism with Dirac notation, Deutsch/Simon/Grover algorithms, quantum Fourier transform, Shor's factoring algorithm, quantum teleportation (Bell states, 3-qubit state evolution), quantum error correction (3-qubit code, 9-qubit Shor code, CSS codes, surface codes), topological quantum computation (Fibonacci anyons), adiabatic quantum computation, measurement-based quantum computation, and quantum entanglement theory. 165 multi-qubit kets, 1579 total kets. Comprehensive treatment of quantum circuits with CNOT, Hadamard, Toffoli gate constructions and Qiskit code examples. | 3/23/2026 | 0 |
| wikipedia-amplitude-amplification | webpage | Wikipedia article on quantum amplitude amplification (generalization of Grover's algorithm). Covers the amplitude amplification operator Q=-(I-2|ψ⟩⟨ψ|)U_f, analysis in 2D subspace of good/bad states, geometric interpretation, success probability, and relationship to Grover's algorithm. 89 displaystyle expressions with ket state analysis. | 3/22/2026 | 0 |
| wikipedia-bell-state | webpage | Wikipedia article on Bell states. Covers all four Bell states (Φ+, Φ-, Ψ+, Ψ-) with full Dirac notation definitions, Bell basis in terms of computational basis |00⟩,|01⟩,|10⟩,|11⟩, circuit construction (Hadamard + CNOT), and applications in quantum teleportation and superdense coding. 60+ LaTeX math expressions including multi-qubit ket derivations. | 3/22/2026 | 0 |
| wikipedia-bernstein-vazirani | webpage | Wikipedia article on the Bernstein-Vazirani algorithm. Covers oracle model, quantum algorithm with Hadamard transform, phase kickback analysis, and correctness proof. Shows how inner product oracle f_s(x)=s·x enables single-query s recovery via Hadamard-oracle-Hadamard circuit. 43 displaystyle expressions. | 3/22/2026 | 0 |
| wikipedia-cnot-gate | webpage | Wikipedia article on the Controlled NOT (CNOT) gate. Covers CNOT action on all four two-qubit computational basis states, Bell state creation with Hadamard+CNOT, CNOT action on superposition states, circuit equivalences including CNOT reversal via Hadamard gates, and controlled-U gate decompositions. 77 displaystyle math expressions with extensive |00⟩,|01⟩,|10⟩,|11⟩ two-qubit ket formulas and gate identity derivations. | 3/22/2026 | 0 |
| wikipedia-deutsch-jozsa-algorithm | webpage | Wikipedia article on the Deutsch-Jozsa algorithm. Full step-by-step state derivation with Dirac notation: initialization |0⟩^n|1⟩, Hadamard transform, oracle application |x⟩|y⊕f(x)⟩, final Hadamard, measurement analysis. Covers both single-qubit Deutsch and n-qubit DJ cases with explicit LaTeX ket expressions. 71 displaystyle math expressions. | 3/22/2026 | 0 |
| wikipedia-five-qubit-error-correcting-code | webpage | Wikipedia article on the five-qubit error correcting code ([[5,1,3]] code, Laflamme-Miquel-Paz-Zurek code). Presents the smallest quantum error correcting code protecting a logical qubit from arbitrary single-qubit errors. 96 multi-qubit kets (5-qubit codewords: |00000⟩, |10010⟩, |01001⟩, |10100⟩, |01010⟩, etc.) with explicit logical codeword definitions for |0⟩_L and |1⟩_L as superpositions of 16 five-qubit basis states. Includes stabilizer generators XZZXI, IXZZX, XIXZZ, ZXIXZ, logical operators X=XXXXX and Z=ZZZZZ, and a quantum circuit diagram for syndrome measurement. 218 displaystyle LaTeX expressions. | 3/22/2026 | 0 |
| wikipedia-ghz-state | webpage | Wikipedia article on the Greenberger-Horne-Zeilinger (GHZ) state. Covers the 3-qubit GHZ state (|000⟩+|111⟩)/√2 and its generalizations, circuit preparation using Hadamard and CNOT gates, entanglement properties, GHZ paradox, and applications in quantum cryptography and teleportation. 50 displaystyle math expressions. | 3/22/2026 | 0 |
| wikipedia-grover-algorithm | webpage | Wikipedia article on Grover's quantum search algorithm. Covers oracle definition U_ω|x⟩=(-1)^f(x)|x⟩, diffusion operator U_s=2|s⟩⟨s|-I, geometric interpretation as rotation in 2D subspace spanned by |ω⟩ and |s'⟩. Includes amplitude amplification derivation, convergence analysis, and extensions. 135 displaystyle math expressions. | 3/22/2026 | 0 |
| wikipedia-hadamard-transform | webpage | Wikipedia article on Hadamard Transform (quantum computing section). Covers: H gate as 1-qubit Hadamard transform mapping |0⟩→(|0⟩+|1⟩)/√2 and |1⟩→(|0⟩-|1⟩)/√2 with H(|+⟩)=|0⟩ and H(|-⟩)=|1⟩, n-qubit Hadamard transform H^n|x⟩=(1/√2^n)Σ(-1)^{x·y}|y⟩ applied in quantum algorithms, H applied twice = identity. 93 displaystyle expressions, 51 ket expressions. Foundational reference for Hadamard gate action formulas used in DJ, BV, Simon, and Grover algorithms. | 3/22/2026 | 0 |
| wikipedia-quantum-error-correction | webpage | Wikipedia article on quantum error correction. Covers 3-qubit bit-flip code with logical encoding |0⟩→|000⟩, |1⟩→|111⟩, encoded state α|000⟩+β|111⟩, syndrome measurement projectors P_0..P_3, and error recovery. Also covers Shor 9-qubit code and stabilizer formalism. 118 displaystyle expressions with concrete multi-qubit ket states. | 3/22/2026 | 0 |
| wikipedia-quantum-fourier-transform | webpage | Wikipedia article on the Quantum Fourier Transform (QFT). Covers QFT definition as unitary on computational basis |j⟩, circuit implementation with Hadamard and controlled-R_k gates, and circuit diagram. Includes the product representation formula, comparison with classical DFT, and complexity analysis. 85 displaystyle math expressions with ket notation. | 3/22/2026 | 0 |
| wikipedia-quantum-logic-gate | webpage | Wikipedia article on quantum logic gates. Comprehensive reference covering single-qubit gates (Hadamard, Pauli X/Y/Z, S, T, phase gates), multi-qubit gates (CNOT, Toffoli, SWAP, controlled-U), with matrix representations and ket action formulas. Circuit diagrams and equivalences included. 307 displaystyle expressions with 116 ket-line derivations. Excellent gate reference compendium. | 3/22/2026 | 4 |
| wikipedia-quantum-phase-estimation | webpage | Wikipedia article on Quantum Phase Estimation (QPE). Full derivation: initialization |Ψ0⟩=|0⟩^n|ψ⟩, Hadamard layer |Ψ1⟩=(1/2^{n/2})Σ|j⟩|ψ⟩, controlled-U applications |Ψ2⟩=Σe^{2πiθk}|k⟩|ψ⟩, inverse QFT to extract phase θ. 121 displaystyle expressions with step-by-step ket state evolution. | 3/22/2026 | 0 |
| wikipedia-quantum-teleportation | webpage | Wikipedia article on quantum teleportation. Contains step-by-step protocol derivation with Dirac notation: Bell pair creation, Alice's measurement, Bob's correction operations. Includes 68+ ket expressions covering the full 3-qubit teleportation circuit with |ψ⟩, |Φ+⟩, |Ψ-⟩ Bell state notation and computational-basis state expansions. | 3/22/2026 | 0 |
| wikipedia-qubit | webpage | Wikipedia article on Qubit. Covers: qubit definition (α|0⟩+β|1⟩), two-qubit product basis states (|00⟩, |01⟩, |10⟩, |11⟩ with explicit 4D vector representations), n-qubit register, quantum entanglement, CNOT gate action on multi-qubit states, Bell state (|00⟩+|11⟩)/√2. 87 ket expressions with 27 multi-qubit computational-basis kets and 98 displaystyle expressions. Includes Bloch sphere representation and physical implementations discussion. | 3/22/2026 | 0 |
| wikipedia-shor-algorithm | webpage | Wikipedia article on Shor's factoring algorithm. Covers order-finding reduction to factoring, quantum phase estimation circuit, QFT over Z_N, period finding with modular exponentiation oracle. 212 displaystyle math expressions including the continued fractions post-processing and worked examples. Step-by-step description of the quantum circuit components. | 3/22/2026 | 0 |
| wikipedia-simon-problem | webpage | Wikipedia article on Simon's problem. Full algorithm derivation with Dirac notation: initial state |0⟩^n|0⟩^n, Hadamard transform (1/√2^n)Σ|k⟩, oracle application producing (1/√2^n)Σ|k⟩|f(k)⟩, final Hadamard analysis showing which j satisfy j·s=0. 168 displaystyle expressions with detailed ket manipulations. | 3/22/2026 | 0 |
| wikipedia-superdense-coding | webpage | Wikipedia article on superdense coding. Covers the protocol for transmitting 2 classical bits using 1 qubit. Includes encoding table: 00→I, 01→X, 10→Z, 11→iY applied to Bell state |Φ+⟩, with explicit ket expressions for all four outcomes (|Φ+⟩, |Ψ+⟩, |Φ-⟩, |Ψ-⟩). 47 displaystyle expressions with 18 multi-qubit |xy⟩ kets. | 3/22/2026 | 0 |
| wildon-quantum-computation-theoretical-minimum | research_paper | Quantum Computation and Quantum Error Correction: The Theoretical Minimum by Mark Wildon (arXiv:2602.13876, February 2026). Introduces quantum computation and QEC emphasizing stabilizers and Lie theory. Covers: one qubit and Bloch sphere, two qubits and CNOT gates with step-by-step derivations (CNOT|0>|psi>=|0>|psi>, Bell state creation CNOT|+>|0>=(|00>+|11>)/sqrt(2), copy rules for circuit identities), Deutsch-Jozsa algorithm, quantum error correction using the Steane [[7,1,3]] code. 697 total ket expressions, 163 multi-qubit kets. Step-by-step CNOT circuit derivations, Bell pair generation, Pauli stabilizer formalism. Written with answers in footnotes. | 3/22/2026 | 0 |
| yuen-columbia-coms4281-quantum-fall2025 | lecture_notes | COMS 4281: Introduction to Quantum Computing (Fall 2025) by Henry Yuen (Columbia University). 17+ slide-format lecture PDFs covering: quantum math and Dirac notation (Sept 16/18), inner products of multi-qubit states (|00>+|01>+|11> examples), no-cloning theorem, partial measurement (47 mq kets in Sept 18), outer products and teleportation (Sept 23), nonstandard measurements and EPR paradox (Sept 25 with 8 mq kets), Bell's theorem and superdense coding (Sept 30), Simon's algorithm (Oct 7-9), QFT and phase estimation (Oct 14, 21, 23), Shor's algorithm and order finding (Oct 30), Grover's search and counting (Nov 6-11), quantum error correction (Nov 13+). 87 multi-qubit kets, 2174 total ket expressions across all available lectures. September-December 2025. | 3/23/2026 | 0 |
| zamberlan-bologna-hhl-algorithm-2019 | research_paper | Quantum software per l'algebra lineare: l'algoritmo HHL e l'IBM quantum experience by Pietro Zamberlan, University of Bologna, 2019. Italian thesis covering the HHL algorithm for solving linear systems (quantum phase estimation, Hamiltonian simulation, ancilla qubit rotation, uncomputation), quantum Fourier transform, and implementation on IBM Q quantum hardware. 73 multi-qubit kets with circuit derivations. Covers: QPE subcircuit, QFT gate sequences, CNOT/Hadamard applications on |00>, |01>, |10>, |11> states. HHL is a priority algorithm for Galleon. | 3/23/2026 | 0 |
| zhang-simplified-teleportation-circuits-2026 | research_paper | The simplified quantum circuits for implementing quantum teleportation by Zhang, Song, Wei (USTB/Tianjin, 2026). Derives simplified teleportation circuits with fewer CNOT gates. Contains step-by-step state evolution: |psi0>=(alpha|0>+beta|1>)|000>234 through multiple intermediate 4-qubit states to final (alpha|0>+beta|1>) recovery. Three circuit variants with explicit tensor product expansions. 226 multi-qubit kets with 96 distinct states including up to 5-qubit states (|01110>). GHZ state (|000>+|111>) preparation included. Circuit optimization tables showing gate counts. | 3/22/2026 | 6 |
| zuppini-usp-computacao-quantica-2011 | lecture_notes | TCC do IME-USP (2011) cobrindo computação quântica: estados, portas, entrelaçamento, QFT, algoritmo de Shor, busca de Grover e correção de erros. 212 kets multi-qubit, 494 total. Derivações passo a passo em notação de Dirac. | 3/23/2026 | 0 |
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