{
  "format": "lean-quantumalg-references v2",
  "purpose": "Resolve citation keys used in Lean docstrings and project docs, and let a reader (or their agent) verify every cited claim against the exact source version.",
  "conventions": {
    "key_style": "LaTeX alpha style: author initials (von prefixes lowercase) + 2-digit year; 5+ authors abbreviate to the first three initials + '+'.",
    "citation_forms": [
      "[<key>]",
      "[<key>, <file.tex>:<line>]"
    ],
    "verification": "Entries with arxiv_id, arxiv_version, and entry_point are TeX-verifiable: download https://arxiv.org/e-print/<arxiv_id><arxiv_version>, extract the TeX source, and read the cited file at the cited line. Line numbers are only meaningful for the pinned arxiv_version.",
    "policy": "Sources without public TeX may appear as citation-only entries for public attribution, but they are not used as TeX verification anchors."
  },
  "entries": [
    {
      "key": "AJL06",
      "authors": [
        "Dorit Aharonov",
        "Vaughan Jones",
        "Zeph Landau"
      ],
      "year": 2006,
      "title": "A Polynomial Quantum Algorithm for Approximating the Jones Polynomial",
      "arxiv_id": "quant-ph/0511096",
      "arxiv_version": "v2",
      "entry_point": "qf2.tex"
    },
    {
      "key": "dW19",
      "authors": [
        "Ronald de Wolf"
      ],
      "year": 2019,
      "title": "Quantum Computing: Lecture Notes",
      "arxiv_id": "1907.09415",
      "arxiv_version": "v5",
      "entry_point": "qcnotes.tex"
    },
    {
      "key": "CEMM98",
      "authors": [
        "Richard Cleve",
        "Artur Ekert",
        "Chiara Macchiavello",
        "Michele Mosca"
      ],
      "year": 1998,
      "title": "Quantum Algorithms Revisited",
      "arxiv_id": "quant-ph/9708016",
      "arxiv_version": "v1",
      "entry_point": "cemm6.tex"
    },
    {
      "key": "Lin22",
      "authors": [
        "Lin Lin"
      ],
      "year": 2022,
      "title": "Lecture Notes on Quantum Algorithms for Scientific Computation",
      "arxiv_id": "2201.08309",
      "arxiv_version": "v1",
      "entry_point": "main.tex"
    },
    {
      "key": "BCWdW01",
      "authors": [
        "Harry Buhrman",
        "Richard Cleve",
        "John Watrous",
        "Ronald de Wolf"
      ],
      "year": 2001,
      "title": "Quantum Fingerprinting",
      "arxiv_id": "quant-ph/0102001",
      "arxiv_version": "v1",
      "entry_point": "main.tex"
    },
    {
      "key": "BBD+96",
      "authors": [
        "Adriano Barenco",
        "Andre Berthiaume",
        "David Deutsch",
        "Artur Ekert",
        "Richard Jozsa",
        "Chiara Macchiavello"
      ],
      "year": 1996,
      "title": "Stabilisation of Quantum Computations by Symmetrisation",
      "arxiv_id": "quant-ph/9604028",
      "arxiv_version": "v1",
      "entry_point": "siam.tex"
    },
    {
      "key": "Sho95",
      "authors": [
        "Peter W. Shor"
      ],
      "year": 1995,
      "title": "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer",
      "arxiv_id": "quant-ph/9508027",
      "arxiv_version": "v2",
      "entry_point": "source.tex"
    },
    {
      "key": "VBE95",
      "authors": [
        "Vlatko Vedral",
        "Adriano Barenco",
        "Artur Ekert"
      ],
      "year": 1995,
      "title": "Quantum Networks for Elementary Arithmetic Operations",
      "arxiv_id": "quant-ph/9511018",
      "arxiv_version": "v1",
      "entry_point": "9511018.tex"
    },
    {
      "key": "Bea02",
      "authors": [
        "Stephane Beauregard"
      ],
      "year": 2002,
      "title": "Circuit for Shor's Algorithm Using 2n+3 Qubits",
      "arxiv_id": "quant-ph/0205095",
      "arxiv_version": "v3",
      "entry_point": "arxivfact.tex"
    },
    {
      "key": "EH17",
      "authors": [
        "Martin Ekerå",
        "Johan Håstad"
      ],
      "year": 2017,
      "title": "Quantum algorithms for computing short discrete logarithms and factoring RSA integers",
      "arxiv_id": "1702.00249",
      "arxiv_version": "v1",
      "entry_point": "source.tex"
    },
    {
      "key": "E23",
      "authors": [
        "Martin Ekera"
      ],
      "year": 2023,
      "title": "On the Success Probability of the Quantum Algorithm for the Short DLP",
      "arxiv_id": "2309.01754",
      "arxiv_version": "v5",
      "entry_point": "arxiv-v5.tex"
    },
    {
      "key": "GE19",
      "authors": [
        "Craig Gidney",
        "Martin Ekerå"
      ],
      "year": 2019,
      "title": "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits",
      "arxiv_id": "1905.09749",
      "arxiv_version": "v3",
      "entry_point": "main.tex"
    },
    {
      "key": "PZ03",
      "authors": [
        "John Proos",
        "Christof Zalka"
      ],
      "year": 2003,
      "title": "Shor's Discrete Logarithm Quantum Algorithm for Elliptic Curves",
      "arxiv_id": "quant-ph/0301141",
      "arxiv_version": "v2",
      "entry_point": "ecc.tex"
    },
    {
      "key": "RNSL17",
      "authors": [
        "Martin Roetteler",
        "Michael Naehrig",
        "Krysta M. Svore",
        "Kristin Lauter"
      ],
      "year": 2017,
      "title": "Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms",
      "arxiv_id": "1706.06752",
      "arxiv_version": "v3",
      "entry_point": "ECDLP.tex"
    },
    {
      "key": "NIST23",
      "authors": [
        "Lily Chen",
        "Dustin Moody",
        "Karen Randall",
        "Andrew Regenscheid",
        "Angela Robinson"
      ],
      "year": 2023,
      "title": "Recommendations for Discrete Logarithm-based Cryptography: Elliptic Curve Domain Parameters",
      "doi": "10.6028/NIST.SP.800-186"
    },
    {
      "key": "HJN+20",
      "authors": [
        "Thomas Haner",
        "Samuel Jaques",
        "Michael Naehrig",
        "Martin Roetteler",
        "Mathias Soeken"
      ],
      "year": 2020,
      "title": "Improved Quantum Circuits for Elliptic Curve Discrete Logarithms",
      "arxiv_id": "2001.09580",
      "arxiv_version": "v1",
      "entry_point": "ECDLP.tex"
    },
    {
      "key": "NC10",
      "authors": [
        "Michael A. Nielsen",
        "Isaac L. Chuang"
      ],
      "year": 2010,
      "title": "Quantum Computation and Quantum Information"
    },
    {
      "key": "BW92",
      "authors": [
        "Charles H. Bennett",
        "Stephen J. Wiesner"
      ],
      "year": 1992,
      "title": "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states",
      "doi": "10.1103/PhysRevLett.69.2881"
    },
    {
      "key": "DJ92",
      "authors": [
        "David Deutsch",
        "Richard Jozsa"
      ],
      "year": 1992,
      "title": "Rapid solution of problems by quantum computation",
      "doi": "10.1098/rspa.1992.0167"
    },
    {
      "key": "BV97",
      "authors": [
        "Ethan Bernstein",
        "Umesh Vazirani"
      ],
      "year": 1997,
      "title": "Quantum complexity theory",
      "doi": "10.1137/S0097539796300921"
    },
    {
      "key": "GHZ89",
      "authors": [
        "Daniel M. Greenberger",
        "Michael A. Horne",
        "Anton Zeilinger"
      ],
      "year": 1989,
      "title": "Going Beyond Bell's Theorem",
      "arxiv_id": "0712.0921"
    },
    {
      "key": "GSLW19",
      "authors": [
        "Andras Gilyen",
        "Yuan Su",
        "Guang Hao Low",
        "Nathan Wiebe"
      ],
      "year": 2019,
      "title": "Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics",
      "arxiv_id": "1806.01838",
      "arxiv_version": "v1",
      "entry_point": "BlockHam.tex"
    },
    {
      "key": "YYLW22",
      "authors": [
        "Zhan Yu",
        "Hongshun Yao",
        "Mujin Li",
        "Xin Wang"
      ],
      "year": 2022,
      "title": "Power and limitations of single-qubit native quantum neural networks",
      "arxiv_id": "2205.07848",
      "arxiv_version": "v2",
      "entry_point": "neurips_2022.tex"
    },
    {
      "key": "WZYW23",
      "authors": [
        "Youle Wang",
        "Lei Zhang",
        "Zhan Yu",
        "Xin Wang"
      ],
      "year": 2023,
      "title": "Quantum Phase Processing and its Applications in Estimating Phase and Entropies",
      "arxiv_id": "2209.14278",
      "arxiv_version": "v3",
      "entry_point": "arxiv_v3.tex"
    },
    {
      "key": "SK18",
      "authors": [
        "Maria Schuld",
        "Nathan Killoran"
      ],
      "year": 2018,
      "title": "Quantum machine learning in feature Hilbert spaces",
      "arxiv_id": "1803.07128",
      "arxiv_version": "v1",
      "entry_point": "featuremap_variational_cvcircuit.tex"
    },
    {
      "key": "Sch21",
      "authors": [
        "Maria Schuld"
      ],
      "year": 2021,
      "title": "Supervised quantum machine learning models are kernel methods",
      "arxiv_id": "2101.11020",
      "arxiv_version": "v1",
      "entry_point": "main.tex"
    },
    {
      "key": "GFE23",
      "authors": [
        "Elies Gil-Fuster",
        "Jens Eisert",
        "Vedran Dunjko"
      ],
      "year": 2023,
      "title": "On the expressivity of embedding quantum kernels",
      "arxiv_id": "2309.14419",
      "arxiv_version": "v1",
      "entry_point": "main.tex"
    },
    {
      "key": "LAT21",
      "authors": [
        "Yunchao Liu",
        "Srinivasan Arunachalam",
        "Kristan Temme"
      ],
      "year": 2021,
      "title": "A rigorous and robust quantum speed-up in supervised machine learning",
      "arxiv_id": "2010.02174",
      "arxiv_version": "v2",
      "entry_point": "arxiv.tex"
    },
    {
      "key": "CVH+23",
      "authors": [
        "M. Cerezo",
        "Guillaume Verdon",
        "Hsin-Yuan Huang",
        "Lukasz Cincio",
        "Patrick J. Coles"
      ],
      "year": 2023,
      "title": "Challenges and Opportunities in Quantum Machine Learning",
      "arxiv_id": "2303.09491",
      "arxiv_version": "v1",
      "entry_point": "Manuscript_Arxiv.tex"
    },
    {
      "key": "SBG+19",
      "authors": [
        "Maria Schuld",
        "Ville Bergholm",
        "Christian Gogolin",
        "Josh Izaac",
        "Nathan Killoran"
      ],
      "year": 2019,
      "title": "Evaluating analytic gradients on quantum hardware",
      "arxiv_id": "1811.11184",
      "arxiv_version": "v3",
      "entry_point": "quantum_gradients.tex"
    },
    {
      "key": "WIWL22",
      "authors": [
        "David Wierichs",
        "Josh Izaac",
        "Cody Wang",
        "Cedric Yen-Yu Lin"
      ],
      "year": 2022,
      "title": "General parameter-shift rules for quantum gradients",
      "arxiv_id": "2107.12390",
      "arxiv_version": "v2",
      "entry_point": "main.tex"
    },
    {
      "key": "RBS+23",
      "authors": [
        "Michael Ragone",
        "Bojko N. Bakalov",
        "Frederic Sauvage",
        "Alexander F. Kemper",
        "Carlos Ortiz Marrero",
        "Martin Larocca",
        "M. Cerezo"
      ],
      "year": 2023,
      "title": "A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits",
      "arxiv_id": "2309.09342",
      "arxiv_version": "v3",
      "entry_point": "Arxiv_Final.tex"
    },
    {
      "key": "TWC+22",
      "authors": [
        "Supanut Thanasilp",
        "Samson Wang",
        "M. Cerezo",
        "Zoe Holmes"
      ],
      "year": 2022,
      "title": "Exponential concentration in quantum kernel methods",
      "arxiv_id": "2208.11060",
      "arxiv_version": "v3",
      "entry_point": "main-update.tex"
    },
    {
      "key": "LJG+21",
      "authors": [
        "Martin Larocca",
        "Nathan Ju",
        "Diego Garcia-Martin",
        "Patrick J. Coles",
        "M. Cerezo"
      ],
      "year": 2021,
      "title": "Theory of overparametrization in quantum neural networks",
      "arxiv_id": "2109.11676",
      "arxiv_version": "v3",
      "entry_point": "main2.tex"
    },
    {
      "key": "LTW+24",
      "authors": [
        "Martin Larocca",
        "Supanut Thanasilp",
        "Samson Wang",
        "Kunal Sharma",
        "Jacob Biamonte",
        "Patrick J. Coles",
        "et al."
      ],
      "year": 2024,
      "title": "Barren plateaus in variational quantum computing",
      "arxiv_id": "2405.00781",
      "arxiv_version": "v2",
      "entry_point": "Nat_Rev_Phys_revised.tex"
    },
    {
      "key": "MBS+18",
      "authors": [
        "Jarrod R. McClean",
        "Sergio Boixo",
        "Vadim N. Smelyanskiy",
        "Ryan Babbush",
        "Hartmut Neven"
      ],
      "year": 2018,
      "title": "Barren plateaus in quantum neural network training landscapes",
      "arxiv_id": "1803.11173",
      "arxiv_version": "v1",
      "entry_point": "maintext.tex"
    },
    {
      "key": "RJT+25",
      "authors": [
        "Manuel S. Rudolph",
        "Tyson Jones",
        "Yanting Teng",
        "Armando Angrisani",
        "Zoe Holmes"
      ],
      "year": 2025,
      "title": "Pauli Propagation: A Computational Framework for Simulating Quantum Systems",
      "arxiv_id": "2505.21606",
      "arxiv_version": "v1",
      "entry_point": "main.tex"
    },
    {
      "key": "CSV+21",
      "authors": [
        "M. Cerezo",
        "Akira Sone",
        "Tyler Volkoff",
        "Lukasz Cincio",
        "Patrick J. Coles"
      ],
      "year": 2021,
      "title": "Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits",
      "arxiv_id": "2001.00550",
      "arxiv_version": "v3",
      "entry_point": "Arxiv_Final.tex"
    },
    {
      "key": "RBN+22",
      "authors": [
        "Michael Ragone",
        "Paolo Braccia",
        "Quynh T. Nguyen",
        "Louis Schatzki",
        "Patrick J. Coles",
        "Frederic Sauvage",
        "Martin Larocca",
        "M. Cerezo"
      ],
      "year": 2022,
      "title": "Representation Theory for Geometric Quantum Machine Learning",
      "arxiv_id": "2210.07980",
      "arxiv_version": "v3",
      "entry_point": "rep_theory_qml.tex"
    },
    {
      "key": "ASY+24",
      "authors": [
        "Jonathan Allcock",
        "Miklos Santha",
        "Pei Yuan",
        "Shengyu Zhang"
      ],
      "year": 2024,
      "title": "On the dynamical Lie algebras of quantum approximate optimization algorithms",
      "arxiv_id": "2407.12587",
      "arxiv_version": "v2",
      "entry_point": "Quantum-main.tex"
    },
    {
      "key": "Web15",
      "authors": [
        "Zak Webb"
      ],
      "year": 2015,
      "title": "The Clifford group forms a unitary 3-design",
      "arxiv_id": "1510.02769",
      "arxiv_version": "v3",
      "entry_point": "Cliffords_are_a_3-design.tex"
    },
    {
      "key": "WKKB24",
      "authors": [
        "Roeland Wiersema",
        "Efekan Kökcü",
        "Alexander F. Kemper",
        "Bojko N. Bakalov"
      ],
      "year": 2024,
      "title": "Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies",
      "arxiv_id": "2309.05690",
      "arxiv_version": "v2",
      "entry_point": "main.tex"
    },
    {
      "key": "CLG+23",
      "authors": [
        "M. Cerezo",
        "Martin Larocca",
        "Diego Garcia-Martin",
        "N. L. Diaz",
        "Paolo Braccia",
        "Enrico Fontana",
        "Manuel S. Rudolph",
        "Pablo Bermejo",
        "Aroosa Ijaz",
        "Supanut Thanasilp",
        "Eric R. Anschuetz",
        "Zoe Holmes"
      ],
      "year": 2023,
      "title": "Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing",
      "arxiv_id": "2312.09121",
      "arxiv_version": "v3",
      "entry_point": null
    },
    {
      "key": "GLC+23",
      "authors": [
        "Matthew L. Goh",
        "Martin Larocca",
        "Lukasz Cincio",
        "M. Cerezo",
        "Frederic Sauvage"
      ],
      "year": 2023,
      "title": "Lie-algebraic classical simulations for quantum computing",
      "arxiv_id": "2308.01432",
      "arxiv_version": "v1",
      "entry_point": null
    }
  ]
}