The Net Advance of Physics:
QUANTUM COMPUTATION

COMPUTATION: QUANTUM:
See also History of Quantum Computing

• General: TEXTBOOKS: Preskill and Kitaev 98/09;
  • Quantum Computing as a High School Module by Anastasia Perry et al. [2019/05] 129 pp.

• General: Quantum Computation Preprint Reviews Server; Quantum Computation Introductions and Tutorials (Oxford); Smolin (homepage); Steane 97/08; Hughes 97/12; Vedral and Plenio 98/02; Scarani 98/04; Rieffel and Polak 98/09; Zalka 98/11; Aharonov 98/12; Patel 99/09; DiVincenzo et al. 99/11; Crottet 2000/03 (in French); Knill and Nielsen 2000/10a; Grover 2000/11; Volovich 2001/09; Mermin 2002/07; Knill et al. 2002/07;
  • Quantum Computations: Fundamentals And Algorithms by Steven Duplij and Illia Shapoval [2006/09]
  • An Introduction to Quantum Computing by Noson S. Yanofsky [2007/08]
  • An Overview of Quantum Computing for Technology Managers by Eleanor G. Rieffel [2008/04]
  • Quantum Memories: A Review based on the European Integrated Project "Qubit Applications (QAP)" by Christoph Simon et al. [2010/03]
  • Quantum Computing by Thaddeus D. Ladd et al. [2010/03]
  • Quantum computer for dummies by Andrey Grozin [2011/08] In Russian.
  • Quantum Computation and Quantum Information by Yazhen Wang [Statistical Science 27, 373 (2012)]
  • Why now is the right time to study quantum computing by Aram W. Harrow [ACM XRDS 18, 32 (2012)]
  • Quantum algorithms: an overview by Ashley Montanaro [2015/11]
  • Recent advances on integrated quantum communications by Adeline Orieux and Eleni Diamanti [Journal of Optics 18, 083002 (2016)]
  • An Introduction to Quantum Computing, Without the Physics by Giacomo Nannicini [2017/08]
  • An Introduction to Superconducting Qubits and Circuit Quantum Electrodynamics by Nicholas Materise [2017/08]
  • A very brief introduction to quantum computing and quantum information theory for mathematicians by J. M. Landsberg [2018/01]
  • Solid-State Qubits by M. Fernando Gonzalez-Zalba [Revista Española de Física 31, 4 (2017)]
  • Quantum Algorithm Implementations for Beginners by Patrick J. Coles et al. [2018/04]
  • Experimental quantum mechanics in the class room: Testing basic ideas of quantum mechanics and quantum computing using IBM quantum computer by Anirban Pathak [2018/05]
  • A Quantum Engineer's Guide to Superconducting Qubits by Philip Krantz et al. [2019/04]
  • Introduction to Experimental Quantum Measurement with Superconducting Qubits by Mahdi Naghiloo [2019/04]
  • Quantum Computing as a High School Module by Anastasia Perry et al. [2019/05] 129 pp.
  • Quantum Computing: An Overview Across the System Stack by Salonik Resch and Ulya R. Karpuzcu [2019/05]
  • Superconducting Qubits: Current State of Play by Morten Kjaergaard et al. [2019/05]
  • Quantum Computing @MIT: The Past, Present, and Future of the Second Revolution by F. Vasconcelos [2020/02]
  • Quantum Computation and Applications by B. Bishnoi [2020/06]
  • Quantum information processing: An essential primer by E. Soljanin [2020/06]
  • Quantum physics without the physics by N. Petersson et al. [2020/12] i.e. for applied mathematicians.
  • Quantum computing forty years later by J. Preskill [2021/06]
  • Towards real-world quantum networks: A review by S.-H. Wei et al. [2022/01]
  • The basics of quantum computing for chemists by D. Claudino [2022/03]
  • Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation by H.-L. Huang et al. [2022/11]
  • Lecture notes on quantum algorithms by K. Khadiev [2022/12]
  • Notes on quantum computation and information by R. G. Jha [2023/01]
  • A short introduction to quantum computing for physicists by O. Zapata [2023/06]
  • Lecture notes on quantum computing by A. F. Kockum et al. [2023/11] 177 pp.
  • Five-year update to 'The Next Steps in Quantum Computing' by K. Brown et al. [2024/03]
  • Quantum computers, quantum computing, and quantum thermodynamics by F. Cleri [2024/04]
  • What you shouldn't know about quantum computers by C. Ferrie [2024/05] 143 pp. Actually, a fairly clear introduction to quantum computing for non-scientists (written in the form of 'myth-busting', the myths being oversimplifications commonly found in popular science).
  • Quantum computation by B. C. Sanders [2024/08]
  • A review and collection of metrics and benchmarks for quantum computers: Definitions, methodologies, and software by D. Lall et al. [2025/02]
  • A minimal introduction to quantum computing by M. M. H. Mahmoud and D. Goldsmith [2025/04]
  • Quantum computation and quantum error correction: The theoretical minimum by M. Wildon [2026/02]
  • An undergraduate course in quantum computing by P. Young [2026/04]
  • Quantum computing: A new frontier for science and society by G. Di Molfetta [2026/07]

• General: HARDWARE:
  • Spin-Based Quantum Computers made by Chemistry: Hows and Whys by P. C. E. Stamp and A. Gaita-Ariño [2008/10]
  • Coherent control of single electrons: a review of current progress by Christopher Bäuerle et al. [Reports on Progress in Physics 81, 056503 (2018)]
  • Introduction to Experimental Quantum Measurement with Superconducting Qubits by Mahdi Naghiloo [2019/04]
  • Quantum Computing: An Overview Across the System Stack by Salonik Resch and Ulya R. Karpuzcu [2019/05]
  • Superconducting Qubits: Current State of Play by Morten Kjaergaard et al. [2019/05]
  • A Review on Quantum Computing: Qubits, Cryogenic Electronics and Cryogenic MOSFET Physics by Farzan Jazaeri et al. [2019/08]
  • Majorana nanowires for topological quantum computation: A tutorial by P. Marra [2022/06]
  • The quantum internet: A hardware review by R. K. Ramakrishnan et al. [2022/06]
  • Integrated photonic platforms for quantum technology: A review by R. K. Ramakrishnan et al. [2022/06]
  • Photonic quantum computers by M. AbuGhanem [2024/09]

• Type: ADIABATIC / D-WAVE:
  • Notes on Adiabatic Quantum Computers by Boaz Tamir and Eliahu Cohen [2015/12]
  • Adiabatic Quantum Computing by Tameem Albash and Daniel A. Lidar [2016/11]

• Type: ATOMIC:
  • Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges by Mark Saffman [2016/05]
  • Single atom qubits: acceptors by J. Salfi [2020/01]
  • A concise review of Rydberg atom based quantum computation and quantum simulation by XL. Wu et al. [2020/12]

• Type: COUPLED-CAVITY ARRAY:
  • Quantum information processing in cavities: A review by N. Meher and S. Sivakumar [2022/04]

• Type: DISTRIBUTIVE:
  • Review of distributed quantum computing: From single QPU to high-performance quantum computing by D. Barral et al. [2024/04]

• Type: FAULT-TOLERANT:
  • An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation by Daniel Gottesman [2009/04]
  • An introduction to reliable quantum computation by Panos Aliferis [2011/07]
  • An introduction to Fault-Tolerant Quantum Computing by Alexandru Paler and Simon J. Devitt [2015/08]
  • Quantum Error Correction by Todd A. Brun [2019/10]
  • Introduction to quantum error correction and fault tolerance by S. M. Girvin [2019 Les Houches]

• Type: FULLERENE:
  • Quantum Computing with Endohedral Fullerenes by Wolfgang Harneit [2017/08]

• Type: GATE-BASED:
  • Tutorial: Gate-based superconducting quantum computing by S. Kwon et al. [2020/09]

• Type: BY LOCAL MEASUREMENT:
  • Quantum computation by local measurement by Robert Raussendorf and Tzu-Chieh Wei [Annual Review of Condensed Matter Physics 3, 239 (2012)]
  • Quantum spin systems for measurement-based quantum computation by T.-C. Wei [2018/12]
  • Measurement-based quantum computation by T.-C. Wei [2021/09]

• Type: MACROSCOPIC:
  • Superconducting qubits by Alexandre Zagoskin and Alexandre Blais [Physics in Canada 63, 215 (2007)]

• Type: NMR:
  • Quantum information processing using nuclear and electron magnetic resonance: review and prospects by Jonathan Baugh et al. [2007/10]
  • NMR quantum information processing by Dawei Lu et al. [2015/01]

• Type: OPTICAL/PHOTONIC:
  • Linear optical quantum computing by Pieter Kok et al. [2005/12]
  • Lecture notes on Optical Quantum Computing by Pieter Kok [2007/05]
  • Optical Quantum Computing by Jeremy L. O'Brien [Science 318, 1467 (2007)]
  • Optical quantum memory by A. I. Lvovsky et al. [Nature Photonics 3, 706 (2009)]
  • Photonic Quantum Information Processing by Pieter Kok [2016/03]
  • Recent advances on integrated quantum communications by Adeline Orieux and Eleni Diamanti [Journal of Optics 18, 083002 (2016)]
  • Photonic quantum information processing by Fulvio Flamini et al. [2018/03]
  • Photonic Quantum Information Processing: A Concise Review by Sergei Slussarenko and Geoff J. Pride [2019/07]
  • Microwaves in quantum computing by J. C. Bardin et al. [2020/11]
  • Integrated photonic platforms for quantum technology: A review by R. K. Ramakrishnan et al. [2022/06]
  • Photonic quantum computers by M. AbuGhanem [2024/09]

• Type: SEMICONDUCTOR:
  • Semiconductor Quantum Computation by Xin Zhang et al. [National Science Review 6, 32 (2019)]
  • Semiconductor Qubits in Practice by A. Chatterjee et al. [2020/05]

• Type: SPIN WAVE:
  • An introduction to spin wave computing by A. Mahmoud et al. [2020/06]

• Type: SUPERCONDUCTING:
  • Quantum information processing with superconducting circuits: a review by Goeran Wendin [2016/10]
  • Superconducting quantum computing: A review by H.-L. Huang et al. [2020/06]
  • Tutorial: Gate-based superconducting quantum computing by S. Kwon et al. [2020/09]

• Type: TOPOLOGICAL: Vedral 2002/12;
  • An Invitation to the Mathematics of Topological Quantum Computation by Eric C. Rowell [2016/01]
  • Programming quantum computers using 3-D puzzles, coffee cups, and doughnuts by Simon J. Devitt [XRDS 23(1), 45 (2016)]
  • Topological Quantum Computing by Ananda Roy and David P. DiVincio [2017/01]
  • Introduction to Topological Quantum Computation by Ville Lahtinen and Jiannis K. Pachos [2017/05]
  • Mathematics of Topological Quantum Computing by Eric C. Rowell and Zhenghan Wang [2017/05]
  • Topological data analysis: Concepts, computation, and applications in chemical engineering by A. D. Smith et al. [2020/06]
  • From Majorana fermions to topological quantum computation in semiconductor/superconductor heterostructures by J. Sau and S. Tewari [2021/05]
  • Majorana nanowires for topological quantum computation: A tutorial by P. Marra [2022/06]
  • Topological quantum computing by F. Hassler [2024/10]

• Type: TRAPPED ION:
  • Tutorial: The trapped-ion qubit toolbox by Roee Ozeri [2011/06]
  • Trapped-Ion Quantum Computing: Progress and Challenges by Colin D. Bruzewicz et al. [2019/04]
  • Quantum computing with trapped ions: A beginner's guide by F. Bernardini et al. [2023/03]

• Type: VARIATIONAL:
  • A review of barren plateaus in variational quantum computing by M. Larocca et al. [2024/05]

• Aspects: ERROR CORRECTING CODES;

• Aspects: ALGORITHMS: Shor 2000/05;
  • Quantum Computations: Fundamentals And Algorithms by Steven Duplij and Illia Shapoval [2006/09]
  • Quantum Algorithms by Michele Mosca [2008/08]
  • Quantum algorithms for algebraic problems by Andrew M. Childs and Wim van Dam [2008/12]
  • A Review on Quantum Search Algorithms by Pulak Ranjan Giri and Vladimir E. Korepin [2016/02]
  • Introduction to Quantum Coding Algorithms: A Tutorial Series Using Pyquil by Daniel Koch et al. [2019/03]
  • Introduction to Coding Quantum Algorithms: A Tutorial Series Using Qiskit by Daniel Koch et al. [2019/03]
  • Programming quantum computers by M. Willsch et al. [2022/01]
  • Lecture notes on quantum algorithms for scientific [matrix] computation by L. Lin [2022/01]
  • Basic quantum algorithms by R. Portugal [2022/01]
  • Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation by H.-L. Huang et al. [2022/11]
  • A brief introduction to quantum algorithms by S.-H. Zhang and L.-Z. Li [2022/12]
  • An introduction to variational quantum algorithms on gate-based quantum computing for combinatorial optimization problems by C. Grange et al. [2022/12]
  • Lecture notes on quantum algorithms by K. Khadiev [2022/12]
  • A review on Quantum Approximate Optimization Algorithm and its variants by K. Blekos et al. [2023/06]
  • Quantum algorithms: A survey of applications and end-to-end complexities by A. M. Dalzell et al. [2023/10] 337 pp.
  • A review of quantum scientific computing algorithms for engineering problems by O. M. Raisuddin and S. De [2024/08]
  • The state of factoring on quantum computers by D. Willsch et al. [2024/10]

• Aspects: ANNEALING:
  • Notes on Adiabatic Quantum Computers by Boaz Tamir and Eliahu Cohen [2017/11]

• Aspects: COMPUTATIONAL SUPREMACY:
  • Quantum Computational Supremacy by Aram W. Harrow and Ashley Montaro [Nature 549, 203 (2018)]

• Aspects: DEVICES: Chen et al. 2003/03;

• Aspects: FINITE-RESOURCE:
  • Quantum Information Processing with Finite Resources - Mathematical Foundations by Marco Tomamichel [2015/04] 135 pp.

• Aspects: INFORMATION PROCESSING: Knill and Nielsen 2000/10b;
  • Designing Quantum Information Processing via Structural Physical Approximation by Joonwoo Bae [2017/07]

• Aspects: ION TRAP METHOD: Hughes 97/12;

• Aspects: LEARNING:
  • An Introduction to Quantum Machine Learning by M. Schuld et al. [2014/09]
  • A Survey of Quantum Learning Theory by Srinavasan Arunachalam and Ronald de Wolf [2017/01]
  • An introduction to quantum machine learning for engineers by O. Simeone [2022/05]
  • A survey on quantum reinforcement learning by N. Meyer et al. [2022/11]
  • A survey of quantum Transformers: Approaches, challenges, and future directions by H. Zhang and Q.-L. Zhao [2025/04]
  • Quantum machine learning by M. Usman [2025/06]
  • A survey of quantum generative adversarial networks: Architectures, use cases, and real-world implementations by M. Islam et al. [2025/06]

• Aspects: MEMORIES:
  • Quantum memories: emerging applications and recent advances by Khabat Heshami et al. [2015/11]

• Aspects: NMR METHOD: Jones et al. 98/05; Cory et al. 2000/04; Laflamme et al. 2002/07;

• Aspects: PLATEAUX:
  • A review of barren plateaus in variational quantum computing by M. Larocca et al. [2024/05]

• Aspects: QUANTUM INFORMATION: Cleve 99/06;

• Aspects: SECURITY:
  • A survey and tutorial on security and resilience of quantum computing by A. Ash Saki et al. [2021/06]
  • A primer on security of quantum computing by S. Ghosh et al. [2023/05]

• Aspects: VERIFICATION:
  • Verification of quantum computation: An overview of existing approaches by Alexandru Gheorghiu et al. [2017/09]

• Re: ANYONS:
  • Introduction to Topological Quantum Computation by Ville Lahtinen and Jiannis K. Pachos [2017/05]
  • It's anyon's game: the race to quantum computation by J. K. Jain [2020/08]

• Re: AUTOMATA:
  • Automata and Quantum Computing by Andris Ambainis and Abuzer Yakaryilmaz [2015/07]

• Re: CHEMISTRY:
  • Quantum computational chemistry by Sam McArdle et al. [2018/08] Meaning the use of quantum computing to solve formerly intractable chemistry problems.
  • The basics of quantum computing for chemists by D. Claudino [2022/03]

• Re: COHERENT STATES: Fujii 2002/07;

• Re: COMPLEXITY: ECCC Lecture Notes;
  • Statistical mechanics of classical and quantum computational complexity by Christopher R. Laumann et al. [Les Houches 2009/05]
  • Quantum complexity in gravity, quantum field theory, and quantum information science by S. Baiguera et al. [2025/03]

• Re: CONTROL THEORY:
  • Quantum computing through the lens of control by J. Berberich and D. Fink [2023/10]

• Re: CRYPTOGRAPHY: Hughes 97/12;
  • Interferometry with Atoms by J.-F. Schaff et al. [2015/04]
  • Advances in Quantum Dense Coding by Yu Guo et al. [2019/04]

• Re: DEEP/MACHINE LEARNING:
  • From quantum graph computing to quantum graph learning: A survey by Y.-H. Tang et al. [2022/02]
  • A survey on quantum machine learning: Current trends, challenges, opportunities, and the road ahead by K. Zaman et al. [2023/10]

• Re: ECONOMICS/FINANCE:
  • Quantum computing for finance: overview and prospects by Roman Orus et al. [2018/07]
  • Quantum computing for finance: State of the art and future prospects by D. J. Egger et al. [2020/06]
  • A survey on quantum computing for finance by D. Herman et al. [2022/01]

• Re: FLUIDS:
  • Quantum computing for fluids: Where do we stand? by S. Succi et al. [2023/07]
  • Quantum machine learning and quantum-inspired methods applied to computational fluid dynamics: a short review by C. A. Amaral et al. [2025/10]

• Re: GEOMETRIC PHASE:
  • Geometric phases in quantum information by Erik Sjöqvist [2015/03]

• Re: GRAPH THEORY:
  • From quantum graph computing to quantum graph learning: A survey by Y.-H. Tang et al. [2022/02]

• Re: JOSEPHSON JUNCTIONS: Makhlin et al. 2000/11;
  • Quantum Bits with Josephson Junctions by Anton Frisk Kockum and Franco Nori [2019/08]

• Re: LATTICE FIELD THEORY:
  • Simulating Lattice Gauge Theories within Quantum Technologies by M. C. Bañuls et al. [2019/11]
  • Review on quantum computing for lattice field theory by L. Funcke et al. [2023/02]

• Re: MAJORANA QUBITS:
  • Majorana Qubits by Fabian Hassler [2014/04]

• Re: MASTER EQUATIONS:
  • A tutorial on quantum master equations: Tips and tricks for quantum optics, quantum computing, and beyond by F. Campaioli et al. [2023/03]

• Re: NANOMATERIALS:
  • Nanomaterials for quantum information science and engineering by A. Alfieri et al. [2022/02]

• Re: NETWORKS
• Quantum Feedback Networks and Control: A Brief Survey by Guofeng Zhang and Matthew R. James [2012/01]
• An Introduction to Quantum Bayesian Networks for Mixed States by Robert R. Tucci [2012/04]
• Tensor Networks in a Nutshell by Jacob Biamonte and Ville Bergholm [2017/08]
• Review of Tensor Network Contraction Approaches by Shi-Ju Ran et al. [2017/08]
• The Tensor Networks Anthology: Simulation Techniques for Many-Body Quantum Lattice Systems by Pietro Silvi et al. [2017/10] 115 pp.
• Tensor networks for complex quantum systems by Roman Orus [2018/12]
• Topics in Quantum Networking by Fengyou Sun [2019/03]
• Lectures on quantum tensor networks by J. Biamonte [2019/12]
• Quantum communications infrastructure architecture: Theoretical background, network structure and technologies by A. M. Lewis and P. F. Scudo [2021/10]
• Developments in tensor networks: From statistical mechanics to quantum entanglement by K. Okunishi [2021/11]
• Towards real-world quantum networks: A review by S.-H. Wei et al. [2022/01]
• Routing protocols for quantum networks: Overview and challenges by B. Kar and P. Kumar [2023/05]
• Quantum communications by M. Hajdušek and R. Van Meter [2023/11] 308-page textbook.
• Complex quantum networks: A topical review by J. Nokkala et al. [2023/11]
• Simulators for quantum network modelling by O. Bel and M. Kiran [2024/08]
• Who can compete with quantum computers? Lecture notes on quantum-inspired tensor-network computational techniques by X. Waintal et al. [2026/01]