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A GUIDE TO QC AND QI

“… the laws of physics present no barrier to reducing the size of computers until bits are the size of atoms, and quantum behavior holds sway.” Richard P. Feynman (1985)

This guide is intended for researchers entering the area of Quantum Computation and Quantum Information Science.

OVERVIEW & PURPOSE

Quantum computing is a multidisciplinary field of research including quantum physics, computer science and linear algebra. The goal of quantum computing is to compute tasks more quickly, by using the laws of quantum physics, which classical computers either do slowly or cannot solve in polynomial time. Of course, classical computers will always stay with the mankind to assist quantum computers at least with error correction and control flow.
The two main resources of the speedup are the so called superposition and entanglement: a quantum system can be in superposition of two (or more) states, also, be entangled with another system. Entanglement is a type of correlation that is stronger than any classical correlation. When there is entanglement involved, one rather think of many-partite system as one (possibly nonlocal) object than a system of correlated objects.
The guide assumes some knowledge of linear algebra and some programming language in order to go deeper into quantum computing research.

Contents

PREREQUISITES

  • LINEAR ALGEBRA
    This MIT course covers matrix theory and linear algebra, emphasizing topics useful in disciplines such as physics, economics and social sciences, natural sciences, and engineering.

  • PROBABILITY THEORY
    G. R. Grimmett and D. R. Stirzaker. Probability and Random Processes. Clarendon Press, Oxford, 1992.
    D. Williams. Probability with Martingales. Cambridge University Press, Cambridge, 1991.

  • NUMBER THEORY
    N. Koblitz. A Course in Number Theory and Cryptography. Springer-Verlag, New York, 1994.
    Chapter 33 of T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, Mass., 1990
    Chapter 10 of G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers, Fourth Edition. Oxford University Press, London, 1960.

  • GROUP THEORY
    J. S. Lomont. Applications of Finite Groups. Dover, New York, 1987.
    Group theory in physics -- M. Hammermesh. Group Theory and its Application to Physical Problems. Dover, New York, 1989.

  • PYTHON
    A good resource for containing a nice introduction to scientific computing as well as more advanced topics in open quantum systems and quantum computation is this Quantum Toolbox in Python
    This gallery of jupyter notebooks contains diverse scientific computing materials.

ONLINE COURSES

MANUALS

  • Michael A. Nielsen & Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, The Edinburgh Building, Cambridge CB2 8RU, UK, 2010
  • S. Lloyd, Quantum Information Science
  • A. Yu. Kitaev, A.H. Shen, and M.N. Vyalyi, Classical and Quantum Computation, American Mathematical Society, Providence, 2002.
  • W.H. Steeb and Y. Hardy, Problems & Solutions in Quantum Computing & Information, World Scientific, River Edge, NJ, 2004.
  • R.P. Feynman, Feynman Lectures on Computation, CRC Press, Taylor & Francis Group, 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742, 1996 (Amazon link)
  • O. Pittenger, An Introduction to Quantum Computing Algorithms, Progress in Computer Science and Applied Logic, v19, 2000
  • Noson S. Yanofsky, Mirco A. Mannucci, Quantum Computing for Computer Scientists, Cambridge University Press, 32 Avenue of the Americas, New York, NY 10013-2473, USA 2008
  • Colin P. Williams, Explorations in Quantum Computing, Springer-Verlag London Limited, 2011
  • E. Rieffel and W. Polak, Quantum Computing, A Gentle Introduction, The MIT Press Cambridge, Massachusetts London, England, 2011
  • Sarah C. Kaiser and Christopher E. Granade, Learn Quantum Computing with Python and Q#
  • Johan Vos, Quantum Computing for Java Developers
  • Jack D. Hidary, Quantum Computing: An Applied Approach
  • 13 Best New Quantum Computing Books To Read In 2020

The Stanford Encyclopedia of Philosophy is a great place to search and read about general topics from more philosophical perspective

LECTURE NOTES

QUANTUM MECHANICS

ONLINE QM COURSES

FEYNMAN LECTURES

A very good start for learning quantum mechanics would be the famous Feynman Lectures on Physics Vol III

GO DEEPER INTO QM

  • A comprehensive guide to literature on the foundations of quantum mechanics is L. E. Ballentine, “Resource letter IQM2: Foundations of quantum mechanics since the Bell Inequalities”, Am. J. Phys 55, 785 (1987)

QM Textbooks:

  • J.J. Sakurai, J. Napolitano, Modern Quantum Mechanics, Cambridge University Press, 2017.
  • L.E. Ballentine, Quantum Mechanics: A Modern Development, World Scientific Publishing Co. Pte. Ltd. 2003
  • Asher Peres, Quantum Theory: Concepts and Methods, Kluwer Academic Publishers, New York, Boston, Dordrecht, London, Moscow 2002

VIDEO LECTURES FROM INTERNATIONAL SUMMER SCHOOLS AND CONFERENCES

QUANTUM PROGRAMMING FRAMEWORKS

There are already a handful of programming frameworks that allow access to quantum virtual machines, some even grant access to their hardware.

Open source quantum software is an excellent github repository that contains information about quantum software projects. List of Open Quantum Projects

STAY UP-TO-DATE

MAILING LISTS
BLOGS
RSS FEEDS

Get alerts from new publications, news and blogs directly in your slack workspace or register in, e.g., https://theoldreader.com/ by adding the below links

Quantum Information - nature.com http://feeds.nature.com/npjqi/rss/current
PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc. http://feeds.aps.org/rss/tocsec/PRL-GeneralPhysicsStatisticalandQuantumMechanicsQuantumInformationetc.xml
PRA: Quantum information http://feeds.aps.org/rss/tocsec/PRA-Quantuminformation.xml
MIT News - Quantum computing http://news.mit.edu/rss/topic/quantum-computing
Shtetl-Optimized https://www.scottaaronson.com/blog/?feed=rss2
Comments on: News https://quantumcomputingreport.com/news/feed/
Physics Today Magazine http://feeds.feedburner.com/physicstoday/pt1?format=xml
Rigetti Tech Blog https://rigetticomputing.github.io/blog/feed.xml
Microsoft Quantum https://cloudblogs.microsoft.com/quantum/feed/
Stories by Rigetti Computing on Medium https://medium.com/feed/@rigetticomputing
Algorithmic Assertions - Craig Gidney's Computer Science Blog http://algassert.com/feed
Quantum Frontiers https://quantumfrontiers.com/feed/
QuTechBlog – Bits of Quantum http://blog.qutech.nl/index.php/author/qutechblog/feed/
The Quantum Pontiff http://dabacon.org/pontiff/?feed=rss2
American Institute of Physics: Journal of Mathematical Physics: Table of Contents https://aip.scitation.org/action/showFeed?type=etoc&feed=rss&jc=jmp
Stories by Dr James Wootton on Medium https://medium.com/feed/@decodoku
quanta rei https://quantarei.wordpress.com/feed/
Quantum, open journal for quantum science https://quantum-journal.org/feed/

QUANTUM COMPUTING STACK EXCHANGE

Quantum computing stack exchange is a good place to ask or answer questions. Quantum Computing Stack Exchange is a question and answer site for engineers, scientists, programmers, and computing professionals interested in quantum computing. Join them.

ROADMAPS

Find out the recent theoretical and experimental developments as well as near- mid- and far-term goals in quantum computing and prediction analyses of its applications in businesses in the following comprehensive roadmaps and reports:

POPULAR PRESS

REPRESENTATIVE PLATERS IN THE FIELD

(update: QxBranch has been acquired by Rigetti)

RESEARCH TOPICS WITH REFERENCES

READING SCIENTIFIC ARTICLES

Before diving deep into research and read scientific papers, we suggest the reader to follow this guideline (adapted from "Quantum Computing for Computer Scientists" manual cited in MANUALS):

Do not be deterred if an article seems impenetrable. Keep in mind that professors and professionals also struggle to understand these articles, and take comfort in this epigram usually attributed to the great physicist Richard Feynman: “If you think you understand quantum mechanics, you don’t understand quantum mechanics.” Some articles are difficult to understand not only because quantum theory is devilishly elusive but also because scientific writing can be opaque. Fortunately, there are techniques for tackling scientific articles, beginning with these preliminary steps:

  • Read the title. It may contain clues about the article’s purpose or findings.
  • Read the abstract. It summarizes the article and will help you recognize important points when you read them.
  • Read the introduction and conclusion. Usually in plain language, the introduction and conclusion will help you decode the rest of the article.
  • Skim the article. Skim to get a sense of the article’s structure, which will help you stay oriented while you read.

Once you understand an article’s purpose and structure, you are ready to read the full article. To maximize comprehension and minimize frustration, follow these tips:

  1. Read actively. Take notes while you read. Underline key phrases; mark important passages; record important points; sketch arguments and proofs; and reproduce calculations. (Of course, don’t write on anything owned by a library; make copies instead)
  2. Don’t dwell. Skim or skip difficult parts and return to them later. They might make more sense after you have read subsequent sections
  3. Consult the bibliography. If something confuses you, one of the cited articles might explain it better or provide helpful background information
  4. Read the article multiple times. You’ll understand more with each pass
  5. Know when to stop. Don’t obsess over an article. At some point, you will have gotten as much as you are going to get (for the time being). Some or even most of the article might still elude you; nevertheless, you will know more after reading the article than you did before you started, and you will then be better equipped to read other articles
  6. Talk about the article. Mull over the article with other group members, and ASK QUESTIONS if you need help. After you have finished the article, keep talking about it. Explain it to a group member, or even to someone unfamiliar with the field. After all, the best way to learn something is to teach it to someone else!

We have collected a list of references classified by topics that may help the reader to focus on a specific topic. The list by no means is comprehensive.

Quantum Computation

  1. A quantum computation roadmap by LANL
  2. A tutorial by Samuel Braunstein
  3. A review by Andrew Steane (1997)
  4. A review by Dorit Aharonov (2008)
  5. D. P. DiVincenzo, “Quantum Computation”, Science 270, 255 (1995)
  6. Rod van Meter's great list of suggested papers/works on Quantum Architecture (2019 Aug)

Quantum Information

  1. By C. E. Shannon, “A Mathematical Theory of Communication”, The Bell System Technical Journal 27, pp. 379-423, 623-656 (1957)
  2. E. B. Davies, “Information and Quantum Measurement”, IEEE trans. on information theory, 24, 596 (1978)
  3. E. Knill et. al., “Introduction to Quantum Information Processing”, arXiv:quant-ph/0207171 (2002)

Quantum Algorithms

20 algrithms implementations on IBM's 5-qubit quantum computer, including Shor's prime factoring, Grover's database search, etc., can be found in

  1. Quantum Algorithm Implementations for Beginners arXiv: 1804.03719 (2018)

Quantum Algorithm Zoo, a comprehensive catalog of quantum algorithms

  1. Algebraic and Number Theoretic Algorithms

Quantum Complexity

  1. L.G. Valiant, “The complexity of computing the permanent”, Theoretical Computer Science 8, 189 (1979).
  2. C. Bennett, “Time/space trade-offs for reversible computation”, Siam J. Comput. 18, 766 (1989)
  3. R. Levine, A. Sherman, “A note on Bennett’s tradeoff for reversible computation”, Siam J. Comput. 19, 673 (1990)
  4. A. Shamir, “IP = PSPACE”, Journal of the Association for Computing Machinery, 39, 869 (1992)
  5. E. Bernstein, U. Vazirani, “Quantum complexity theory”, Siam J. Comput. 26, 1411 (1997)
  6. J. Preskill, “Quantum Computing in the NISQ era and beyond”, arXiv:1801.00862 (2018)
  7. S. Aaronson, “PDQP/qpoly = ALL”, arXiv:1805.08577 (2018)
  8. R. Raz, A. Tal, “Oracle Separation of BQP and PH”, Electronic Colloquium on Computational Complexity, Report 107 (2018)

Quantum Simulation

  1. S. Lloyd “Universal quantum simulators”, Science 273, 1073 (1996)
  2. D. Bacon et. al., “Universal simulation of Markovian quantum dynamics”, arXiv:quant-ph/0008070 (2001)
  3. I. Kassal et. al., "Simulating Chemistry Using Quantum Computers", Annu. Rev. Phys. Chem., 62, 185, (2011)
  4. I. Bloch et. al., “Quantum simulation with ultracold atomic gases” Nat. Phys. 8, 267 (2012)
  5. R. Blatt et. al. “Quantum simulation with trapped ions” Nat. Phys. 8, 277 (2012)
  6. S. Trotzky et. al., “Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas” Nat. Phys. 8, 325 (2012)
  7. I. Georgescu et. al., “Quantum simulation” Rev. Mod. Phys. 86, 153 (2014)
  8. J. Eisert et. al., “Quantum many-body systems out of equilibrium” Nat. Phys. 11, 124 (2015)
  9. P. J. J. O’Malley et. al., “Scalable Quantum Simulation of Molecular Energies”, Phys. Rev. X 6, 031007 (2016)
  10. A. M. Childs et. al., “Toward the first quantum simulation with quantum speedup” arXiv:1711.10980 (2017)
  11. H. Lamm, “Simulation of Nonequilibrium Dynamics on a Quantum Computer”, arXiv:1806.06649v3 (2018)
  12. S. McArdle et. al., "Quantum computational chemistry", arXiv:1808.10402 (2018)
  13. Y. Cao et. al., "Quantum Chemistry in the Age of Quantum Computing", arXiv:1812.09976 (2018)

Quantum Hardware (Physical Realizations)

General review
  1. T. D. Ladd et. al., “Quantum computers” nature 464, 45 (2010)
Ion traps
  1. R. Blatt et. al., “Entangled states of trapped atomic ions”, Nature 453, 1008 (2008)
  2. J. P. Home et. al., “Complete methods set for scalable ion trap quantum information processing”, Science 325, 1227 (2009) D.R. Leibrandt et. al., “Demonstration of a scalable, multiplexed ion trap for quantum information processing”, Quantum Information and Computation, 9, 901 (2009)
  3. C. Monroe et. al., “Scaling the ion trap quantum processor”, Science 339, 1164 (2013)
Spin
  1. D Loss et. al., “Quantum computation with quantum dots” Phys. Rev A 57, 120 (1998)
  2. J. M. Elzerman et. al., “Single-shot read-out of an individual electron spin in a quantum dot”, nature 430, 431 (2004)
  3. F. H. L. Koppens et. al., “Driven coherent oscillations of a single electron spin in a quantum dot”, nature 442, 766 (2006)
  4. R. Hanson et. al., “Spins in few-electron quantum dots”, Rev. Mod. Phys, 79, 1217 (2007)
  5. M. Veldhorst et. al., “An addressable quantum dot qubit with fault-tolerant control-fidelity”, nature nanotechnology, 9, 981 (2014)
  6. M. Veldhorst et. al., “A two-qubit logic gate in silicon”, nature 526, 410 (2015)
  7. L. M. K. Vandersypen et. al., “Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent”, npj Quantum Information 3, 1 (2017), open access doi:10.1038/s41534-017-0038-y
  8. T. F. Watson et. al., “A programmable two-qubit quantum processor in silicon”, nature 555, 633 (2018)
NV-centers
  1. G. Waldherr et. al. “Quantum error correction in a solid-state hybrid spin register”, nature 506, 204 (2014)
  2. B. Hensen et. al., “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres”, nature, 526, 682 (2015)
  3. G. Tosi et. al., “Silicon quantum processor with robust long-distance qubit couplings” Nat. Commun. 8, 450 (2017)
  4. P.C. Humphreys et. al., “Deterministic delivery of remote entanglement on a quantum network”, nature, 558, 268 (2018)
Photonic
  1. E. Knill et. al., “A scheme for efficient quantum computation with linear optics”, nature, 409, 46 (2001)
  2. J.L. O'Brien, “Optical Quantum Computing”, Science 318, 1567 (2007)
  3. Xing-Can Yao et. al., “Experimental demonstration of topological error correction”, nature 482, 489 (2012)
  4. T. Meany et. al., “Engineering integrated photonics for heralded quantum gates”, Sci. Rep. 6, 25126 (2016)
  5. J-I Yoshikawa et. al., “Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing”, APL Photon. 1, 060801 (2016)
Superconducting
  1. Before diving deep into "superconducting" papers, it is recommended to study this introduction to the subject that adopts the elegant Lagrangian formalism to set up the field.
  1. Y. Nakamura et. al., “Coherent control of macroscopic quantum states in a single-cooper-pair box”, Nature 398, 786 (1999)
  2. Alexandre Blais et. al., “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation ”Phys. Rev A 69, 062320 (2004)
  3. Jens Koch et. al., “Charge-insensitive qubit design derived from the Cooper pair box”, Phys. Rev. A 76, 042319 (2007)
  4. J. A. Schreier et. al., “Suppressing charge noise decoherence in superconducting charge qubits”, Phys. Rev. B 77, 180502(R) (2008)
  5. Austin G. Fowler, “Surface codes: Towards practical large-scale quantum computation”, Phys. Rev. A 86, 032324 (2012)
  6. M.H. Devoret et. al., “Superconducting circuits for quantum information: an outlook” Science 339, 1169 (2013)
  7. Jerry M. Chow et. al., “Implementing a strand of a scalable fault-tolerant quantum computing fabric”, nature communications 5, 1 (2014)
  8. S. Asaad et. al., “Independent, extensible control of same-frequency superconducting qubits by selective broadcasting”, npj Quantum Information 2, 1 (2016), open access doi:10.1038/npjqi.2016.29
  9. T. Walter et. al., Rapid High-Fidelity Single-Shot Dispersive Readout of Superconducting Qubits Phys., Rev. Applied 7, 054020 (2017)
  10. R. Versluis et. al., “Scalable Quantum Circuit and Control for a Superconducting Surface Code”, Phys. Rev Applied 8, 034021 (2017)
Topological
  1. Y. Oreg et. al., “Helical Liquids and Majorana Bound States in Quantum Wires”, Phys. Rev. Lett. 105, 177002 (2010)
  2. V. Mourik et. al., “Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices”, Science 336, 1003 (2012)
  3. T. Hyart et. al., “Flux-controlled quantum computation with Majorana fermions”, Phys. Rev. B 88, 035121 (2013)
  4. S.R. Plissard, “Formation and electronic properties of InSb nanocrosses”, nature nanotechnology 8, 589 (2013)
  5. D. Car, “Rationally Designed Single-Crystalline Nanowire Networks”, Adv. Mater., 26, 4875 (2014)
  6. S. Nadj-Perge et. al., “Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor”, Science 346, 602 (2014)
  7. D. Aasen et. al., “Milestones Toward Majorana-Based Quantum Computing”, Phys. Rev. X 6, 031016 (2016)
  8. S. Vijay et. al., “Teleportation-based quantum information processing with Majorana zero modes”, Phys. Rev. B 94, 235446 (2016)
  9. S. M. Albrecht, “Exponential protection of zero modes in Majorana islands”, nature 531, 206 (2016)
  10. S. Gazibegovic, “Epitaxy of advanced nanowire quantum devices”, nature 548, 434 (2017)
  11. R.M. Lutchyn et. al., “Transport through a Majorana Island in the Strong Tunneling Regime”, Phys. Rev. Lett. 119, 057002 (2017)
  12. V.T. Lahtinen et. al., “A Short Introduction to Topological Quantum Computation”, arXiv:1705.04103 (2017)
  13. T. Karzig et. al., “Scalable designs for quasiparticle - poisoning - protected topological quantum computation with Majorana zero modes”, Phys. Rev. B 95, 235305 (2017)
  14. H. Zhang, “Quantized Majorana conductance” nature 556, 74 (2018)

Quantum Cryptography

  1. A. Boaron et. al., Secure Quantum Key Distribution over 421 km of Optical Fiber, PRL 121, 190502 (2018)
  2. A. Dahlberg, S. Wehner, SimulaQron - A simulator for developing quantum internet software (2018)
  3. A. Shenoy-Hejamadi et. al., Quantum Cryptography: Key Distribution and Beyond (2018)
  4. M. Tomamichel, A. Leverrier, A largely self-contained and complete security proof for quantum key distribution (2017)
  5. C. Bennet, G. Brassard, Quantum Cryptography: Public key distribution and coin tossing, Theor. Comp. Sci. 560, 7 (2014)
  6. M. Berta et. al., Quantum to Classical Randomness Extractors (2012)
  7. S. Aaronson, Quantum Copy-Protection and Quantum Money (2011)
  8. A Quantum Cryptography Roadmap by LANL (2009)
  9. R. Renner, Security of Quantum Key Distribution, PhD Thesis
  10. A. Childs, Secure Assisted Quantum Computation (2005)
  11. P. Shor, J. Preskill, Simple Proof of Security of the BB84 Quantum Key Distribution Protocol (2000)
  12. D. Mayers, Quantum Key Distribution and String Oblivious Transfer in Noisy Channels (1996)
  13. C. Bennett, Quantum Cryptography Using Any Two Nonorthogonal States, PRL 68, 3121 (1992)
  14. A. Ekert, Quantum Cryptography Based on Bell's Theorem, PRL, 67, 661 (1991)
  15. C. Bennet, G. Brassard, J-M. Robert, Privacy Amplification by Public Discussion, Siam J. Comput. 17, 210 (1988)

Quantum Error Correction

  1. S. J. Devitt, “Quantum Error Correction for Beginners”, arXiv:0905.2794 (2013)
  2. E. Knill et. al., “Introduction to Quantum Error Correction”, arxiv:quant-ph/0207170 (2008)
  3. D. Gottesman, “Stabilizer Codes and Quantum Error Correction” (Thesis) arXiv:quant-ph/9705052 (1997)
  • Group theoretic approach
  1. A. R. Calderbank et. al., “Quantum Error Correction and Orthogonal Geometry”, Phys. Rev. Lett. 78, 405 (1997)
  2. A. R. Calderbank et. al.,, “Quantum Error Correction Via Codes Over GF (4)”, arXiv:quant-ph/9608006 (1997)
  • Fault tolerance
  1. P.W Shor, “Fault-tolerant quantum computation”, arXiv:quant-ph/9605011 (1996)
  2. J. Preskill, “Fault-tolerant quantum computation” arXiv:quant-ph/9712048 (1997)
  3. A.R. Calderbank and P.W. Shor, “Good quantum error-correcting codes exist”, Phys. Rev. A 54, 1098 (1996)

Quantum Machine Learning

  1. A github repository of resources

More topics (Mainly Open Areas of Research)

  • Quantum Error Correction Beyond Stabilizer States
  • Efficient Classical Simulation of Stabilizer Circuits
  • What is the Threshold for Reliable Classical Computation
  • Simulating Quantum Mechanics from the Gottesman-Knill Theorem
  • Canonical Decompositions of Quantum Circuits
  • Fault Tolerant Quantum Computation with 5-qubit and CWS Codes
  • Magic States for Universal Quantum Computing
  • Classical Circuits and the Ck Family
  • Threshold for Fault-Tolerant Quantum Computation
  • Blind Quantum Computation
  • New Quantum Algorithms for Hard Problems
  • Quantum Algorithm on Graphs
  • Shur: Beyond the Quantum Fourier Transform
  • Post-Quantum Cryptography
  • Entropies of Various Quantum Sources
  • Quantum Bit-Commitment
  • Optimal Two-Qubit Gates
  • Quantum Channel Capacities

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This guide is for researchers entering the area of Quantum Computation and Quantum Information Science.

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