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 manypartite 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
 ONLINE COURSES
 MANUALS
 LECTURE NOTES
 QUANTUM MECHANICS
 VIDEO LECTURES FROM INTERNATIONAL SUMMER SCHOOLS AND CONFERENCES
 QUANTUM PROGRAMMING FRAMEWORKS
 STAY UPTODATE
 ROADMAPS and REPORTS
 POPULAR PRESS
 REPRESENTATIVE PLAYERS IN THE FIELD
 RESEARCH TOPICS WITH REFERENCES

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. SpringerVerlag, 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
 Quantum Mechanics and Quantum Computation (Umesh Vazirani)
 Quantum information science I: Part 1 (Peter Shor)
 Quantum information science I: Part 2 (Peter Shor)
 Quantum information science I: Part 3 (Peter Shor)
 Quantum information science II (Advanced) Part 1: quantum states, noise and error correction (Aram Harrow)
 Quantum information science II (Advanced) Part 2: efficient quantum computing  fault tolerance and complexity (Aram Harrow)
 Quantum information science II (Advanced) Part 3:Advanced quantum algorithms and information theory (Aram Harrow)
 Building blocks of a quantum computer: part 1 (Delft University)
 Building blocks of a quantum computer: part 2 (Delft University)
 Quantum internet and quantum computers (Delft University)
 Quantum Computing (in Russian) (Saint Petersburg State University)
 Introduction to Quantum Information and Computation from a Foundational Standpoint (Jeffrey Bup)
 Quantum Information (Raymond Laflamme)
 Explorations in Quantum Information (David Cory)
 Quantum Information (Multiple Lecturers)
 Quantum Information Review (Andrew Childs)
 Quantum Information (Daniel Gottesman)
 Quantum Error Correction (D. Gottesman and B. Yoshida)
 Quantum Cryptography (T. Vidick and S. Wehner)
 Quantum Machine Learning (P. Wittek, Uni of Toronto)
 Quantum Computing Fundamentals Online Program, MITxPro
 Quantum Computing Realities Online Program, MITxPro
 CS 269Q: Quantum Computer Programming(W. Zeng, Stanford, Spring 2019)
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 334872742, 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 100132473, USA 2008
 Colin P. Williams, Explorations in Quantum Computing, SpringerVerlag 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
 John Preskill, Notes on Quantum Computation, Caltech
 John. Watrous, Lecture Notes, Waterloo
 Scott Aaronson, Lecture Notes, UT Austin
 Birgitta Whaley, Lecture Notes, Berkeley
 Isaak Chuang, Lecture Notes, MIT
 Michael Locef, A Course in Quantum Computing, Foothill College
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
 Rigetti Advantage 2020
 QIP 2020, January 610, Shenzhen, China
 EPiQC 2018  Enabling PracticalScale Quantum Computing  An NSF Expedition in Computing
 Boulder School 2018: lecture notes and videos
 Quantum Information for Developers 2018
 ISCA 2018 Tutorial: Grand Challenges and Research Tools for Quantum Computing
 CROSSING Winter School on Quantum Security, 2016
 QuICS Workshop on the Frontiers of Quantum Information and Computer Science (September 28, 2015)
 Canadian Summer School on Quantum Information 2012, University of Waterloo
 QIP conferences since 1998
 Quantum Internet Proposed Research Group meeting 1, meeting 2
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.
 Rigetti PyQuil
 IBM QisKit
 Xanadu Strawberry Fields
 Google Cirq
 Microsoft Q#
 Quantum Katas: a set of programming exercises for learning Q# and quantum computing
 QuTech Quantum Inspire
 DWave Leap
Open source quantum software is an excellent github repository that contains information about quantum software projects. List of Open Quantum Projects
STAY UPTODATE
MAILING LISTS
 Get updates from ORNL Quantum Computing Institute: News and press releases, Call for papers, proposals, Conferences, workshops and standards, and Job postings by subscribing via this link
 Sign up here for Quantum Computing Report Alerts to get a notification when there are updates on the website https://quantumcomputingreport.com/
BLOGS
 Scott Aaronson: theoretical computer scientist, Computer Science at the University of Texas at Austin
 Quantum NonEquilibrium Systems at the University of Nottingham (United Kingdom)
 Quantum Computing Report
 Bits of Quantum by QuTech
 Dr James Wootton
 Quantum Frontiers by CalTech
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/PRLGeneralPhysicsStatisticalandQuantumMechanicsQuantumInformationetc.xml
PRA: Quantum information http://feeds.aps.org/rss/tocsec/PRAQuantuminformation.xml
MIT News  Quantum computing http://news.mit.edu/rss/topic/quantumcomputing
ShtetlOptimized 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://quantumjournal.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 farterm goals in quantum computing and prediction analyses of its applications in businesses in the following comprehensive roadmaps and reports:
 Quantum technologies in Russia (2019)
 National Academies of Sciences, Engineering, and Medicine. Quantum Computing: Progress and Prospects (2018)
 A. Acín et. al., “The quantum technologies roadmap: a European community view”, New J. Phys. 20 080201 (2018)
 Focus on Quantum Science and Technology Initiatives Around the World, Quantum Science and Technology
 A quantum computation roadmap by LANL
 A Quantum Cryptography Roadmap by LANL (2009)
POPULAR PRESS
 Deloite insights, The realist’s guide to quantum technology and national security, Feb 6, 2020
 J. Hilton, “Quantum’s Road To Commercialization Forbes Technology Council, Nov 19, 2019
 Boston Consulting Group’s (BCG) report Where Will Quantum Computers Create Value—and When?
 Forbes interview with deep tech investor The Investor View: What Does 2019 Hold For European Quantum Computing Startups?
 Quantum devices  The Economist
 Quantum Zeitgeist on How to invest in the Quantum Computing revolution, public companies you can invest in right now (Aug, 2019)
 Gartner  The CIO’s Guide to Quantum Computing (2019)
 J. Dongarra, 2018, “The U.S. Once Again Has the World’s Fastest Supercomputer. Keep Up the Hustle,” The Washington Post, June 25
 J. Nicas, 2017, “How Google’s Quantum Computer Could Change the World,” Wall Street Journal, October 16
 J. Asmundsson, 2017, “Quantum Computing Might Be Here Sooner than You Think,” Bloomberg, June 14
 D. Castevecchi, 2017, “Quantum computers ready to leap out of the lab in 2017”, Nature 541(7635):910
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:
 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)
 Don’t dwell. Skim or skip difficult parts and return to them later. They might make more sense after you have read subsequent sections
 Consult the bibliography. If something confuses you, one of the cited articles might explain it better or provide helpful background information
 Read the article multiple times. You’ll understand more with each pass
 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
 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
 A quantum computation roadmap by LANL
 A tutorial by Samuel Braunstein
 A review by Andrew Steane (1997)
 A review by Dorit Aharonov (2008)
 D. P. DiVincenzo, “Quantum Computation”, Science 270, 255 (1995)
 Rod van Meter’s great list of suggested papers/works on Quantum Architecture (2019 Aug)
Quantum Information
 By C. E. Shannon, “A Mathematical Theory of Communication”, The Bell System Technical Journal 27, pp. 379423, 623656 (1957)
 E. B. Davies, “Information and Quantum Measurement”, IEEE trans. on information theory, 24, 596 (1978)
 E. Knill et. al., “Introduction to Quantum Information Processing”, arXiv:quantph/0207171 (2002)
Quantum Algorithms
20 algrithms implementations on IBM’s 5qubit quantum computer, including Shor’s prime factoring, Grover’s database search, etc., can be found in
 Quantum Algorithm Implementations for Beginners arXiv: 1804.03719 (2018)
Quantum Algorithm Zoo, a comprehensive catalog of quantum algorithms
Quantum Complexity
 L.G. Valiant, “The complexity of computing the permanent”, Theoretical Computer Science 8, 189 (1979).
 C. Bennett, “Time/space tradeoffs for reversible computation”, Siam J. Comput. 18, 766 (1989)
 R. Levine, A. Sherman, “A note on Bennett’s tradeoff for reversible computation”, Siam J. Comput. 19, 673 (1990)
 A. Shamir, “IP = PSPACE”, Journal of the Association for Computing Machinery, 39, 869 (1992)
 E. Bernstein, U. Vazirani, “Quantum complexity theory”, Siam J. Comput. 26, 1411 (1997)
 J. Preskill, “Quantum Computing in the NISQ era and beyond”, arXiv:1801.00862 (2018)
 S. Aaronson, “PDQP/qpoly = ALL”, arXiv:1805.08577 (2018)
 R. Raz, A. Tal, “Oracle Separation of BQP and PH”, Electronic Colloquium on Computational Complexity, Report 107 (2018)
Quantum Simulation
 S. Lloyd “Universal quantum simulators”, Science 273, 1073 (1996)
 D. Bacon et. al., “Universal simulation of Markovian quantum dynamics”, arXiv:quantph/0008070 (2001)
 I. Kassal et. al., “Simulating Chemistry Using Quantum Computers”, Annu. Rev. Phys. Chem., 62, 185, (2011)
 I. Bloch et. al., “Quantum simulation with ultracold atomic gases” Nat. Phys. 8, 267 (2012)
 R. Blatt et. al. “Quantum simulation with trapped ions” Nat. Phys. 8, 277 (2012)
 S. Trotzky et. al., “Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas” Nat. Phys. 8, 325 (2012)
 I. Georgescu et. al., “Quantum simulation” Rev. Mod. Phys. 86, 153 (2014)
 J. Eisert et. al., “Quantum manybody systems out of equilibrium” Nat. Phys. 11, 124 (2015)
 P. J. J. O’Malley et. al., “Scalable Quantum Simulation of Molecular Energies”, Phys. Rev. X 6, 031007 (2016)
 A. M. Childs et. al., “Toward the first quantum simulation with quantum speedup” arXiv:1711.10980 (2017)
 H. Lamm, “Simulation of Nonequilibrium Dynamics on a Quantum Computer”, arXiv:1806.06649v3 (2018)
 S. McArdle et. al., “Quantum computational chemistry”, arXiv:1808.10402 (2018)
 Y. Cao et. al., “Quantum Chemistry in the Age of Quantum Computing”, arXiv:1812.09976 (2018)
Quantum Hardware (Physical Realizations)
General review
 T. D. Ladd et. al., “Quantum computers” nature 464, 45 (2010)
Ion traps
 R. Blatt et. al., “Entangled states of trapped atomic ions”, Nature 453, 1008 (2008)
 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)
 C. Monroe et. al., “Scaling the ion trap quantum processor”, Science 339, 1164 (2013)
Spin
 D Loss et. al., “Quantum computation with quantum dots” Phys. Rev A 57, 120 (1998)
 J. M. Elzerman et. al., “Singleshot readout of an individual electron spin in a quantum dot”, nature 430, 431 (2004)
 F. H. L. Koppens et. al., “Driven coherent oscillations of a single electron spin in a quantum dot”, nature 442, 766 (2006)
 R. Hanson et. al., “Spins in fewelectron quantum dots”, Rev. Mod. Phys, 79, 1217 (2007)
 M. Veldhorst et. al., “An addressable quantum dot qubit with faulttolerant controlfidelity”, nature nanotechnology, 9, 981 (2014)
 M. Veldhorst et. al., “A twoqubit logic gate in silicon”, nature 526, 410 (2015)
 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/s415340170038y
 T. F. Watson et. al., “A programmable twoqubit quantum processor in silicon”, nature 555, 633 (2018)
NVcenters
 G. Waldherr et. al. “Quantum error correction in a solidstate hybrid spin register”, nature 506, 204 (2014)
 B. Hensen et. al., “Loopholefree Bell inequality violation using electron spins separated by 1.3 kilometres”, nature, 526, 682 (2015)
 G. Tosi et. al., “Silicon quantum processor with robust longdistance qubit couplings” Nat. Commun. 8, 450 (2017)
 P.C. Humphreys et. al., “Deterministic delivery of remote entanglement on a quantum network”, nature, 558, 268 (2018)
Photonic
 E. Knill et. al., “A scheme for efficient quantum computation with linear optics”, nature, 409, 46 (2001)
 J.L. O’Brien, “Optical Quantum Computing”, Science 318, 1567 (2007)
 XingCan Yao et. al., “Experimental demonstration of topological error correction”, nature 482, 489 (2012)
 T. Meany et. al., “Engineering integrated photonics for heralded quantum gates”, Sci. Rep. 6, 25126 (2016)
 JI Yoshikawa et. al., “Generation of onemillionmode continuousvariable cluster state by unlimited timedomain multiplexing”, APL Photon. 1, 060801 (2016)
Superconducting
 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.
 U. Vool, M. Devoret, Introduction to Quantum Electromagnetic Circuits arXiv:1610.03438 (2017)
 Y. Nakamura et. al., “Coherent control of macroscopic quantum states in a singlecooperpair box”, Nature 398, 786 (1999)
 Alexandre Blais et. al., “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation ”Phys. Rev A 69, 062320 (2004)
 Jens Koch et. al., “Chargeinsensitive qubit design derived from the Cooper pair box”, Phys. Rev. A 76, 042319 (2007)
 J. A. Schreier et. al., “Suppressing charge noise decoherence in superconducting charge qubits”, Phys. Rev. B 77, 180502(R) (2008)
 Austin G. Fowler, “Surface codes: Towards practical largescale quantum computation”, Phys. Rev. A 86, 032324 (2012)
 M.H. Devoret et. al., “Superconducting circuits for quantum information: an outlook” Science 339, 1169 (2013)
 Jerry M. Chow et. al., “Implementing a strand of a scalable faulttolerant quantum computing fabric”, nature communications 5, 1 (2014)
 S. Asaad et. al., “Independent, extensible control of samefrequency superconducting qubits by selective broadcasting”, npj Quantum Information 2, 1 (2016), open access doi:10.1038/npjqi.2016.29
 T. Walter et. al., Rapid HighFidelity SingleShot Dispersive Readout of Superconducting Qubits Phys., Rev. Applied 7, 054020 (2017)
 R. Versluis et. al., “Scalable Quantum Circuit and Control for a Superconducting Surface Code”, Phys. Rev Applied 8, 034021 (2017)
Topological
 Y. Oreg et. al., “Helical Liquids and Majorana Bound States in Quantum Wires”, Phys. Rev. Lett. 105, 177002 (2010)
 V. Mourik et. al., “Signatures of Majorana Fermions in Hybrid SuperconductorSemiconductor Nanowire Devices”, Science 336, 1003 (2012)
 T. Hyart et. al., “Fluxcontrolled quantum computation with Majorana fermions”, Phys. Rev. B 88, 035121 (2013)
 S.R. Plissard, “Formation and electronic properties of InSb nanocrosses”, nature nanotechnology 8, 589 (2013)
 D. Car, “Rationally Designed SingleCrystalline Nanowire Networks”, Adv. Mater., 26, 4875 (2014)
 S. NadjPerge et. al., “Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor”, Science 346, 602 (2014)
 D. Aasen et. al., “Milestones Toward MajoranaBased Quantum Computing”, Phys. Rev. X 6, 031016 (2016)
 S. Vijay et. al., “Teleportationbased quantum information processing with Majorana zero modes”, Phys. Rev. B 94, 235446 (2016)
 S. M. Albrecht, “Exponential protection of zero modes in Majorana islands”, nature 531, 206 (2016)
 S. Gazibegovic, “Epitaxy of advanced nanowire quantum devices”, nature 548, 434 (2017)
 R.M. Lutchyn et. al., “Transport through a Majorana Island in the Strong Tunneling Regime”, Phys. Rev. Lett. 119, 057002 (2017)
 V.T. Lahtinen et. al., “A Short Introduction to Topological Quantum Computation”, arXiv:1705.04103 (2017)
 T. Karzig et. al., “Scalable designs for quasiparticle  poisoning  protected topological quantum computation with Majorana zero modes”, Phys. Rev. B 95, 235305 (2017)
 H. Zhang, “Quantized Majorana conductance” nature 556, 74 (2018)
Quantum Cryptography
 A. Boaron et. al., Secure Quantum Key Distribution over 421 km of Optical Fiber, PRL 121, 190502 (2018)
 A. Dahlberg, S. Wehner, SimulaQron  A simulator for developing quantum internet software (2018)
 A. ShenoyHejamadi et. al., Quantum Cryptography: Key Distribution and Beyond (2018)
 M. Tomamichel, A. Leverrier, A largely selfcontained and complete security proof for quantum key distribution (2017)
 C. Bennet, G. Brassard, Quantum Cryptography: Public key distribution and coin tossing, Theor. Comp. Sci. 560, 7 (2014)
 M. Berta et. al., Quantum to Classical Randomness Extractors (2012)
 S. Aaronson, Quantum CopyProtection and Quantum Money (2011)
 A Quantum Cryptography Roadmap by LANL (2009)
 R. Renner, Security of Quantum Key Distribution, PhD Thesis
 A. Childs, Secure Assisted Quantum Computation (2005)
 P. Shor, J. Preskill, Simple Proof of Security of the BB84 Quantum Key Distribution Protocol (2000)
 D. Mayers, Quantum Key Distribution and String Oblivious Transfer in Noisy Channels (1996)
 C. Bennett, Quantum Cryptography Using Any Two Nonorthogonal States, PRL 68, 3121 (1992)
 A. Ekert, Quantum Cryptography Based on Bell’s Theorem, PRL, 67, 661 (1991)
 C. Bennet, G. Brassard, JM. Robert, Privacy Amplification by Public Discussion, Siam J. Comput. 17, 210 (1988)
Quantum Error Correction
 S. J. Devitt, “Quantum Error Correction for Beginners”, arXiv:0905.2794 (2013)
 E. Knill et. al., “Introduction to Quantum Error Correction”, arxiv:quantph/0207170 (2008)
 D. Gottesman, “Stabilizer Codes and Quantum Error Correction” (Thesis) arXiv:quantph/9705052 (1997)
 Group theoretic approach
 A. R. Calderbank et. al., “Quantum Error Correction and Orthogonal Geometry”, Phys. Rev. Lett. 78, 405 (1997)
 A. R. Calderbank et. al.,, “Quantum Error Correction Via Codes Over GF (4)”, arXiv:quantph/9608006 (1997)
 Fault tolerance
 P.W Shor, “Faulttolerant quantum computation”, arXiv:quantph/9605011 (1996)
 J. Preskill, “Faulttolerant quantum computation” arXiv:quantph/9712048 (1997)
 A.R. Calderbank and P.W. Shor, “Good quantum errorcorrecting codes exist”, Phys. Rev. A 54, 1098 (1996)
Quantum Machine Learning
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 GottesmanKnill Theorem
 Canonical Decompositions of Quantum Circuits
 Fault Tolerant Quantum Computation with 5qubit and CWS Codes
 Magic States for Universal Quantum Computing
 Classical Circuits and the Ck Family
 Threshold for FaultTolerant Quantum Computation
 Blind Quantum Computation
 New Quantum Algorithms for Hard Problems
 Quantum Algorithm on Graphs
 Shur: Beyond the Quantum Fourier Transform
 PostQuantum Cryptography
 Entropies of Various Quantum Sources
 Quantum BitCommitment
 Optimal TwoQubit Gates
 Quantum Channel Capacities