Resources, Readings, and References

Textbooks

The primary textbook for the course is [Nielsen and Chuang, 2010]. This is a thorough but quite accessible textbook with many reference and has served as the standard reference in the field.

More accessible is Quantum computing for the very curious, [Matuschak and Nielsen, 2019] which includes a set of review questions delivered over an extended time to help you remember the concepts (they call it a “new mnemonic medium”). The direct technical goal of this course is for you to understand in detail everything discussed in this and the related articles.

Linear Algebra

• Essence of linear algebra: A great set of highly visual videos by 3Blue1Brown getting you up to abstract vector spaces.

• MIT 18.06 Linear Algebra: A set of video lectures and accompanying material for the MIT Linear Algebra course.

• Qiskit Linear Algebra: A short introduction that is part of the Qiskit platform.

• Appendix A of [Mermin, 2007] has a nice short review of Dirac notation.

Additional Quantum Computing and Information Resources

• (John Preskill) Quantum Computing and the Entanglement Frontier: Fairly recent lecture (Feb 2022) giving a good overview of the state of the field. By the end of the course you should be able to understand the details of this talk. (For example, where the 85.4% comes from as was asked at the end of the talk.)

• Qiskit Textbook: This is the textbook put out by IBM for learning how to use their Qiskit software development kit (SDK). It has a pretty good introduction, and if you want to move forward with quantum computing, then it is worth having a look at Qiskit as it is one of the main platforms available for performing quantum computations on real platforms.

• Introduction to Classical and Quantum Computing (Tom Wong): [Wong, 2022] provides a very accessible introduction to the field without any assumed prerequisites beyond trigonometry.

For example, Mermin is adamant about calling qubits “Qbits” in analogy to “Cbits”.

• Quantum Computer Science: An Introduction: [Mermin, 2007] has an opinionated account of quantum computer science which provides an alternative and useful prespective. In general, I recommend this as an alternate presentation for you to gain another perspective and secure your knowledge, but there are a few useful sections to read thoroughly, especially appendices A, B, and C.

• Geometry of Quantum States: An Introduction to Quantum Entanglement: [Bengtsson and Życzkowski, 2017] has a mathematically sophisticated description of the geometry of quantum mechanics and entanglement. The mathematics in this book does obscure some of the physics, but I think that it has the potential to provide some good insight.

General Articles

The following are good general (not technical) articles that help place quantum computing and its potential capabilities in context:

• Das Sarma:2022 Quantum computing has a hype problem.

Technologies

• Discussion about Majorana Modes between Sankar Das Sarma and Chetan Nayak. If you are interested in this technology, be sure to consider Sergey Frolov’s work which found issues with some of the reported technical claims at having identified Majorana modes. (Sergey gave a thought-provoking colloquium here at WSU Fall 2022.)

Quantum Computing Simulators

These are platforms that allow you to program and simulate running your programs as if the were running on a quantum computer. Ultimately the work you do year should be able to be run on real quantum hardware when it is available. If you are interested in employment in the field of quantum computing, then it is probably important to have some experience with one of these platforms. Certification might help in some cases (but is expensive and time-consuming).

• Qiskit: IBM’s platform. If you don’t have a reason to prefer one of the other platforms, this is probably the best place to start.

  One of the exercises in this course will be to work through the Qiskit field guide:

  • Learn quantum computing: a field guide

Interactive Demonstrations

Here are some interactive demonstrations (some quantum):

• https://www.falstad.com/mathphysics.html

  • https://www.falstad.com/ripple/

  • https://www.falstad.com/qm1d/

• https://acephysics.net/: Nice interactive approach to learning about spin measurements, but rather annoying interface for simple exploring. I suggest you work through this once after you think you understand spins and measurement.

Classical Mechanics

If your physics background is a little rusty and you want to play with some classical mechanics simulations to build intuition, these are fun:

• https://www.myphysicslab.com/

• https://www.falstad.com/mathphysics.html: Has some great simulations. The Ripple Tank is very impressive. (Look at the low-pass filter for example.)

Research

Here are some random references that might be of interest to various research projects:

• How many quantum gates do gauge theories require?: An accounting of how many gates would be required to solve lattice gauge theories like QCD. Unfortunately, the number is quite high.

References

Bar13

Edwin Barnes. Analytically solvable two-level quantum systems and Landau-Zener interferometry. Phys. Rev. A, July 2013. doi:10.1103/physreva.88.013818.

BZyczkowski17

Ingemar Bengtsson and Karol Życzkowski. Geometry of Quantum States: An Introduction to Quantum Entanglement. Cambridge University Press, August 2017. ISBN 978-1-108-29469-0. URL: https://doi.org/10.1017%2F9781139207010, doi:10.1017/9781139207010.

CT06

Thomas M. Cover and Joy A. Thomas. Elements of Information Theory. Wiley-Interscience, 2006. ISBN 9780471748823. doi:10.1002/047174882X.

DRST02

Duane A. Dicus, Wayne W. Repko, Roy F. Schwitters, and Todd M. Tinsley. Time development of a quasistationary state. Phys. Rev. A, 65:032116, February 2002. URL: https://link.aps.org/doi/10.1103/PhysRevA.65.032116, doi:10.1103/PhysRevA.65.032116.

Gez20

Alex Gezerlis. Numerical Methods in Physics with Python. Cambridge University Press, 2020. doi:10.1017/9781108772310.

Gol91

David Goldberg. What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys, 1991. doi:0360-0300/91/0300-0005.

GKP94

Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley, 2 edition, 1994. ISBN 978-0-201-55802-9.

Jaf10

Robert L.. Jaffe. Reflection above the barrier as tunneling in momentum space. Amer. J. Phys., 78(6):620–623, June 2010. doi:10.1119/1.3298428.

Jog09

Yogesh N. Joglekar. Particle in a box with a δ-function potential: Strong and weak coupling limits. Amer. J. Phys., 77(8):734–736, August 2009. URL: https://doi.org/10.1119%2F1.3119178, doi:10.1119/1.3119178.

Kli06

Israel Klich. Lower entropy bounds and particle number fluctuations in a fermi sea. J. Phys. A, 39(4):L85–L91, January 2006. URL: https://doi.org/10.1088%2F0305-4470%2F39%2F4%2Fl02, doi:10.1088/0305-4470/39/4/l02.

MN19

Andy Matuschak and Michael A. Nielsen. Quantum computing for the very curious”. https://quantum.country/qcvc, 2019. URL: https://quantum.country/qcvc.

Mer07(1,2)

N. D. Mermin. Quantum Computer Science: An Introduction. Cambridge University Press, 2007. ISBN 978-0-511-33982-0. URL: https://www.cambridge.org/core/books/quantum-computer-science/66462590D10C8010017CF1D7C45708D7, doi:10.1017/CBO9780511813870.

ML03

Cleve Moler and Charles Van Loan. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45(1):3–49, 2003. URL: http://dx.doi.org/10.1137/S00361445024180, doi:10.1137/S00361445024180.

NC10

Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010. URL: https://doi.org/10.1017%2Fcbo9780511976667, doi:10.1017/cbo9780511976667.

OB05

Ognyan Oreshkov and Todd A. Brun. Weak measurements are universal. Phys. Rev. Lett., September 2005. URL: https://doi.org/10.1103%2Fphysrevlett.95.110409, doi:10.1103/physrevlett.95.110409.

PVZ14

Murray Peshkin, Alexander Volya, and Vladimir Zelevinsky. Non-exponential and oscillatory decays in quantum mechanics. Europhys. Lett., 107(4):40001, August 2014. URL: https://doi.org/10.1209%2F0295-5075%2F107%2F40001, doi:10.1209/0295-5075/107/40001.

WG92

James S. Walker and J. Gathright. A transfer-matrix approach to one-dimensional quantum mechanics using mathematica. Computers in Physics, 6(4):393, 1992. URL: https://doi.org/10.1063%2F1.168430, doi:10.1063/1.168430.

Wil11

Colin P. Williams. Explorations in Quantum Computing. Texts in Computer Science. Springer, London, 2 edition, 2011. ISBN 978-1-84628-887-6. doi:10.1007/978-1-84628-887-6.

Won22

Thomas Wong. Introduction to Classical and Quantum Computing. Rooted Grove, Omaha, Nebraska, 2022. ISBN 979-8-9855931-0-5. URL: https://www.thomaswong.net.