Chapter 40 Further Reading: Capstone — Quantum Computing: From Qubits to Algorithms

Tier 1: Essential References

Nielsen, M. A. & Chuang, I. L. — Quantum Computation and Quantum Information, 10th Anniversary ed. (2010)

The bible of quantum information science. Chapters 1-4 cover qubits, gates, and circuits. Chapters 5-6 cover Shor's and Grover's algorithms. Chapter 7 covers quantum simulation. Chapters 10-12 cover error correction and fault tolerance. Every serious student of quantum computing should own this book. - Best for: Comprehensive, rigorous treatment of all topics in this chapter.

Preskill, J. — "Quantum Computing in the NISQ Era and Beyond" (2018)

Quantum 2, 79. John Preskill's influential paper that introduced the term "NISQ" (Noisy Intermediate-Scale Quantum) and laid out the landscape of near-term quantum computing. Essential context for understanding where the field stands. - Best for: Placing current quantum computing in historical and technological context.

Mermin, N. D. — Quantum Computer Science: An Introduction (2007)

A quantum computing textbook written by a physicist for physicists. Mermin's trademark clarity and wit make this the most accessible graduate-level introduction. Covers circuits, algorithms (Deutsch-Jozsa, Grover, Shor), and error correction. - Best for: Physicists who want to understand quantum computing without wading through computer science formalism.

Kaye, P., Laflamme, R. & Mosca, M. — An Introduction to Quantum Computing (2007)

A clear, concise textbook covering the standard topics (circuits, algorithms, error correction) with many worked examples. More accessible than Nielsen & Chuang, with a good balance of rigor and intuition. - Best for: Upper-level undergraduates or beginning graduate students.

Tier 2: Supplementary and Enrichment

Algorithms

Shor, P. W. — "Algorithms for quantum computation: discrete logarithms and factoring" (1994) Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 124-134. The paper that launched quantum computing as a serious field. Shor's algorithm is presented clearly, though the notation is somewhat dated.

Grover, L. K. — "A fast quantum mechanical algorithm for database search" (1996) Proceedings of the 28th Annual ACM Symposium on Theory of Computing, 212-219. The original Grover's algorithm paper. Short and elegant.

Montanaro, A. — "Quantum algorithms: an overview" (2016) npj Quantum Information 2, 15023. An excellent survey of known quantum algorithms and their applications, organized by speedup type (exponential, polynomial, constant). Good for understanding the algorithmic landscape beyond Shor and Grover.

Error Correction and Fault Tolerance

Gottesman, D. — "An introduction to quantum error correction and fault-tolerant quantum computation" (2010) Proceedings of Symposia in Applied Mathematics 68, 13-58. A clear introduction by one of the founders of the field. Covers stabilizer codes, the Steane and Shor codes, and the threshold theorem. Available on arXiv: 0904.2557.

Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. — "Surface codes: Towards practical large-scale quantum computation" (2012) Physical Review A 86, 032324. The definitive reference for the surface code — the leading error correction approach for superconducting qubits.

Terhal, B. M. — "Quantum error correction for quantum memories" (2015) Reviews of Modern Physics 87, 307-346. A comprehensive review of quantum error correction, from basic codes through the threshold theorem to topological codes.

Hardware

Krantz, P. et al. — "A quantum engineer's guide to superconducting qubits" (2019) Applied Physics Reviews 6, 021318. A thorough tutorial on superconducting qubit physics and engineering, written for experimentalists.

Bruzewicz, C. D. et al. — "Trapped-ion quantum computing: Progress and challenges" (2019) Applied Physics Reviews 6, 021314. The trapped-ion equivalent of the Krantz review.

Slussarenko, S. & Pryde, G. J. — "Photonic quantum information processing: A concise review" (2019) Applied Physics Reviews 6, 041303. A review of photonic approaches to quantum computing.

Quantum Advantage

Arute, F. et al. (Google AI Quantum) — "Quantum supremacy using a programmable superconducting processor" (2019) Nature 574, 505-510. Google's claim of quantum advantage with the Sycamore processor.

Kim, Y. et al. (IBM) — "Evidence for the utility of quantum computing before fault tolerance" (2023) Nature 618, 500-505. IBM's demonstration of quantum utility for condensed matter physics.

Aaronson, S. — Quantum Computing Since Democritus (2013) Based on a lecture course at the University of Waterloo. Aaronson's irreverent style makes computational complexity theory accessible and entertaining. Chapters 9-10 on quantum computing are outstanding. - Best for: Students who enjoy thinking about the deep connections between physics, mathematics, and computation.

Bernhardt, C. — Quantum Computing for Everyone (2019) An accessible introduction that assumes no background in physics or computer science. Good for building intuition before tackling the technical material.

Hidary, J. D. — Quantum Computing: An Applied Approach, 2nd ed. (2021) A practical, code-oriented introduction with Python examples using Qiskit and Cirq. Good companion to the theoretical treatment in this chapter. - Best for: Students who want to run quantum algorithms on real hardware immediately.

Tier 3: Original Papers

  • Feynman, R. P. (1982). "Simulating physics with computers." International Journal of Theoretical Physics 21, 467-488.
  • Deutsch, D. (1985). "Quantum theory, the Church-Turing principle and the universal quantum computer." Proceedings of the Royal Society A 400, 97-117.
  • Shor, P. W. (1994). "Algorithms for quantum computation: discrete logarithms and factoring." Proc. 35th FOCS, 124-134.
  • Grover, L. K. (1996). "A fast quantum mechanical algorithm for database search." Proc. 28th STOC, 212-219.
  • Shor, P. W. (1995). "Scheme for reducing decoherence in quantum computer memory." Physical Review A 52, R2493.
  • Steane, A. M. (1996). "Error correcting codes in quantum theory." Physical Review Letters 77, 793-797.
  • Kitaev, A. Y. (2003). "Fault-tolerant quantum computation by anyons." Annals of Physics 303, 2-30.
  • DiVincenzo, D. P. (2000). "The physical implementation of quantum computation." Fortschritte der Physik 48, 771-783.
  • Koch, J. et al. (2007). "Charge-insensitive qubit design derived from the Cooper pair box." Physical Review A 76, 042319. (The transmon paper.)
  • Cirac, J. I. & Zoller, P. (1995). "Quantum computations with cold trapped ions." Physical Review Letters 74, 4091-4094.

Reading Strategy

  1. Everyone: Read Preskill's "NISQ" paper for context, then Mermin's book chapters 1-3 for the clearest introduction to quantum circuits and algorithms.
  2. For algorithms: Read Shor's and Grover's original papers, then Montanaro's survey for the broader landscape.
  3. For error correction: Read Gottesman's introduction, then Fowler et al. for the surface code.
  4. For hardware: Read the Krantz (superconducting) or Bruzewicz (trapped ion) review, depending on your interest.
  5. For the philosophical perspective: Read Aaronson's book, especially the chapters on quantum computing and complexity theory.
  6. For hands-on experience: Work through Hidary's book with Qiskit, running circuits on real IBM hardware via the cloud.