The following references provide background on quantum noise, random circuits, and entanglement dynamics. The presented notes are inspired by these research directions but focus on a simplified, empirical description of noise sensitivity based on effective scaling variables. I found them all interesting and hope you will too.
H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control. Cambridge, U.K.: Cambridge Univ. Press, 2009
K. Jacobs and D. A. Steck, “A straightforward introduction to continuous quantum measurement,” Contemporary Physics, vol. 47, no. 5, pp. 279–303, 2006.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge, U.K.: Cambridge Univ. Press, 2000.
J. Preskill, “Quantum computing in the NISQ era and beyond,” Quantum, vol. 2, p. 79, 2018.
L. Willsch et al., “Benchmarking the QASMBench quantum circuits,” arXiv:2005.11227, 2020.
A. M. Dalzell, J. R. Garrison, Z. Kim, and J. Klassen, “Random quantum circuits transform local noise into global white noise,” arXiv:2111.14907, 2021.
A. M. Dalzell et al., “How noise transforms quantum circuits,” Communications in Mathematical Physics, 2024.
Y. Takahashi, S. Tani, and K. Sato, “Simulating quantum circuits with noise,” Theoretical Computer Science, vol. 876, pp. 1–18, 2021.
S. Bravyi, D. Gosset, and R. König, “Quantum advantage with shallow circuits,” Science, vol. 362, no. 6412, pp. 308–311, 2018.
D. N. Page, “Average entropy of a subsystem,” Physical Review Letters, vol. 71, no. 9, pp. 1291–1294, 1993.
A. W. Harrow and R. A. Low, “Random quantum circuits are approximate 2-designs,” Communications in Mathematical Physics, vol. 291, pp. 257–302, 2009.
A. W. Cross, G. Smith, and J. A. Smolin, “Quantum circuits for strongly mixing states,” Physical Review A, vol. 89, 2014.
Y. Zhang, B. Skinner, and A. Nahum, “Universal entanglement dynamics in noisy quantum circuits,” arXiv:2205.13999, 2022.
P. Hayden, D. Leung, and A. Winter, “Aspects of generic entanglement,” Communications in Mathematical Physics, vol. 265, pp. 95–117, 2006.
M. Urbanek et al., “Mitigating depolarizing noise on quantum computers,” arXiv:2103.08591, 2021.
K. Temme, S. Bravyi, and J. M. Gambetta, “Error mitigation for short-depth quantum circuits,” Physical Review Letters, vol. 119, p. 180509, 2017.
S. Endo, S. C. Benjamin, and Y. Li, “Practical quantum error mitigation for near-future applications,” Physical Review X, vol. 8, p. 031027, 2018.
A. Kandala et al., “Error mitigation extends the computational reach of a noisy quantum processor,” Nature, vol. 567, pp. 491–495, 2019.
A. Bouland, B. Fefferman, C. Nirkhe, and U. Vazirani, “On the complexity and verification of quantum random circuit sampling,” Nature Physics, vol. 15, pp. 159–163, 2019.
B. Fefferman and R. Umans, “The power of quantum Fourier sampling,” SIAM Journal on Computing, vol. 45, no. 2, pp. 551–575, 2016.
A. Nahum, J. Ruhman, S. Vijay, and J. Haah, “Quantum entanglement growth under random unitary dynamics,” Physical Review X, vol. 7, 2017.
B. Fefferman et al., “The effect of noise on quantum circuits,” PRX Quantum, vol. 5, 2024.