Analysis of Reversibility and Critical Depth in Quantum Computers  under Noise via Circuit Simulation

Sittinon Chotirotpon

doi:10.65205/jcct.2026.e3448

Authors

Sittinon Chotirotpon Science and Technology Program, Thaksin University Demonstration Secondary School, Phatthalung Province, 93210, Thailand https://orcid.org/0009-0000-1267-3294

DOI:

https://doi.org/10.65205/jcct.2026.e3448

Keywords:

Quantum Computing, Circuit Simulation, Loschmidt Echo, Noise, Critical Depth

Abstract

This research aims to: 1) simulate the time-reversibility behavior in chaotic quantum systems (Ising model), 2) analyze the quantitative relationship between noise levels (ε) and system sizes (N), and 3) propose the critical depth criterion for evaluating the preliminary limits of quantum computers. The research methodology involves simulating the behavior of quantum systems via circuit simulation using Qiskit to evaluate the return probability under depolarizing error ranging from 0-2%. The results indicate that noise causes a rapid decay in the system's reversibility. Larger systems (N = 6) demonstrate approximately 45% higher sensitivity to noise than smaller systems (N = 4), based on the relative reduction of the critical depth, which decreases from 15 steps to 11 steps at a 1% noise level. Based on these findings, this study proposes critical depth as a simulation-based index for evaluating noise-induced limitations in NISQ-era quantum computers.

Downloads

Download data is not yet available.

References

Aleksandrowicz, G., Alexander, T., Barkoutsos, P., Bello, L., Ben-Haim, Y., Bucher, D., Cabrera-Hernández, F. J., Carballo-Franquis, J., Chen, A., Chen, C.-F., Chow, J. M., Córcoles-Gonzales, A. D., Cross, A. J., Cross, A., Cruz-Benito, J., Culver, C., De La Puente González, S., De La Torre, E., Ding, D., … Zoufal, C. (2019). Qiskit: An Open-source Framework for Quantum Computing [Computer Software]. Zenodo. https://doi.org/10.5281/ZENODO.2562111

Anand, A., Srivastava, S., Gangopadhyay, S., & Ghose, S. (2024). Simulating Quantum Chaos on a Quantum Computer. Scientific Reports, 14, 26890. https://doi.org/10.1038/s41598-024-76448-0 DOI: https://doi.org/10.1038/s41598-024-76448-0

Goussev, A., Jalabert, R. A., Pastawski, H. M., & Wisniacki, D. A. (2012). Loschmidt Echo. Scholarpedia, 7(8), 11687. https://doi.org/10.4249/scholarpedia.11687 DOI: https://doi.org/10.4249/scholarpedia.11687

Jurcevic, P., Javadi-Abhari, A., Bishop, L. S., Lauer, I., Bogorin, D. F., Brink, M., Capelluto, L., Günlük, O., Itoko, T., Kanazawa, N., Kandala, A., Keefe, G. A., Krsulich, K., Landers, W., Lewandowski, E. P., McClure, D. T., Nannicini, G., Narasgond, A., Nayfeh, H. M., … Gambetta, J. M. (2021). Demonstration of Quantum Volume 64 on a Superconducting Quantum Computing System. Quantum Science and Technology, 6(2), 025020. https://doi.org/10.1088/2058-9565/abe519 DOI: https://doi.org/10.1088/2058-9565/abe519

Kim, Y., Eddins, A., Anand, S., Wei, K. X., van den Berg, E., Rosenblatt, S., Nayfeh, H., Wu, Y., Zaletel, M., Temme, K., & Kandala, A. (2023). Evidence for the Utility of Quantum Computing Before Fault Tolerance. Nature, 618(7965), 500-505. https://doi.org/10.1038/s41586-023-06096-3 DOI: https://doi.org/10.1038/s41586-023-06096-3

Lesovik, G. B., Sadovskyy, I. A., Suslov, M. V., Lebedev, A. V., & Vinokur, V. M. (2019). Arrow of Time and Its Reversal on the IBM Quantum Computer. Scientific Reports, 9(1), 4396. https://doi.org/10.1038/s41598-019-40765-6 DOI: https://doi.org/10.1038/s41598-019-40765-6

Peres, A. (1984). Stability of Quantum Motion in Chaotic and Regular Systems. Physical Review A, 30(4), 1610-1615. https://doi.org/10.1103/PhysRevA.30.1610 DOI: https://doi.org/10.1103/PhysRevA.30.1610

Preskill, J. (2018). Quantum Computing in the NISQ Era and Beyond. Quantum, 2, 79. https://doi.org/10.22331/q-2018-08-06-79 DOI: https://doi.org/10.22331/q-2018-08-06-79