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

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.