Abstract
Quantum information processing is fundamentally constrained by measurement backaction and environmental noise. This work develops a unified quantitative study of quantum state degradation and reconstruction across two complementary dynamical regimes: continuous weak measurement described by stochastic master equations (SME), and discrete gate-based quantum circuits subject to depolarizing and readout noise.
In the continuous regime, we demonstrate stable exponential convergence of a stochastic quantum filter toward the true conditional state under finite detection efficiency. In the circuit regime, we analyze a bounded subset of QASMBench OpenQASM circuits under a structured noise sweep and measure output distributional divergence using Total Variation Distance (TVD). We identify an empirical exponential saturation law and show that degradation collapses onto a compact effective interaction variable.
Keywords: quantum state reconstruction, stochastic master equation, continuous weak measurement, quantum circuit noise, total variation distance, exponential scaling law