Quantum recovery protocols for stabilizer codes: Deterministic Monte-Carlo simulation

Abstract

The quantum noise encumbrance caused by quantum error-correcting protocols is studied via numerical treatments. Noise evolution implies that the noise magnitude order may change dynamically during quantum computations. The rate of noise level deterioration is a function of the computer’s architecture and physical implementation. Various stabilizer codes with small blocks are studied under dynamic noise regimes, which change the noise magnitude order within a specified time period. The Monte-Carlo sampling simulation method is used to determine the survival probabilities for these codes under evolving error rates. A hypothetical q-step quantum algorithm is stabilized by the repeated application of the recovery protocol, and the proposed estimation method is applied. The estimation method is applied concurrently with the execution of the algorithm. The recovery process is simulated with the aid of a software tool that can be parameterized based on the noise model and the encoding error-correction scheme. Examples show the utility of this tool for quantum coding studies.