Numerical and analytical research of the impact of decoherence on quantum circuits

TL;DR

This paper investigates how decoherence affects quantum circuits using vector, density matrix, and Choi-Jamiolkowski models, providing implementation details and analytical estimates of fidelity loss.

Contribution

It introduces a fixed rank approximation technique for density matrix modeling and compares different noisy quantum scheme models.

Findings

Implementation methods for noisy quantum schemes on computers and supercomputers.

Analytical estimates of fidelity degradation due to decoherence.

Validation of the fixed rank approximation technique.

Abstract

Three different levels of noisy quantum schemes modeling are considered: vectors, density matrices and Choi-Jamiolkowski related states. The implementations for personal computers and supercomputers are described, and the corresponding results are shown. For the level of density matrices, we present the technique of the fixed rank approximation and show some analytical estimates of the fidelity level.