Universal fidelity reduction of quantum operations from weak dissipation

TL;DR

This paper derives a universal formula for how weak dissipation reduces the fidelity of quantum operations, showing the reduction depends only on operation time and dissipation, regardless of the specific operation.

Contribution

It provides a simple, operation-independent formula for fidelity reduction due to weak dissipation in quantum systems, and analyzes the impact of correlated dissipation on quantum error correction.

Findings

Fidelity reduction depends only on operation time and dissipation strength.

Correlated dissipation can have similar effects as uncorrelated dissipation.

The formula applies universally to any quantum operation under weak dissipation.

Abstract

Quantum information processing is in real systems often limited by dissipation, stemming from remaining uncontrolled interaction with microscopic degrees of freedom. Given recent experimental progress, we consider weak dissipation, resulting in a small error probability per operation. Here, we find a simple formula for the fidelity reduction of any desired quantum operation. Interestingly, this reduction is independent of the specific operation; it depends only on the operation time and the dissipation. Using our formula, we investigate the situation where dissipation in different parts of the system have correlations, which is detrimental for the successful application of quantum error correction. Surprisingly, we find that a large class of correlations gives the same fidelity reduction as uncorrelated dissipation of similar strength.