Universal fidelity reduction of quantum operations from weak dissipation

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 and interestingly this reduction is independent of the specific gate and depends only on the operation time and the dissipation. Using this 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.