Kraus map closed-form solution for general master equation dynamics

TL;DR

This paper presents a closed-form Kraus map solution for general quantum master equations, enabling precise modeling of quantum dynamics under strong driving without approximations, which is crucial for quantum computing applications.

Contribution

It introduces a novel, exact Kraus map formulation for arbitrary strong driving in quantum master equations, overcoming previous limitations of approximate or non-closed-form solutions.

Findings

The Kraus solution converges rapidly with Riemann sums.

Numerical demonstrations show high-precision modeling of quantum dynamics.

Applicable to large rotation gates with complex noise mechanisms.

Abstract

The Kraus representation of quantum channels allows for a precise emulation of the complex dynamics that take place on quantum processors, whether for benchmarking algorithms, predicting the performance of error correction and mitigation, or in the myriad other uses of compiled digital sequences. Nonetheless, starting from first principles to obtain continuous quantum master equations involves various approximations such as weak coupling to the environment. Further, converting these equations to Kraus operators cannot generally be obtained in closed-form due to the complicated commutator structure of the problem. In our work, we bridge this gap by providing a general closed form formulation for arbitrarily strong driving while remaining linear in the dissipator. The Kraus solution is expressed as a Riemann sum where higher terms can converge quickly to high precision, which we demonstrate numerically. Such a formulation is highly relevant to quantum computing and gate-based models, where effective models are highly sought for large rotation gate angles, even under the influence of underlying non-trivial noise mechanisms.