Kraus decomposition for chaotic environments including time-dependent subsystem Hamiltonians

TL;DR

This paper derives an exact Kraus decomposition for a quantum system interacting with a chaotic environment and time-dependent Hamiltonians, validated against numerical simulations of a quantum gate.

Contribution

It introduces a new exact Kraus decomposition applicable to systems with time-dependent Hamiltonians and chaotic environments, validated by numerical experiments.

Findings

Kraus decomposition matches numerical results closely

Effective for small environment sizes

Applicable to quantum computing scenarios

Abstract

We derive an exact and explicit Kraus decomposition for the reduced density of a quantum system simultaneously interacting with time-dependent external fields and a chaotic environment of thermodynamic dimension. We test the accuracy of the Kraus decomposition against exact numerical results for a CNOT gate performed on two qubits of an $(N+2)$-qubit statically flawed isolated quantum computer. Here the $N$ idle qubits comprise the finite environment. We obtain very good agreement even for small $N$.