Commutation simulator for open quantum dynamics

TL;DR

This paper introduces a novel quantum simulation method using commutation simulators to analyze time-dependent quantum states, enabling direct computation of their properties and dynamics with potential applications in quantum eigenvalue problems and decoherence studies.

Contribution

It presents a new approach employing generalized quantum commutation simulators to directly evaluate properties of quantum states and their evolution, including applications to the von Neumann and Lindblad equations.

Findings

Demonstrated the method on a single-qubit system

Proposed extension to multi-qubit systems

Potential for practical quantum simulation applications

Abstract

Recent progress in quantum simulation and algorithms has demonstrated a rapid expansion in capabilities. The search continues for new techniques and applications to exploit quantum advantage. Here we propose an innovative method to investigate directly the properties of a time-dependent density operator $\hat{\rho}(t)$. Using generalised quantum commutation simulators, we can directly compute the expectation value of the commutation relation and thus of the rate of change of $\hat{\rho}(t)$. The approach can be utilised as a quantum eigen-vector solver for the von Neumann equation and a decoherence investigator for the Lindblad equation, by using just the statistics of single-qubit measurements. A simple but important example is demonstrated in the single-qubit case and we discuss extension of the method for practical quantum simulation with many qubits, towards investigation of more realistic quantum systems.