Quantum algorithm for simulating the dynamics of an open quantum system

TL;DR

This paper introduces a quantum algorithm that efficiently simulates the dynamics of open quantum systems, including both Markovian and certain non-Markovian cases, using ancilla qubits to represent the environment.

Contribution

It presents a novel quantum algorithm for simulating open quantum system dynamics directly on a quantum computer, reducing classical computational complexity.

Findings

Single ancilla qubit can represent the environment for slow decoherence.

Parameters for simulation derived from system+environment Hamiltonian.

Algorithm applicable to Markovian and some non-Markovian dynamics.

Abstract

In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment and their interaction: one basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system+environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.