Simulation of single-qubit open quantum systems

TL;DR

This paper introduces a quantum algorithm for efficiently simulating the dynamics of single-qubit open quantum systems governed by Markovian processes, requiring minimal resources and leveraging recent channel approximation techniques.

Contribution

It presents a novel quantum simulation algorithm for arbitrary single-qubit Markovian dynamics with minimal ancilla qubits and resource-efficient gate complexity.

Findings

Requires only ((||\u2113||_{(1; 1)} t)^{3/2}/) gates

Uses a decomposition technique inspired by Hamiltonian simulation

Requires only a single ancilla qubit for channel approximation

Abstract

A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single qubit quantum channels $\{T_t\}$ specified by a generator $\mathcal{L}$. This algorithm requires only $\mathcal{O}\big((||\mathcal{L}||_{(1\rightarrow 1)} t)^{3/2}/\epsilon^{1/2} \big)$ single qubit and CNOT gates and approximates the channel $T_t = e^{t\mathcal{L}}$ up to chosen accuracy $\epsilon$. Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilised which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a non-unitary single-qubit quantum channel.