Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators

TL;DR

This paper introduces a universal quantum algorithm that decomposes non-unitary operators into a linear combination of four unitaries, enabling the simulation of open quantum systems on quantum computers.

Contribution

The authors present a novel method to implement any non-unitary operator as a combination of four unitaries, facilitating open system simulations on quantum devices.

Findings

Exact decomposition of non-unitary operators into four unitaries.

Successful simulation of amplitude damping channels.

Agreement with classical calculations confirms method validity.

Abstract

Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a non-unitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here we present a general algorithm for implementing the action of any non-unitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating non-unitary operations on intermediate-term and future quantum devices.