Divide-and-Conquer Simulation of Open Quantum Systems

TL;DR

This paper introduces a divide-and-conquer quantum simulation method for open quantum systems that reduces circuit depth and resource requirements, enabling more practical simulations on current quantum hardware.

Contribution

It proposes a novel divide-and-conquer strategy for preparing mixed states that combines Kraus operator dilations, improving simulation efficiency for open quantum systems.

Findings

Reduces circuit depth compared to traditional methods

Enables simulation of open quantum systems on NISQ devices

Demonstrates proof-of-concept with Fenna-Matthews-Olson model

Abstract

One of the promises of quantum computing is to simulate physical systems efficiently. However, the simulation of open quantum systems - where interactions with the environment play a crucial role - remains challenging for quantum computing, as it is impossible to implement deterministically non-unitary operators on a quantum computer without auxiliary qubits. The Stinespring dilation can simulate an open dynamic but requires a high circuit depth, which is impractical for NISQ devices. An alternative approach is parallel probabilistic block-encoding methods, such as the Sz.-Nagy and Singular Value Decomposition dilations. These methods result in shallower circuits but are hybrid methods, and we do not simulate the quantum dynamic on the quantum computer. In this work, we describe a divide-and-conquer strategy for preparing mixed states to combine the output of each Kraus operator dilation and obtain the complete dynamic on quantum hardware with a lower circuit depth. The work also introduces a balanced strategy that groups the original Kraus operators into an expanded operator, leading to a trade-off between circuit depth, CNOT count, and number of qubits. We perform a computational analysis to demonstrate the advantages of the new method and present a proof-of-concept simulation of the Fenna-Matthews-Olson dynamic on current quantum hardware.