Simulating quantum circuits using the multi-scale entanglement renormalization ansatz

TL;DR

This paper introduces a scalable method using the multi-scale entanglement renormalization ansatz (MERA) and Riemannian optimization to approximate and simulate intermediate-size quantum circuits, advancing classical simulation capabilities.

Contribution

The authors develop a novel scalable technique combining MERA tensor networks and Riemannian optimization for simulating complex quantum circuits beyond traditional methods.

Findings

Successfully simulated quantum circuits with up to 243 qubits

Achieved efficient approximation for circuits with up to 20 layers

Demonstrated the potential of MERA-based methods for quantum many-body systems

Abstract

Understanding the limiting capabilities of classical methods in simulating complex quantum systems is of paramount importance for quantum technologies. Although many advanced approaches have been proposed and recently used to challenge quantum advantage experiments, novel efficient methods for the approximate simulation of complex quantum systems are still in high demand. Here we propose a scalable technique for approximate simulations of intermediate-size quantum circuits on the basis of the multi-scale entanglement renormalization ansatz (MERA) and Riemannian optimization. The MERA is a tensor network, whose geometry together with orthogonality constraints imposed on its tensors allow approximating many-body quantum states lying beyond the area-law scaling of the entanglement entropy. We benchmark the proposed technique for brick-wall quantum circuits of up to 243 qubits with various depths up to 20 layers. Our approach paves a way to exploring efficient simulation techniques for quantum many-body systems.