Quantum-classical eigensolver using multiscale entanglement renormalization

TL;DR

This paper introduces a variational quantum eigensolver based on MERA that efficiently simulates strongly-correlated quantum systems on NISQ devices, with low qubit requirements and scalability to large systems.

Contribution

It presents a quantum algorithm leveraging MERA for efficient simulation of quantum matter, compatible with noisy intermediate-scale quantum devices, and scalable to large system sizes.

Findings

The algorithm has lower computational costs than classical methods.

It can be implemented on NISQ devices with limited qubits.

Numerical tests show accuracy comparable to full MERA with few Trotter steps.

Abstract

We propose a variational quantum eigensolver (VQE) for the simulation of strongly-correlated quantum matter based on a multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimization. This MERA quantum eigensolver can have substantially lower computation costs than corresponding classical algorithms. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediate-scale quantum (NISQ) devices and still describe large systems. It is particularly attractive for ion-trap devices with ion-shuttling capabilities. The number of required qubits is system-size independent, and increases only to a logarithmic scaling when using quantum amplitude estimation to speed up gradient evaluations. Translation invariance can be used to make computation costs square-logarithmic in the system size and describe the thermodynamic limit. We demonstrate the approach numerically for a MERA with Trotterized disentanglers and isometries. With a few Trotter steps, one recovers the accuracy of the full MERA.