Riemannian quantum circuit optimization based on matrix product operators

TL;DR

This paper introduces a novel Riemannian optimization method combined with tensor networks to significantly improve the accuracy of quantum circuit simulations for large and complex quantum systems without relying on symmetry assumptions.

Contribution

The paper presents a scalable, symmetry-agnostic optimization technique using matrix product operators that enhances quantum simulation accuracy across various Hamiltonians and molecular systems.

Findings

Up to four orders of magnitude error reduction in spin chain simulations.

Achieved up to eight orders of magnitude error improvement in molecular system simulations.

Method is scalable to large systems with 50+ qubits.

Abstract

We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our method imposes no symmetry assumptions, such as translational invariance, on the quantum systems. This technique is scalable to large systems through the use of a matrix product operator representation of the reference time evolution propagator. Our optimization routine is applied to various spin chains and fermionic systems described by the transverse-field Ising Hamiltonian, the Heisenberg Hamiltonian, and the spinful Fermi-Hubbard Hamiltonian. In these cases, our approach achieves a relative error improvement of up to four orders of magnitude for systems of 50 qubits, although our method is also applicable to larger systems. Furthermore, we demonstrate the versatility of our method by applying it to molecular systems, specifically lithium hydride, achieving an error improvement of up to eight orders of magnitude. This proof of concept highlights the potential of our approach for broader applications in quantum simulations.