Time Evolution of Uniform Sequential Circuits

TL;DR

This paper introduces a hybrid quantum-classical algorithm for simulating the time evolution of one-dimensional uniform quantum systems, achieving polynomial scaling in parameters and suitable for near-term quantum computers.

Contribution

It presents a novel layered uniform sequential quantum circuit ansatz for infinite translation-invariant states with polynomial parameter scaling, enabling efficient time evolution simulations.

Findings

Polynomial parameter scaling with evolution time for fixed accuracy

Successful benchmarking on classical computers and quantum hardware

Potential for classical and quantum computational improvements

Abstract

Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work, we present a polynomially scaling hybrid quantum-classical algorithm for time evolving a one-dimensional uniform system in the thermodynamic limit. This algorithm uses a layered uniform sequential quantum circuit as a variational ansatz to represent infinite translation-invariant quantum states. We show numerically that this ansatz requires a number of parameters polynomial in the simulation time for a given accuracy. Furthermore, this favourable scaling of the ansatz is maintained during our variational evolution algorithm. All steps of the hybrid optimization are designed with near-term digital quantum computers in mind. After benchmarking the evolution algorithm on a classical computer, we demonstrate the measurement of observables of this uniform state using a finite number of qubits on a cloud-based quantum processing unit. With more efficient tensor contraction schemes, this algorithm may also offer improvements as a classical numerical algorithm.