Parallel quantum simulation of large systems on small NISQ computers

F Barratt,Vid Stojevic,Matthias Bal,James Dborin,Frank Pollmann,A G Green

doi:10.1038/s41534-021-00420-3

Abstract

Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given.

Highlights

The insight underpinning Steve White’s formulation of the density matrix renormalisation group (DMRG) is that entanglement is the correct resource to focus upon to formulate accurate, approximate descriptions of large quantum systems[1]
Later understood as an algorithm to optimise a matrix product state (MPS)[2], this notion underpins the use of tensor networks as a variational parametrisation of wavefunctions with quantified entanglement resources
Retaining λα only above some threshold value provides a way to compress representations of a quantum state; the MPS construction can be obtained by applying this procedure sequentially along a spin chain[4]

Summary

Introduction

The insight underpinning Steve White’s formulation of the density matrix renormalisation group (DMRG) is that entanglement is the correct resource to focus upon to formulate accurate, approximate descriptions of large quantum systems[1]. Later understood as an algorithm to optimise a matrix product state (MPS)[2], this notion underpins the use of tensor networks as a variational parametrisation of wavefunctions with quantified entanglement resources. Such approaches allow one to concentrate computational resources in the appropriate region of Hilbert space and provide an effective and universal way to simulate quantum systems[3,4]. They provide an effective framework to distribute entanglement resources in simulation on noisy intermediate-scale quantum (NISQ) computers. Since the finite-depth quantum circuit may be equivalently described as a tensor network[11], tensor networks provide a convenient framework with which to distribute entanglement to the useful regions of Hilbert space and to make efficient use of this relatively scarce resource

Methods

Results

Conclusion