Divide and conquer approach to quantum Hamiltonian simulation

Stuart Hadfield,Anargyros Papageorgiou

doi:10.1088/1367-2630/aab1ef

Abstract

We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.

Highlights

Classical simulation of quantum mechanical systems is a very difficult problem
This led to a large body of research dealing with quantum algorithms for Hamiltonian simulation [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29], with numerous applications to problems in physics and chemistry [30,31,32,33,34,35]
In the limit the bound (1) holds with m replaced by 2. This suggests that when many Hamiltonians are small in norm one should be able to improve the cost estimate (1) by partitioning them into groups and, for instance, using splitting formulas of different orders as we indicate in figure 1, and we will explain in detail later

Summary

Introduction

Classical simulation of quantum mechanical systems is a very difficult problem. The computational cost of the best classical deterministic algorithm known grows exponentially with the system size. As Feynman proposed [1], quantum computers may be able to carry out the simulation more efficiently than classical computers This led to a large body of research dealing with quantum algorithms for Hamiltonian simulation [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29], with numerous applications to problems in physics and chemistry [30,31,32,33,34,35].

Objectives

Methods

Findings

Conclusion