Hardware-efficient variational quantum algorithms for time evolution

Marcello Benedetti,Mattia Fiorentini,Michael Lubasch

doi:10.1103/physrevresearch.3.033083

Marcello Benedetti, Mattia Fiorentini + Show 1 more

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https://doi.org/10.1103/physrevresearch.3.033083

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Abstract

Parameterized quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational algorithms need to be as hardware-efficient as possible. Here we present alternatives to the time-dependent variational principle that are hardware-efficient and do not require matrix inversion. In relation to imaginary time evolution, our approach significantly reduces the hardware requirements. With regards to real time evolution, where high precision can be important, we present algorithms of systematically increasing accuracy and hardware requirements. We numerically analyze the performance of our algorithms using quantum Hamiltonians with local interactions.

Highlights

Small quantum computers are available today and offer the exciting opportunity to explore classically difficult problems for which a quantum advantage may be achievable
Promising examples of quantum advantage obtained with parameterized quantum circuit (PQC) have already been identified for time evolution [17,18] and in other contexts such as for nonlinear partial differential equations [19,20], dynamical mean field theory [21,22], and machine learning [23]
We analyze the hardware/accuracy trade-off and show that for imaginary time evolution our algorithm significantly reduces the hardware requirements over existing methods and produces accurate ground state approximations

Summary

Introduction

Small quantum computers are available today and offer the exciting opportunity to explore classically difficult problems for which a quantum advantage may be achievable. The simulation of time evolution of quantum systems is an example of such problems where the advantage of using a quantum computer over a classical one is well understood [1,2,3,4,5]. This simulation is important for our understanding of quantum chemistry and materials science which are key application areas for future quantum computers [6,7,8,9]. Promising examples of quantum advantage obtained with PQCs have already been identified for time evolution [17,18] and in other contexts such as for nonlinear partial differential equations [19,20], dynamical mean field theory [21,22], and machine learning [23]

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