The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry.

Ivana Miháliková,Martin Friák,Mojmír Šob,Matej Pivoluska,Martin Plesch,Daniel Nagaj

doi:10.3390/nano12020243

Abstract

New approaches into computational quantum chemistry can be developed through the use of quantum computing. While universal, fault-tolerant quantum computers are still not available, and we want to utilize today’s noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE)—an algorithm for calculating the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, and physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal method of running the hybrid classical-quantum optimization is to: (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but ensure a high final readout precision; (ii) emphasize efficient problem encoding and ansatz parametrization; and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently, it is quite difficult to perform trustworthy calculations of molecular energies.

Highlights

Computer simulations of quantum systems constitute a crucial tool for a deeper understanding of behavior and properties of matter at the atomic scale
There are several possible sources of error for the energies calculated by the variational quantum eigensolver (VQE): first, the statistical errors in intermediate and final energy estimations, caused by the probabilistic nature of quantum mechanics; second, Hamiltonian representation and statepreparation ansatz errors, caused by approximations in the Hamiltonian, as well as the space of states we search over, given by our parametrized quantum circuit; third, hardware errors present in noisy quantum devices running the quantum part of VQE
We have only limited access to the quantum processors, which severely restricts the number of shots we can use for each datapoint

Summary

Introduction

Computer simulations of quantum systems constitute a crucial tool for a deeper understanding of behavior and properties of matter at the atomic scale. We resort to many clever types of approximations [1,2,3,4,5,6,7,8,9] Oftentimes, though, they are not good enough, or start to scale badly. The concept of a quantum computer, based on the laws of quantum physics, was first proposed by Richard Feynman [10]. He envisioned that the way to deal with the exponential amount of information appropriate to study physical systems was to use quantum systems as computers themselves. We have come a long way since and today we have access to the first small, programmable quantum chips, together with 25 years of development of quantum algorithms [11,12,13] and protocols

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