Guided sampling ans\"atzes for variational quantum computing

TL;DR

This paper introduces guided sampling ansatzes for variational quantum computing, enabling efficient and accurate quantum simulations of molecules with minimal circuit executions on current quantum hardware.

Contribution

The paper presents a new class of guided sampling ansatzes tailored to system interactions and measurements, improving accuracy with fewer quantum circuit executions.

Findings

Achieved chemical accuracy for hydronium cation with 200 circuit runs

Demonstrated effectiveness on IonQ Aria quantum computer

Reduced quantum resource requirements for molecular simulations

Abstract

Quantum computing is a promising technology because of the ability of quantum computers to process vector spaces with dimensions that increase exponentially with the simulated system size. Extracting the solution, however, is challenging as the number of quantum gate operations and quantum circuit executions must still scale at most polynomially. Consequently, choosing a good ansatz--a polynomial subset of the exponentially many possible solutions--will be critical to maintain accuracy for larger systems. To address this challenge, we introduce a class of guided sampling ans\"atzes (GSAs) that depend on the system interactions and measured state samples as well as a parameter space. We demonstrate a minimal ansatz for the hydronium cation H$_3$O$^+$ and found that with only 200 circuit executions per structure on the IonQ Aria quantum computer, our calculations produced total energies around the relaxed structure with errors well below $1.59\times10^{-3}$ Ha, thus exceeding chemical accuracy.