Quantum Simulations of Chemistry in First Quantization with any Basis Set

TL;DR

This paper introduces a new quantum algorithm for solving molecular ground-state problems in first quantization with any basis set, achieving significant resource efficiency improvements over previous methods.

Contribution

The authors develop a versatile first quantization quantum algorithm applicable to any basis set, with asymptotic speedup and resource improvements over existing second and first quantization approaches.

Findings

Achieves asymptotic speedup in Toffoli count for molecular orbitals.

Orders of magnitude resource improvement using dual plane waves.

Comparable or lower resources than previous first quantization plane wave algorithms.

Abstract

Quantum computation of the energy of molecules and materials is one of the most promising applications of fault-tolerant quantum computers. Practical applications require development of quantum algorithms with reduced resource requirements. Previous work has mainly focused on quantum algorithms where the Hamiltonian is represented in second quantization with compact basis sets while existing methods in first quantization are limited to a grid-based basis. In this work, we present a new method to solve the generic ground-state chemistry problem in first quantization using any basis set. We achieve asymptotic speedup in Toffoli count for molecular orbitals, and orders of magnitude improvement using dual plane waves as compared to the second quantization counterparts. In some instances, our approach provides similar or even lower resources compared to previous first quantization plane wave algorithms that, unlike our approach, avoids the loading of the classical data. The developed methodology can be applied to variety of applications, where the matrix elements of a first quantized Hamiltonian lack simple circuit representation.