Universal quantum circuits for quantum chemistry

TL;DR

This paper introduces controlled single-excitation gates, specifically Givens rotations, as a universal set for particle-conserving unitaries in quantum chemistry, enabling efficient state preparation and circuit compilation.

Contribution

It proves the universality of Givens rotations for particle-conserving unitaries and provides explicit methods for circuit compilation and state preparation.

Findings

Givens rotations form a universal gate set for particle-conserving unitaries.

Explicit compilation methods for arbitrary particle-conserving unitaries are provided.

Analytical gradient formulas and decompositions into standard gates are derived.

Abstract

Universal gate sets for quantum computing have been known for decades, yet no universal gate set has been proposed for particle-conserving unitaries, which are the operations of interest in quantum chemistry. In this work, we show that controlled single-excitation gates in the form of Givens rotations are universal for particle-conserving unitaries. Single-excitation gates describe an arbitrary $U(2)$ rotation on the two-qubit subspace spanned by the states $|01\rangle, |10\rangle$, while leaving other states unchanged -- a transformation that is analogous to a single-qubit rotation on a dual-rail qubit. The proof is constructive, so our result also provides an explicit method for compiling arbitrary particle-conserving unitaries. Additionally, we describe a method for using controlled single-excitation gates to prepare an arbitrary state of a fixed number of particles. We derive analytical gradient formulas for Givens rotations as well as decompositions into single-qubit and CNOT gates. Our results offer a unifying framework for quantum computational chemistry where every algorithm is a unique recipe built from the same universal ingredients: Givens rotations.