Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions

TL;DR

This paper introduces a particle-hole Hamiltonian transformation and optimized wavefunction parameterizations to enhance the efficiency and scalability of quantum algorithms for electronic structure calculations, notably improving the UCC method within VQE.

Contribution

It proposes a particle-hole Hamiltonian transformation, optimized trial wavefunctions, and a new quantum circuit family for more efficient quantum chemistry simulations.

Findings

Particle-hole transformation improves Hamiltonian representation.

Single Trotter step accurately reproduces ground state energies.

New quantum circuits reduce gate count and circuit depth.

Abstract

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole (p/h) picture, which offers a better starting point for the expansion of the trial wavefunction. The state of the molecular system at study is parametrized in a way to efficiently explore the sector of the molecular Fock space that contains the desired solution. To this end, we explore several trial wavefunctions to identify the most efficient parameterization of the molecular ground state. Taking advantage of known post-Hartree Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the Unitary Coupled Cluster (UCC) method within the Variational Quantum Eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC , with important advantages compared to the straightforward 'translation' of the classical Coupled Cluster counterpart. In particular, we show how a single Trotter step can accurately and efficiently reproduce the ground state energies of simple molecular systems.