Benchmarking quantum trial wavefunctions for phaseless auxiliary-field quantum Monte Carlo

TL;DR

This study benchmarks various quantum trial wavefunctions for the ph-AFQMC method, assessing their accuracy, expressibility, and scalability in modeling strongly correlated systems, and highlights the potential of adaptive ansatze for efficient quantum simulations.

Contribution

It provides a comprehensive comparison of different quantum trial wavefunctions within the ph-AFQMC framework, including adaptive ansatze, revealing insights into their performance and resource efficiency.

Findings

Several ansatz families achieve chemically accurate energies across dissociation curves.

Different ansatzes with similar parameters yield comparable results despite varying energies and circuit depths.

Adaptive ansatze can outperform fixed ones in strongly correlated regimes with more compact circuits.

Abstract

The phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method is a stochastic imaginary-time projection technique for computing ground-state properties of strongly correlated quantum systems, with accuracy that depends critically on the choice of trial wavefunction. Here, we investigate ph-AFQMC with trial states prepared using parameterized quantum circuits. In this work, we present a comprehensive benchmarking study of quantum trial wavefunctions spanning unitary coupled-cluster, Hamiltonian-informed, Jastrow-inspired, and adaptively constructed ansatze. The benchmarking evaluates accuracy, expressibility, and scalability of these ansatze within the QC-AFQMC framework. We test these ansatze on linear hydrogen chains under bond stretching and find that several ansatz families produce chemically accurate ph-AFQMC energies across the dissociation curve. We have performed simulations using the CUDA-Q quantum development platform on the GPU partition of the Perlmutter supercomputer. When comparing ansatze at similar numbers of variational parameters, we find that different ansatz families yield comparable ph-AFQMC results despite exhibiting substantially different variational energies, optimization costs, and circuit depths. Our results indicate that the variational energy of an ansatz is not always a reliable indicator of its quality for ph-AFQMC and reveal instances of over-parameterization. In the strongly correlated regime, trial wavefunctions obtained from adaptive ansatze, exemplified here by ADAPT-VQE with the UCCSD operator pool, can outperform their fixed-ansatz counterparts (UCCSD) in terms of projected energies while using substantially more compact circuits, providing a flexible route to optimize quantum resources within the ph-AFQMC framework.