Gradient-Based Excitation Filter for Molecular Ground-State Simulation

TL;DR

This paper presents a gradient-based method to simplify the UCCSD ansatz for molecular ground-state simulations, significantly reducing circuit depth and runtime on classical computers, thus improving near-term quantum computing feasibility.

Contribution

It introduces a classical gradient-based approach to efficiently truncate excitations in the UCCSD ansatz, avoiding quantum optimization and enabling more compact quantum circuits.

Findings

Achieves up to 46% parameter reduction

Reduces circuit depth by 60%

Speeds up computation by 678 times

Abstract

Molecular ground-state simulation is one of the most promising fields for demonstrating practical quantum advantage on near-term quantum computers. However, the Variational Quantum Eigensolver (VQE), a leading algorithm for this task, still faces significant challenges due to excessive circuit depth. This paper introduces a method to efficiently simplify the Unitary Coupled-Cluster with Single and Double Excitations (UCCSD) ansatz on classical computers. We propose to estimate the correlation energy contributions of excitations using their gradients at Hartree-Fock state, supported by a theoretical proof. For molecular systems with $K$ orbitals, these gradients can be obtained with complexity only $O(K^8)$, which can be efficiently implemented on classical computers, especially in parallel. By sorting and truncating the excitations based on these gradients, the simplified ansatz can be obtained immediately, avoiding the challenging task of optimizing ansatz structure on a quantum computer. Furthermore, we introduce a strategy to indirectly identify critical excitations through spin-adapted constraints, reducing gradient computations by $60\%$. Numerical experiments on prototype molecular systems (H${_4}$, HF, H${_2}$O, BeH${_2}$ and NH$_3$) demonstrate that our approach achieves up to $46\%$ parameter decrease, $60\%$ circuit depth reduction and $678\times$ runtime speedup compared to the state-of-the-art ADAPT-VQE algorithm, enabling significantly more compact quantum circuits with enhanced near-term feasibility.