Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations

TL;DR

This paper introduces a symmetry-based Hilbert space partitioning strategy for variational quantum eigensolvers (VQE) that reduces quantum circuit complexity and maintains high accuracy in quantum chemical calculations, especially on noisy quantum devices.

Contribution

The authors develop a symmetry-inspired Hilbert space partitioning method and a scoring system for excitation operators, significantly reducing circuit depth while preserving accuracy in VQE.

Findings

Achieves near full UCCSD accuracy with fewer CNOT gates.

Reduces quantum circuit depth by up to 35 times.

First few operators suffice for chemical accuracy on noisy simulators.

Abstract

Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupled cluster ansatz, we demonstrate that partitioning of the Hilbert space made possible by the point group symmetry of the molecular systems greatly reduces the number of variational operators by confining the variational search within a subspace. In addition, we found that instead of including all subterms for each excitation operator, a single-term representation suffices to reach required accuracy for various molecules tested, resulting in an additional shortening of the quantum circuit. With these strategies, VQE calculations on a noiseless quantum simulator achieve energies within a few meVs of those obtained with the full UCCSD ansatz for $\mathrm{H}_4$ square, $\mathrm{H}_4$ chain and $\mathrm{H}_6$ hexagon molecules; while the number of controlled-NOT (CNOT) gates, a measure of the quantum-circuit depth, is reduced by a factor of as large as 35. Furthermore, we introduced an efficient "score" parameter to rank the excitation operators, so that the operators causing larger energy reduction can be applied first. Using $\mathrm{H}_4$ square and $\mathrm{H}_4$ chain as examples, We demonstrated on noisy quantum simulators that the first few variational operators can bring the energy within the chemical accuracy, while additional operators do not improve the energy since the accumulative noise outweighs the gain from the expansion of the variational ansatz.