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arXiv · 2411.16915

Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions

Hamzat A. Akande·Alexandre Perrin·Bruno Senjean·Matthieu Saubanere
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Abstract

Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and Quantum Subspace Methods, offer practical solutions but face limitations in circuit depth and measurement overhead. In this article, we propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for the extraction of low-lying energy states. We show that, under certain conditions, our approach leads to a tridiagonal representation similar to that obtained with the Lanczos algorithm. The iterative process allows control over the trade-off between circuit depth, the number of variational parameters, and the number of measurements required to achieve the desired accuracy, making it suitable for current quantum hardware. As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.

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Hamzat A. Akande, Alexandre Perrin, Bruno Senjean, Matthieu Saubanere. 2024-11-25. Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions. https://doi.org/10.1103/6hpp-zl5h

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