Quantum Seniority-based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for Efficient Quantum Measurements (2509.01061v1)

Abstract: Quantum SENiority-based Subspace Expansion (Q-SENSE) is a hybrid quantum-classical algorithm that interpolates between the Variational Quantum Eigensolver (VQE) and Configuration Interaction (CI) methods. It constructs Hamiltonian matrix elements on a quantum device and solves the resulting eigenvalue problem classically. This seniority-symmetry-based approach reduces one of the primary limitations of VQE on near-term quantum hardware - circuit depth - by exchanging lower circuit complexity for the need to compute additional matrix elements. Unlike other expansion-based methods - such as Quantum Subspace Expansion (QSE), Quantum Krylov Subspace Expansion, and the Non-orthogonal Quantum Eigensolver - Q-SENSE leverages symmetry-induced orthogonality to construct basis states in distinct symmetry sectors. This not only guarantees orthogonality but also reduces the number of Hamiltonian terms that must be measured, as many terms are zero between different symmetry subspaces. By systematically combining symmetry principles with matrix-based techniques, Q-SENSE offers a scalable and resource-efficient potential route to quantum advantage on near-term quantum devices and in the early fault-tolerant regime.