Quantum Seniority-based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for the Electronic Structure Problem

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. Unlike other expansion-based methods -- such as Quantum Subspace Expansion (QSE), Quantum Krylov Algorithms, and the Non-Orthogonal Quantum Eigensolver -- Q-SENSE introduces seniority operators as artificial symmetries to construct orthogonal basis states. This seniority-symmetry-based approach reduces one of the primary limitations of VQE on near-term quantum hardware -- circuit depth -- at the cost of measuring additional matrix elements. The artificial symmetries also reduce the number of Hamiltonian terms that must be measured, as only a small fraction of the terms couple basis states in different seniority subspaces. With all these merits, Q-SENSE offers a scalable and resource-efficient route to quantum advantage on near-term quantum devices and in the early fault-tolerant regime.