Quantum SENiority-based Subspace Expansion (Q-SENSE) and Its Extensions: Linear Combinations of Short-Circuit Unitary Transformations for the Electronic Structure Problem
Artur Izmaylov
University of Toronto
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.
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