Quantum Seniority-based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for the Electronic Structure Problem
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914184187346944 |
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| author | Patel, Smik Jayakumar, Praveen Huang, Rick Zeng, Tao Izmaylov, Artur F. |
| author_facet | Patel, Smik Jayakumar, Praveen Huang, Rick Zeng, Tao Izmaylov, Artur F. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Seniority-based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for the Electronic Structure Problem Patel, Smik Jayakumar, Praveen Huang, Rick Zeng, Tao Izmaylov, Artur F. Quantum Physics Chemical Physics 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. |
| title | Quantum Seniority-based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for the Electronic Structure Problem |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2509.01061 |