CANOE: Classically Assisted Non-Orthogonal Eigensolver
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908884585676800 |
|---|---|
| author | Park, Jihyeon Frink, Collin C. D. Otten, Matthew |
| author_facet | Park, Jihyeon Frink, Collin C. D. Otten, Matthew |
| contents | In the early fault-tolerant regime, where quantum resources remain limited, hybrid quantum-classical strategies offer one possible route toward quantum advantage. We introduce CANOE, the Classically Assisted Non-Orthogonal Eigensolver, as such an approach, distributing Rayleigh-Ritz basis states between quantum and classical hardware. This approach leverages the expressive power of quantum states, which are costly to reproduce classically, while augmenting them with a large pool of classically generated basis states that can be incorporated at negligible computational cost. We validate this through numerical simulations of a 76-qubit chromium atom system, quantifying how each additional quantum basis state enhances ground-state representability and how the inclusion of classical states further amplifies this improvement. Such a hybrid basis framework necessarily requires an efficient protocol on quantum hardware for evaluating overlaps between quantum and classical states in the resulting generalized eigenvalue formulation. We address this by introducing a histogram-based protocol and demonstrate through numerical simulations that it can approach chemical accuracy at moderate sampling cost. To solve the resulting generalized eigenvalue problem stably, CANOE incorporates a Schur-complement-based stabilization procedure that mitigates ill-conditioning caused by linear dependencies in the hybrid basis. Taken together, these results position CANOE as a practical framework for combining limited quantum resources with expansive classical resources for early fault-tolerant quantum simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | CANOE: Classically Assisted Non-Orthogonal Eigensolver Park, Jihyeon Frink, Collin C. D. Otten, Matthew Quantum Physics In the early fault-tolerant regime, where quantum resources remain limited, hybrid quantum-classical strategies offer one possible route toward quantum advantage. We introduce CANOE, the Classically Assisted Non-Orthogonal Eigensolver, as such an approach, distributing Rayleigh-Ritz basis states between quantum and classical hardware. This approach leverages the expressive power of quantum states, which are costly to reproduce classically, while augmenting them with a large pool of classically generated basis states that can be incorporated at negligible computational cost. We validate this through numerical simulations of a 76-qubit chromium atom system, quantifying how each additional quantum basis state enhances ground-state representability and how the inclusion of classical states further amplifies this improvement. Such a hybrid basis framework necessarily requires an efficient protocol on quantum hardware for evaluating overlaps between quantum and classical states in the resulting generalized eigenvalue formulation. We address this by introducing a histogram-based protocol and demonstrate through numerical simulations that it can approach chemical accuracy at moderate sampling cost. To solve the resulting generalized eigenvalue problem stably, CANOE incorporates a Schur-complement-based stabilization procedure that mitigates ill-conditioning caused by linear dependencies in the hybrid basis. Taken together, these results position CANOE as a practical framework for combining limited quantum resources with expansive classical resources for early fault-tolerant quantum simulations. |
| title | CANOE: Classically Assisted Non-Orthogonal Eigensolver |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.13188 |