CANOE: Classically Assisted Non-Orthogonal Eigensolver

• URL: http://arxiv.org/abs/2603.13188v1
• Date: Fri, 13 Mar 2026 17:21:14 GMT
• Title: CANOE: Classically Assisted Non-Orthogonal Eigensolver
• Abstract summary: We introduce CANOE, which distributes Rayleigh-Ritz basis states between quantum and classical hardware.<n>We validate this through numerical simulations of a 76-qubit chromium atom system.<n>These results position CANOE as a practical framework for combining limited quantum resources with expansive classical resources.
• Score: 0.4779196219827507
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: 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.

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