Certified Optimal Measurement Reduction over Quantum Context Landscapes

arXiv:2607.16866v1 Announce Type: new Abstract: Quantum-measurement reduction contains two distinct global-optimization layers: a continuous problem of splitting an observable and allocating shots within a fixed measurement dictionary, and a nonconvex outer problem of designing the dictionary and calibrating its data-driven uncertainty model. We solve the inner layer globally and certifiably as a second-order cone program (SOCP), and use RANGE, a robust adaptive nature-inspired global optimizer, for the combinatorial and statistical outer layer. For any declared set of contexts, per-shot costs, score functions, and covariance model, the SOCP returns the minimum leading shot cost among unbiased linear stratified estimators. The conic dual supplies an independently checkable lower-bound witness; after feasibility repair, an external verifier recomputes $L \le \Phi \le U$ from stored data without trusting the optimizer. Pilot measurements yield simultaneous finite-sample covariance brackets, and the dual becomes a pricing oracle for omitted contexts. Discrete RANGE searches covering sub-dictionaries, Pareto compression fronts, and candidate contexts; continuous RANGE performs an explicitly empirical, coverage-constrained calibration of covariance-radius models, while rigorous certificates retain the proved finite-sample radius. RANGE compresses molecular context dictionaries by 4.3-6.1x at 0.2-2.1% certified-frontier excess. Standard strategies are exactly optimal for H2 yet leave factors of 2.1-7.7 in shots within their own settings by H2O. Adding fully commuting contexts lowers the certified optimum by up to 56%; on 29-35-qubit production f-element Hamiltonians under a declared Hartree-Fock-proxy covariance model, the capped-dictionary enlargement saves 31-70% of the shots, and transformations reducing block-encoding cost need not reduce sampling cost.

Abstract:Quantum-measurement reduction contains two distinct global-optimization layers: a continuous problem of splitting an observable and allocating shots within a fixed measurement dictionary, and a nonconvex outer problem of designing the dictionary and calibrating its data-driven uncertainty model. We solve the inner layer globally and certifiably as a second-order cone program (SOCP), and use RANGE, a robust adaptive nature-inspired global optimizer, for the combinatorial and statistical outer layer. For any declared set of contexts, per-shot costs, score functions, and covariance model, the SOCP returns the minimum leading shot cost among unbiased linear stratified estimators. The conic dual supplies an independently checkable lower-bound witness; after feasibility repair, an external verifier recomputes $L \le \Phi \le U$ from stored data without trusting the optimizer. Pilot measurements yield simultaneous finite-sample covariance brackets, and the dual becomes a pricing oracle for omitted contexts. Discrete RANGE searches covering sub-dictionaries, Pareto compression fronts, and candidate contexts; continuous RANGE performs an explicitly empirical, coverage-constrained calibration of covariance-radius models, while rigorous certificates retain the proved finite-sample radius. RANGE compresses molecular context dictionaries by 4.3-6.1x at 0.2-2.1% certified-frontier excess. Standard strategies are exactly optimal for H2 yet leave factors of 2.1-7.7 in shots within their own settings by H2O. Adding fully commuting contexts lowers the certified optimum by up to 56%; on 29-35-qubit production f-element Hamiltonians under a declared Hartree-Fock-proxy covariance model, the capped-dictionary enlargement saves 31-70% of the shots, and transformations reducing block-encoding cost need not reduce sampling cost.

Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph)

arXiv:2607.16866 [quant-ph]

(or arXiv:2607.16866v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.16866 arXiv-issued DOI via DataCite (pending registration)

From: Federico Zahariev Dr. [view email] [v1] Sat, 18 Jul 2026 16:06:52 UTC (40 KB)

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Certified Optimal Measurement Reduction over Quantum Context Landscapes

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