aiqbench analysis
This research presents a certifiable framework for quantum measurement reduction that combines second-order cone programming with nature-inspired global optimization. The method provides independently verifiable bounds on shot costs while significantly compressing molecular context dictionaries without sacrificing accuracy. By addressing the nonconvex outer problem of dictionary design, this work advances practical efficiency in resource-constrained quantum simulations.
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)
Full text under the publisher's open licence · 276 words
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