arXiv subjects

Vanda Glezakou

Publications and source records attributed to Vanda Glezakou.

2 recordsLinked to original sources

arXiv2026

Certified Optimal Measurement Reduction over Quantum Context Landscapes

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.

quant-ph↗

arXiv2026

Beyond Orbital Rotations: Correlation-Rank Limits and Clifford-Accessible Measurement, from Algebra and Global Optimization

Algebra and RANGE global optimization play complementary, explicitly separated roles in identifying measurement structure beyond orbital rotations. In the fixed (1,1)-particle sector of two spatial orbitals per spin, algebra proves that one particle-number-preserving orbital-rotation context contributes a rank-one two-body correlation block $T$: an observable needs at least $\mathrm{rank}\,T$ such contexts, and its best $K$-context correlation-block approximation is exactly the Eckart-Young singular-value tail, attained by the truncated SVD. A continuous RANGE search over the physical rotation angles independently corroborates this exact trade-off. A Bell-diagonal, Heisenberg-type witness has correlation rank three: it needs at least three orbital-rotation contexts, while one explicit physical Clifford circuit measures its commuting Pauli representatives. For spin-conserving Jordan-Wigner molecular Hamiltonians we also prove the parity ceiling $r_X \le 2(N-1)$ for any Pauli subset, tight even within commuting subsets; $X$-rank is a routing diagnostic, and the strict separation is carried by the correlation-rank theorem. The discrete mode of RANGE locates high-$X$-rank commuting families across molecular and production f-element Hamiltonians, finding ceiling-saturating witnesses for CH4 and NdO; values are best found unless a proved ceiling is attained. Applying the companion certificate framework, enlarging product settings by fully commuting, Clifford-accessible settings reduces the certified leading shot cost by 31-70% on four 29-35-qubit f-element Hamiltonians, a QWC-versus-QWC+FC result rather than a Gaussian-versus-Clifford pricing. Controlled-Pauli insertions in Hadamard tests are Clifford; these zero-$T$ statements concern measurement circuitry only, while shot counts and state preparation retain their full costs.

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