Reducing quantum measurements in qubit-based overlapping grouping methods for quantum energy estimation through better initializations

• URL: http://arxiv.org/abs/2607.02794v1
• Date: Thu, 02 Jul 2026 22:12:00 GMT
• Title: Reducing quantum measurements in qubit-based overlapping grouping methods for quantum energy estimation through better initializations
• Abstract summary: Grouping strategies significantly reduce the cost of estimating expectation values of Hamiltonians.<n>Overlapping methods require i) a non-overlapping grouping of the Hamiltonian, typically obtained from the Sorted Insertion (SI) algorithm as an initial.<n>VarSI grouping leverages the covariance-informed dictionaries, already required by overlapping methods, to construct better non-overlapping groups.
• Score: 0.8594140167290097
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The measurement cost for estimating expectation values of Hamiltonians is a central bottleneck in variational quantum algorithms. Grouping strategies significantly reduce this cost, with overlapping techniques being the state of the art in the field. Overlapping grouping methods require i) a non-overlapping grouping of the Hamiltonian, typically obtained from the Sorted Insertion (SI) algorithm as initialization, and ii) the construction of covariance dictionaries from approximate wavefunctions to guide the optimization. It was recently shown that different initializations can potentially reduce measurement costs for overlapping methods. Motivated by these findings, we introduce variance-aware SI (VarSI), a family of covariance-informed non-overlapping Pauli grouping heuristics to reduce measurement counts. VarSI grouping leverages the covariance dictionaries, already required by overlapping methods, to construct better non-overlapping groups. We propose three variants: a global greedy grouping insertion rule, a variance-informed SI analog, and a local refinement step initialized from SI or our variance-informed variant. We showcase the use of groupings generated by our VarSI heuristic algorithms to initialize overlapping methods using the iterative coefficient-splitting (ICS) algorithm. Molecular benchmarks with 130 Hamiltonians demonstrate consistent, non-overlapping measurement improvements over SI of 38\% and enhanced downstream ICS results when initialized from VarSI groups. We find that the initializations considered here achieve up to 70\% measurement reductions for ICS, compared to the standard SI initialization with mean reductions of 9--15.3\% depending on qubit mappings and covariance dictionaries used. These results show that non-overlapping grouping remains a consequential design step even when the final estimator uses overlapping fragments.

Related papers

• Total Variation Guarantees for Sampling with Stochastic Localization [0.0]
  We present a rigorous convergence analysis of SLIPS, a sampling algorithm based on localization.<n>We establish the first guarantee for SLIPS in total variation distance.<n>We further provide theoretical insights into the empirically observed optimal choice of discretization points.
  arXiv  Detail & Related papers  (2026-03-31T10:34:42Z)
• Analysis of Hessian Scaling for Local and Global Costs in Variational Quantum Algorithm [0.42970700836450487]
  We quantify the entrywise resolvability of the Hessian for Variational Quantum Algorithms.<n>We show two distinct scaling regimes that govern the sample complexity required to resolve Hessian entries against shot noise.
  arXiv  Detail & Related papers  (2026-01-31T15:49:23Z)
• Matrix Factorization Framework for Community Detection under the Degree-Corrected Block Model [48.989531198582704]
  We show that DCBM inference can be reformulated as a constrained nonnegative matrix factorization problem.<n>Our approach is to any specific network structure and applies to graphs with any structure representable by a DCBM.<n> Experiments on synthetic and real benchmark networks show that our method detects communities comparable to those found by DCBM inference.
  arXiv  Detail & Related papers  (2026-01-09T19:16:29Z)
• Improved parameter initialization for the (local) unitary cluster Jastrow ansatz [0.3017117582063482]
  We propose two methods to improve the parameters of quantum algorithms for chemistry.<n>The first method, which is applicable to both expectation value- and sample-based algorithms, uses compressed double factorization of the CCSD amplitudes.<n>The second method, which is applicable to sample-based algorithms, uses approximate tensor network simulation to improve the quality of samples produced by the ansatz circuit.
  arXiv  Detail & Related papers  (2025-11-27T14:05:18Z)
• Improved seeding strategies for k-means and k-GMM [1.8416014644193064]
  We revisit the randomized seeding techniques for k-means clustering and k-GMM.<n>We formalize their three key ingredients: the metric used for seed sampling, the number of candidate seeds, and the metric used for seed selection.<n>Experiments show a consistent constant factor improvement over classical contenders in terms of the final metric.
  arXiv  Detail & Related papers  (2025-06-26T14:10:40Z)
• Online Covariance Estimation in Nonsmooth Stochastic Approximation [14.818683408659764]
  We consider applying approximation (SA) methods to solve nonsmooth variational inclusion problems.<n>Our convergence construction establish the best-known for statistical estimation methods.
  arXiv  Detail & Related papers  (2025-02-07T20:16:51Z)
• A Fresh Look at Generalized Category Discovery through Non-negative Matrix Factorization [83.12938977698988]
  Generalized Category Discovery (GCD) aims to classify both base and novel images using labeled base data. Current approaches inadequately address the intrinsic optimization of the co-occurrence matrix $barA$ based on cosine similarity. We propose a Non-Negative Generalized Category Discovery (NN-GCD) framework to address these deficiencies.
  arXiv  Detail & Related papers  (2024-10-29T07:24:11Z)
• Quantization of Large Language Models with an Overdetermined Basis [73.79368761182998]
  We introduce an algorithm for data quantization based on the principles of Kashin representation. Our findings demonstrate that Kashin Quantization achieves competitive or superior quality in model performance.
  arXiv  Detail & Related papers  (2024-04-15T12:38:46Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Information-Theoretic Generalization Bounds for Iterative Semi-Supervised Learning [81.1071978288003]
  In particular, we seek to understand the behaviour of the em generalization error of iterative SSL algorithms using information-theoretic principles. Our theoretical results suggest that when the class conditional variances are not too large, the upper bound on the generalization error decreases monotonically with the number of iterations, but quickly saturates.
  arXiv  Detail & Related papers  (2021-10-03T05:38:49Z)
• On the Convergence of Stochastic Extragradient for Bilinear Games with Restarted Iteration Averaging [96.13485146617322]
  We present an analysis of the ExtraGradient (SEG) method with constant step size, and present variations of the method that yield favorable convergence. We prove that when augmented with averaging, SEG provably converges to the Nash equilibrium, and such a rate is provably accelerated by incorporating a scheduled restarting procedure.
  arXiv  Detail & Related papers  (2021-06-30T17:51:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.