Optimal qudit overlapping tomography and optimal measurement order

• URL: http://arxiv.org/abs/2601.10059v1
• Date: Thu, 15 Jan 2026 04:24:07 GMT
• Title: Optimal qudit overlapping tomography and optimal measurement order
• Authors: Shuowei Ma, Qianfan Wang, Lvzhou Li, Fei Shi,
• Abstract summary: Overlapping tomography is essential for characterizing quantum systems, but it becomes infeasible for large systems due to exponential resource scaling.<n>Here, we investigate optimal qudit overlapping tomography, constructing local measurement settings from generalized Gell-Mann matrices.<n>We prove that pairwise tomography requires at most $8 + 56leftlceil log_8 n rightrceil$ measurement settings, and provide an explicit scheme achieving this bound.
• Score: 14.6984428694541
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum state tomography is essential for characterizing quantum systems, but it becomes infeasible for large systems due to exponential resource scaling. Overlapping tomography addresses this challenge by reconstructing all $k$-body marginals using few measurement settings, enabling the efficient extraction of key information for many quantum tasks. While optimal schemes are known for qubits, the extension to higher-dimensional qudit systems remains largely unexplored. Here, we investigate optimal qudit overlapping tomography, constructing local measurement settings from generalized Gell-Mann matrices. By establishing a correspondence with combinatorial covering arrays, we present two explicit constructions of optimal measurement schemes. For $n$-qutrit systems, we prove that pairwise tomography requires at most $8 + 56\left\lceil \log_{8} n \right\rceil$ measurement settings, and provide an explicit scheme achieving this bound. Furthermore, we develop an efficient algorithm to determine the optimal order of these measurement settings, minimizing the experimental overhead associated with switching configurations. Compared to the worst-case ordering, our optimized schedule reduces switching costs by approximately 50\%. These results provide a practical pathway for efficient characterization of qudit systems, facilitating their application in quantum communication and computation.

Related papers

• Scalable Preparation of Matrix Product States with Sequential and Brick Wall Quantum Circuits [0.0]
  Matrix Product States (MPS) admit more efficient constructions when accuracy is traded for circuit complexity.<n>This work introduces an end-to-end MPS preparation framework that combines the strengths of both strategies within a single pipeline.
  arXiv  Detail & Related papers  (2026-02-12T15:07:11Z)
• Optimal scheme for distributed quantum metrology [3.330069889084255]
  We develop optimal schemes for distributed quantum metrology that characterize the ultimate precision limits in distributed systems.<n>We prove that the optimal control operations can be implemented locally on each sensor, eliminating the need for non-local control operations across distant nodes.
  arXiv  Detail & Related papers  (2025-09-22T18:55:11Z)
• Optimal Overlapping Tomography [6.868087671163721]
  We present protocols for overlapping tomography that are optimal with respect to the number of measurement settings.<n>Results will find applications in learning noise and interaction patterns in quantum computers as well as characterising fermionic systems in quantum chemistry.
  arXiv  Detail & Related papers  (2024-08-11T08:59:08Z)
• Meta-Learning Based Optimization for Large Scale Wireless Systems [45.025621137165025]
  It is known that the limitation of conventional optimization algorithms in the literature often increases with the number of transmit antennas and communication users in wireless system. This paper proposes an unsupervised meta-learning based approach to perform non-diaconfigurable optimization at significantly reduced complexity.
  arXiv  Detail & Related papers  (2024-07-01T21:45:27Z)
• Retrieving space-dependent polarization transformations via near-optimal quantum process tomography [55.41644538483948]
  We investigate the application of genetic and machine learning approaches to tomographic problems. We find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes.
  arXiv  Detail & Related papers  (2022-10-27T11:37:14Z)
• Automatic and effective discovery of quantum kernels [41.61572387137452]
  Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data.<n>We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML.<n>The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach.
  arXiv  Detail & Related papers  (2022-09-22T16:42:14Z)
• Tight Cram\'{e}r-Rao type bounds for multiparameter quantum metrology through conic programming [61.98670278625053]
  It is paramount to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. Here, we give a concrete way to find uncorrelated measurement strategies with optimal precisions. We show numerically that there is a strict gap between the previous efficiently computable bounds and the ultimate precision bound.
  arXiv  Detail & Related papers  (2022-09-12T13:06:48Z)
• Multipoint-BAX: A New Approach for Efficiently Tuning Particle Accelerator Emittance via Virtual Objectives [47.52324722637079]
  We propose a new information-theoretic algorithm, Multipoint-BAX, for black-box optimization on multipoint queries. We use Multipoint-BAX to minimize emittance at the Linac Coherent Light Source (LCLS) and the Facility for Advanced Accelerator Experimental Tests II (FACET-II)
  arXiv  Detail & Related papers  (2022-09-10T04:01:23Z)
• Versatile Single-Loop Method for Gradient Estimator: First and Second Order Optimality, and its Application to Federated Learning [45.78238792836363]
  We present a single-loop algorithm named SLEDGE (Single-Loop-E Gradient Estimator) for periodic convergence. Unlike existing methods, SLEDGE has the advantage of versatility; (ii) second-order optimal, (ii) in the PL region, and (iii) smaller complexity under less of data.
  arXiv  Detail & Related papers  (2022-09-01T11:05:26Z)
• Combinatorial optimization for low bit-width neural networks [23.466606660363016]
  Low-bit width neural networks have been extensively explored for deployment on edge devices to reduce computational resources. Existing approaches have focused on gradient-based optimization in a two-stage train-and-compress setting. We show that a combination of greedy coordinate descent and this novel approach can attain competitive accuracy on binary classification tasks.
  arXiv  Detail & Related papers  (2022-06-04T15:02:36Z)
• Large-Scale Sequential Learning for Recommender and Engineering Systems [91.3755431537592]
  In this thesis, we focus on the design of an automatic algorithms that provide personalized ranking by adapting to the current conditions. For the former, we propose novel algorithm called SAROS that take into account both kinds of feedback for learning over the sequence of interactions. The proposed idea of taking into account the neighbour lines shows statistically significant results in comparison with the initial approach for faults detection in power grid.
  arXiv  Detail & Related papers  (2022-05-13T21:09:41Z)
• Distributed Learning and Democratic Embeddings: Polynomial-Time Source Coding Schemes Can Achieve Minimax Lower Bounds for Distributed Gradient Descent under Communication Constraints [46.17631511884969]
  We consider the problem of compressing a vector in the n-dimensional Euclidean space, subject to a bit-budget of R-bits per dimension. We show that Democratic and Near-Democratic source-coding schemes are (near) optimal in the sense that the covering efficiency of the resulting quantizer is either dimension independent, or has a very weak logarithmic dependence. We propose a distributed optimization algorithm: DGD-DEF, which employs our proposed coding strategy, and achieves the minimax optimal convergence rate to within (near) constant factors.
  arXiv  Detail & Related papers  (2021-03-13T00:04:11Z)
• Integration of spectator qubits into quantum computer architectures for hardware tuneup and calibration [0.0]
  We focus on the challenge of measuring spatially inhomogeneous quasi-static calibration errors using spectator qubits. We introduce a novel architectural concept for such spectator qubits: arranging them spatially according to prescriptions from optimal 2D approximation theory. We show that this insight allows for efficient reconstruction of inhomogeneities in qubit calibration.
  arXiv  Detail & Related papers  (2020-04-27T18:00:33Z)

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.