Improving shadow estimation with locally-optimal dual frames

• URL: http://arxiv.org/abs/2511.02555v1
• Date: Tue, 04 Nov 2025 13:11:38 GMT
• Title: Improving shadow estimation with locally-optimal dual frames
• Authors: Keijo Korhonen, Stefano Mangini, Joonas Malmi, Hetta Vappula, Daniel Cavalcanti,
• Abstract summary: We investigate a variation of the classical shadows protocol in which the measurements are kept local while allowing the resulting classical shadows themselves to be correlated.<n>By constructing locally optimal shadows, we obtain unbiased estimators that outperform state-of-the-art methods, achieving the same accuracy with substantially fewer measurements.
• Score: 0.3131740922192114
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Accurate estimation of observables in quantum systems is a central challenge in quantum information science, yet practical implementations are fundamentally constrained by the limited number of measurement shots. In this work we explore a variation of the classical shadows protocol in which the measurements are kept local while allowing the resulting classical shadows themselves to be correlated. By constructing locally optimal shadows, we obtain unbiased estimators that outperform state-of-the-art methods, achieving the same accuracy with substantially fewer measurements. We validate our approach through numerical experiments on molecular Hamiltonians with up to 40 qubits and a 50-qubit Ising model consistently observing significant reductions in estimation errors.

Related papers

• Shadow measurements for feedback-based quantum optimization [0.0]
  We present an implementation of the recently introduced Feedback-based algorithm for quantum optimization (FALQON) with the Ket quantum programming platform.<n>We employ classical shadows for the feedback routine of parameter estimation and compare this approach with the direct estimation of observables.<n>Our results show that depending on the graph geometry for the MaxCut problem, the number of measurements required to estimate expected values of observables with classical shadows can be up to 16 times lower than with direct observable estimation.
  arXiv  Detail & Related papers  (2025-02-27T18:36:30Z)
• Classical optimisation of reduced density matrix estimations with classical shadows using N-representability conditions under shot noise considerations [0.13048920509133807]
  We build upon previous research by choice of an improved estimator within classical shadow tomography.<n>We explore the specific regimes where these methods outperform the unbiased estimator of the standalone classical shadow protocol.
  arXiv  Detail & Related papers  (2024-11-27T15:13:37Z)
• Lindblad-like quantum tomography for non-Markovian quantum dynamical maps [46.350147604946095]
  We introduce Lindblad-like quantum tomography (L$ell$QT) as a quantum characterization technique of time-correlated noise in quantum information processors.<n>We discuss L$ell$QT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function.
  arXiv  Detail & Related papers  (2024-03-28T19:29:12Z)
• Biased Estimator Channels for Classical Shadows [0.0]
  We consider a biased scheme, intentionally introducing a bias by rescaling the conventional classical shadows estimators.<n>We analytically prove average case as well as worst- and best-case scenarios, and rigorously prove that it is, in principle, always worth biasing the estimators.
  arXiv  Detail & Related papers  (2024-02-14T19:00:01Z)
• Enhanced observable estimation through classical optimization of informationally over-complete measurement data -- beyond classical shadows [0.0]
  We propose a method to optimize the dual POVM operators after the measurements have been carried out. We show that it can significantly reduce statistical errors with respect to canonical duals on multiple observable estimations.
  arXiv  Detail & Related papers  (2024-01-31T18:13:42Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Shadow tomography on general measurement frames [37.69303106863453]
  We provide a new perspective on shadow tomography by demonstrating its deep connections with the general theory of measurement frames. We show that the formalism of measurement frames offers a natural framework for shadow tomography. We demonstrate that a sought-after target of shadow tomography can be achieved for the entire class of tight rank-1 measurement frames.
  arXiv  Detail & Related papers  (2023-01-30T19:00:17Z)
• SQuAT: Sharpness- and Quantization-Aware Training for BERT [43.049102196902844]
  We propose sharpness- and quantization-aware training (SQuAT) Our method can consistently outperform state-of-the-art quantized BERT models under 2, 3, and 4-bit settings by 1%. Our experiments on empirical measurement of sharpness also suggest that our method would lead to flatter minima compared to other quantization methods.
  arXiv  Detail & Related papers  (2022-10-13T16:52:19Z)
• Neural network enhanced measurement efficiency for molecular groundstates [63.36515347329037]
  We adapt common neural network models to learn complex groundstate wavefunctions for several molecular qubit Hamiltonians. We find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables.
  arXiv  Detail & Related papers  (2022-06-30T17:45:05Z)
• Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables [0.0]
  We introduce a method for performing a single joint measurement that can be implemented locally. We derive bounds on the number of experimental repetitions required to estimate energies up to a certain precision. We adapt the joint measurement strategy to minimise the sample complexity when the implementation of measurements is assumed noisy.
  arXiv  Detail & Related papers  (2022-06-17T17:42:54Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• Neural network quantum state tomography in a two-qubit experiment [52.77024349608834]
  Machine learning inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states greatly improves the quality of the reconstructed states.
  arXiv  Detail & Related papers  (2020-07-31T17:25:12Z)
• Direct estimation of quantum coherence by collective measurements [54.97898890263183]
  We introduce a collective measurement scheme for estimating the amount of coherence in quantum states. Our scheme outperforms other estimation methods based on tomography or adaptive measurements. We show that our method is accessible with today's technology by implementing it experimentally with photons.
  arXiv  Detail & Related papers  (2020-01-06T03:50:42Z)

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.