Classical shadows for sample-efficient measurements of gauge-invariant observables

• URL: http://arxiv.org/abs/2511.02904v1
• Date: Tue, 04 Nov 2025 19:00:01 GMT
• Title: Classical shadows for sample-efficient measurements of gauge-invariant observables
• Authors: Jacob Bringewatt, Henry Froland, Andreas Elben, Niklas Mueller,
• Abstract summary: We develop three classical shadow protocols tailored to systems with local (or gauge) symmetries.<n>We demonstrate these trade-offs using a $mathZ$ gauge theory, where a dual formulation enables a rigorous analysis of resource requirements.
• Score: 0.002718525106069543
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classical shadows provide a versatile framework for estimating many properties of quantum states from repeated, randomly chosen measurements without requiring full quantum state tomography. When prior information is available, such as knowledge of symmetries of states and operators, this knowledge can be exploited to significantly improve sample efficiency. In this work, we develop three classical shadow protocols tailored to systems with local (or gauge) symmetries to enable efficient prediction of gauge-invariant observables in lattice gauge theory models which are currently at the forefront of quantum simulation efforts. For such models, our approaches can offer exponential improvements in sample complexity over symmetry-agnostic methods, albeit at the cost of increased circuit complexity. We demonstrate these trade-offs using a $\mathbb{Z}_2$ lattice gauge theory, where a dual formulation enables a rigorous analysis of resource requirements, including both circuit depth and sample complexity.

Related papers

• Simulating Fully Gauge-Fixed SU(2) Hamiltonian Dynamics on Digital Quantum Computers [1.0716269823733435]
  This work focuses on the quantum simulation of the smallest non-trivial system: two plaquettes with open boundary conditions.<n>It is found that as few as three qubits per plaquette is sufficient to reach per-mille level precision on predictions for observables.
  arXiv  Detail & Related papers  (2025-12-28T04:56:25Z)
• Signatures of Topological Symmetries on a Noisy Quantum Simulator [0.0]
  Topological symmetries, invertible and otherwise, play a fundamental role in the investigation of quantum field theories.<n>Quantum simulators based on engineered solid-state devices provide a novel alternative to conventional condensed matter systems for realizing these models.<n>In this work, eigenstates of impurity Hamiltonians and loop operators associated with the topological symmetries for the Ising conformal field theory are realized on IBM's Kingston simulator.
  arXiv  Detail & Related papers  (2025-10-16T15:51:56Z)
• Excitation Amplitude Sampling for Low Variance Electronic Structure on Quantum Computers [0.0]
  We combine classicalenergetics with partial shadow tomography to enable efficient protocols for extracting information from correlated ab initio electronic systems encoded on quantum devices.<n>We can demonstrate an almost two order of magnitude of reduction in required number of shots for a given quantum state excitation amplitudes.<n>We find a high-degree of noise resilience of these estimators on real quantum devices, with up to an order of magnitude increase in the tolerated noise compared to traditional techniques.
  arXiv  Detail & Related papers  (2025-06-18T13:13:09Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Restoring symmetries in quantum computing using Classical Shadows [0.0]
  We introduce a method to enforce some symmetries starting from a trial wave-function prepared on quantum computers that might not respect these symmetries. We show that the present scheme can be competitive to predict observables on symmetry-restored states once optimization through derandomization is employed.
  arXiv  Detail & Related papers  (2023-11-08T10:11:01Z)
• Efficient Classical Shadow Tomography through Many-body Localization Dynamics [4.923287660970805]
  We introduce an alternative approach founded on the dynamics of many-body localization. We demonstrate that our scheme achieves remarkable efficiency comparable to shallow circuits.
  arXiv  Detail & Related papers  (2023-09-03T19:50:28Z)
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution [44.99833362998488]
  We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate quantum systems classically. We prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias. We show that a different scheme based on the solution of an optimization problem at each time step is free from such problems.
  arXiv  Detail & Related papers  (2023-05-23T17:38:10Z)
• Generalization Metrics for Practical Quantum Advantage in Generative Models [68.8204255655161]
  Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
  arXiv  Detail & Related papers  (2022-01-21T16:35:35Z)
• Sampling asymmetric open quantum systems for artificial neural networks [77.34726150561087]
  We present a hybrid sampling strategy which takes asymmetric properties explicitly into account, achieving fast convergence times and high scalability for asymmetric open systems. We highlight the universal applicability of artificial neural networks, underlining the universal applicability of neural networks.
  arXiv  Detail & Related papers  (2020-12-20T18:25:29Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

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.