Classical shadows for non-iid quantum sources

• URL: http://arxiv.org/abs/2603.05137v1
• Date: Thu, 05 Mar 2026 13:05:28 GMT
• Title: Classical shadows for non-iid quantum sources
• Authors: Leonardo Zambrano,
• Abstract summary: We introduce a robust classical shadow protocol based on a truncated mean estimator.<n>We prove that its sample complexity matches the standard i.i.d. scaling governed by the shadow norm.<n>Our results establish the robustness of the shadow formalism beyond the i.i.d. regime.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical shadow tomography has emerged as a powerful framework for predicting properties of quantum many-body systems with favorable sample complexity. Standard theoretical guarantees, however, rely on the assumption that experimental rounds are independent and identically distributed (i.i.d.). This idealization is often violated in practice, where parameter drift, environmental noise, and active feedback generate history-dependent sequences of states or channels. To address this, we introduce a robust classical shadow protocol based on a truncated mean estimator. We prove that its sample complexity for predicting properties of the time-averaged state or channel matches the standard i.i.d. scaling governed by the shadow norm, even when experimental rounds depend arbitrarily on the past. Our results establish the robustness of the shadow formalism beyond the i.i.d. regime.

Related papers

• How Sampling Shapes LLM Alignment: From One-Shot Optima to Iterative Dynamics [65.67654005892469]
  We show that proper instance-dependent sampling can yield stronger ranking guarantees, while skewed on-policy sampling can induce excessive concentration under structured preferences.<n>We then analyze iterative alignment dynamics in which the learned policy feeds back into future sampling and reference policies.<n>Our theoretical insights extend to Direct Preference Optimization, indicating the phenomena we captured are common to a broader class of preference-alignment methods.
  arXiv  Detail & Related papers  (2026-02-12T17:11:08Z)
• 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)
• Stability of classical shadows under gate-dependent noise [0.4574830585715129]
  We prove that any shadow estimation involving Clifford gate stabilizers is stable for bounded noise circuits.<n>We find that so-called robust shadows can introduce a large presence of gate-dependent noise compared to unmitigated classical shadows.<n>On a level, we identify average noise channels that affect shadow estimators and allow for a more fine-grained control of noise-induced biases.
  arXiv  Detail & Related papers  (2023-10-30T19:00:18Z)
• A U-turn on Double Descent: Rethinking Parameter Counting in Statistical Learning [68.76846801719095]
  We show that double descent appears exactly when and where it occurs, and that its location is not inherently tied to the threshold p=n. This provides a resolution to tensions between double descent and statistical intuition.
  arXiv  Detail & Related papers  (2023-10-29T12:05:39Z)
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling [44.99833362998488]
  A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient.<n>We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics.<n>We establish that scaling predictions are matched by a privileged process and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all time scales.
  arXiv  Detail & Related papers  (2023-10-17T15:41:50Z)
• Testing quantum Darwinism dependence on observers' resources [62.997667081978825]
  We use time-frequency signal processing techniques to understand if and how the emergent classical picture is changed. We show the crucial role of correlations in the reconstruction procedure and point to the importance of studying the type of measurements that must be done to access an objective classical data.
  arXiv  Detail & Related papers  (2023-06-26T15:02:24Z)
• On Classical and Hybrid Shadows of Quantum States [0.0]
  Classical shadows are a computationally efficient approach to storing quantum states on a classical computer. We discuss the advantages and limitations of using classical shadows to simulate many-body dynamics. We introduce the notion of a hybrid shadow, constructed from measurements on a part of the system instead of the entirety.
  arXiv  Detail & Related papers  (2022-06-14T06:25:24Z)
• Exponential Tail Local Rademacher Complexity Risk Bounds Without the Bernstein Condition [30.401770841788718]
  The local Rademacher toolbox is one of the most successful general-purpose toolboxes. Applying the Bernstein theory to problems where optimal performance is only achievable via non-probable settings yields an exponential-tail excess risk. Our results apply to improper prediction regimes not covered by the toolbox.
  arXiv  Detail & Related papers  (2022-02-23T12:27:53Z)
• Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences [41.42601188771239]
  We create non-classical states of light in three-dimensional microwave cavities. These states are useful for quantum computation. We show that this way of creating non-classical states is robust to fluctuations of the system parameters.
  arXiv  Detail & Related papers  (2021-11-15T18:20:38Z)
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics [0.0]
  We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles. We numerically demonstrate our approach for finite-depth local unitary circuits and finite-time local-Hamiltonian generated evolutions.
  arXiv  Detail & Related papers  (2021-07-10T11:34:51Z)
• Deterministic Gibbs Sampling via Ordinary Differential Equations [77.42706423573573]
  This paper presents a general construction of deterministic measure-preserving dynamics using autonomous ODEs and tools from differential geometry. We show how Hybrid Monte Carlo and other deterministic samplers follow as special cases of our theory.
  arXiv  Detail & Related papers  (2021-06-18T15:36:09Z)
• A Bayesian analysis of classical shadows [0.2867517731896504]
  We investigate classical shadows through the lens of Bayesian mean estimation (BME) In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations. We introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows.
  arXiv  Detail & Related papers  (2020-12-16T14:45:18Z)
• Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes [32.02612871707347]
  We propose ConvNP, which endows Neural Processes (NPs) with translation equivariance and extends convolutional conditional NPs to allow for dependencies in the predictive distribution. We demonstrate the strong performance and generalization capabilities of ConvNPs on 1D, regression image completion, and various tasks with real-world-temporal data.
  arXiv  Detail & Related papers  (2020-07-02T18:25:27Z)

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.