Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.11846

Universal Sequential Changepoint Detection of Quantum Observables via Classical Shadows

Matteo Zecchin, Osvaldo Simeone, Aaditya Ramdas

quant-phcs.ITSubmitted Feb 12, 2026• Announced Feb 13, 2026• 0 citations
arXivHTMLPDF

Abstract

We study sequential quantum changepoint detection in settings where the pre- and post-change regimes are specified through constraints on the expectation values of a finite set of observables. We consider an architecture with separate measurement and detection modules, and assume that the observables relevant to the detector are unknown to the measurement device. For this scenario, we introduce shadow-based sequential changepoint e-detection (eSCD), a novel protocol that combines a universal measurement strategy based on classical shadows with a nonparametric sequential test built on e-detectors. Classical shadows provide universality with respect to the detector's choice of observables, while the e-detector framework enables explicit control of the average run length (ARL) to false alarm. Under an ARL constraint, we establish finite-sample guarantees on the worst-case expected detection delay of eSCD. Numerical experiments validate the theory and demonstrate that eSCD achieves performance competitive with observable-specific measurement strategies, while retaining full measurement universality.

Related papers

Autonomous Hamiltonian certification and changepoint detection

Steven T. Flammia, Dmitrii Khitrin, Muzhou Ma +3 more

Modern quantum devices require high-precision Hamiltonian dynamics, but environmental noise can cause calibrated Hamiltonian parameters to drift over time, necessitating expensive recalibration. Detecting when recalibration is needed is challenging, especially since the very gates required for sophisticated verification protocols may themselves be miscalibrated. While cloud quantum computing services implement heuristic routines for triggering recalibration, the fundamental limits of optimal recalibration are not yet known. We develop efficient Hamiltonian certification and changepoint detection protocols in the autonomous setting, where we cannot rely on an external noiseless device and use only single-qubit gates and measurements, making the protocols robust to the calibration issues for multi-qubit operations they aim to detect. For unknown $n$-qubit Hamiltonians $H$ and $H_0$ with operator norm bounded by $M$, our certification protocol distinguishes whether $\|H-H_0\|_F\geqε$ or $\|H-H_0\|_F\leq O(ε/\sqrt{n})$ with sample complexity $O(nM^2\ln(1/δ)/ε^2)$ and total evolution time $O(nM\ln(1/δ)/ε^2)$. We achieve this by evolving random stabilizer product states and performing adaptive single-qubit measurements based on a classically simulable hypothesis state. Extending this to continuous monitoring, we develop an online changepoint detection algorithm using the CUSUM procedure that achieves a detection delay time bound of $O(nM\ln(M\mathbb{E}_\infty[T])/ε^2)$, matching the known asymptotically optimal scaling with respect to false alarm run time $\mathbb{E}_\infty[T]$. Our approach enables quantum devices to autonomously monitor their own calibration status without requiring ancillary systems, entangling operations, or a trusted reference device, offering a practical solution for robust quantum computing with contemporary noisy devices.

quant-pharXiv:2603.26655•Mar 30, 2026•0 citations

Ultimate Limits for Quickest Quantum Change-Point Detection

Marco Fanizza, Christoph Hirche, John Calsamiglia

Detecting abrupt changes in data streams is crucial because they are often triggered by events that have important consequences if left unattended. Quickest change-point detection has become a vital sequential analysis primitive that aims at designing procedures that minimize the expected detection delay of a change subject to a bounded expected false alarm time. We put forward the quantum counterpart of this fundamental primitive on streams of quantum data. We give a lower bound on the mean minimum delay when the expected time of a false alarm is asymptotically large, under the most general quantum detection strategy, which is given by a sequence of adaptive collective (potentially weak) measurements on the growing string of quantum data. In addition, we give particular strategies based on repeated measurements on independent blocks of samples that asymptotically attain the lower bound and thereby establish the ultimate quantum limit for quickest change-point detection. Finally, we discuss online change-point detection in quantum channels.

arXiv:2208.03265•Physical Review Letters•Jul 14, 2023•13 citations

Asymptotically Optimal Quantum Universal Quickest Change Detection

Arick Grootveld, Haodong Yang, Nandan Sriranga +3 more

This paper investigates the quickest change detection of quantum states in a universal setting: specifically, where the post-change quantum state is not known a priori. We establish the asymptotic optimality of a two-stage approach in terms of worst average delay to detection. The first stage employs block POVMs with classical outputs that preserve quantum relative entropy to arbitrary precision. The second stage leverages a recently proposed windowed-CUSUM algorithm that is known to be asymptotically optimal for quickest change detection with an unknown post-change distribution in the classical setting.

quant-pharXiv:2602.02950•IEEE International Symposium on Information Theory (ISIT)•Feb 4, 2026•0 citations

Certifying quantum states without independence assumptions

Mariana Navarro, Leonardo Zambrano

Standard quantum verification and certification protocols often assume that experimental sources emit independent and identically distributed (i.i.d.) states. In realistic scenarios, however, temporal drift, memory effects, feedback, and correlated noise can violate this assumption, causing standard analyses to underestimate uncertainty and overestimate device performance. Here, we introduce a general framework for quantum verification and certification in which the state produced in each round may depend arbitrarily on the preceding experimental history. Our method provides rigorous confidence intervals for observable expectation values averaged over the experimental trajectory. The framework covers both full verification, in which every state is measured, and spot-checking certification, in which a randomly selected subset is tested to certify the average observable value of the complementary, remaining systems. We apply the framework to importance-sampled Pauli measurements for direct fidelity estimation, energy estimation, and entanglement witnessing, and to classical shadows, allowing multiple observables to be certified simultaneously from the same test data. We illustrate the framework numerically and demonstrate it experimentally through Bell-state certification on a quantum processor.

quant-pharXiv:2606.31913•Jul 1, 2026•0 citations

Estimating Quantum Hamiltonians via Joint Measurements of Noisy Noncommuting Observables

Daniel McNulty, Filip B. Maciejewski, Michał Oszmaniec

Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this Letter, we introduce a method for this purpose based on performing a single joint measurement that can be implemented locally and whose marginals yield noisy (unsharp) versions of the target set of noncommuting Pauli observables. We derive bounds on the number of experimental repetitions required to estimate energies up to a certain precision. We compare this strategy to the classical shadow formalism and show that our method yields the same performance as the locally biased classical shadow protocol. We also highlight some general connections between the two approaches by showing that classical shadows can be used to construct joint measurements and vice versa. Finally, we adapt the joint measurement strategy to minimise the sample complexity when the implementation of measurements is assumed noisy. This can provide significant efficiency improvements compared to known generalizations of classical shadows to noisy scenarios.

arXiv:2206.08912•Physical Review Letters•Mar 9, 2023•17 citations

Finite-Sample Selected Covariance Spectra in Classical Shadows

Masahito Hayashi

Classical shadows use a single measurement snapshot to estimate many observables. These estimates are jointly distributed, and their covariance is not determined by their expectation values or individual variances. It also differs from physical correlations between observables because it depends on the measurement and reconstruction protocol. We study the covariance matrix for a fixed set of shadow estimates and its spectrum. For general shadow protocols, we give a finite-sample operator-norm bound for the empirical covariance computed using the sample mean. This bound also controls the eigenvalues and isolated spectral subspaces of the covariance matrix. For local product shadow protocols with fixed local dimension, observables supported on a bounded number of sites lead to bounds that do not depend on the total system size, provided that the number of selected observables and the relevant local reconstruction factors remain bounded. For biased local Pauli shadows, we obtain explicit finite-sample bounds and an exact covariance formula determined by Pauli compatibility and local basis probabilities. A comparison with global Clifford shadows shows that dimension-independent covariance estimation depends on the measurement protocol and does not follow from the general theory alone.

quant-pharXiv:2606.00527•Jun 2, 2026•0 citations
We study sequential quantum changepoint detection in settings where the pre- and post-change regimes are specified through constraints on the expectation values of a finite set of observables. We consider an architecture with separate measurement and detection modules, and assume that the observables relevant to the detector are unknown to the measurement device. For this scenario, we introduce shadow-based sequential changepoint e-detection (eSCD), a novel protocol that combines a universal measurement strategy based on classical shadows with a nonparametric sequential test built on e-detectors. Classical shadows provide universality with respect to the detector's choice of observables, while the e-detector framework enables explicit control of the average run length (ARL) to false alarm. Under an ARL constraint, we establish finite-sample guarantees on the worst-case expected detection delay of eSCD. Numerical experiments validate the theory and demonstrate that eSCD achieves performance competitive with observable-specific measurement strategies, while retaining full measurement universality.
Modern quantum devices require high-precision Hamiltonian dynamics, but environmental noise can cause calibrated Hamiltonian parameters to drift over time, necessitating expensive recalibration. Detecting when recalibration is needed is challenging, especially since the very gates required for sophisticated verification protocols may themselves be miscalibrated. While cloud quantum computing services implement heuristic routines for triggering recalibration, the fundamental limits of optimal recalibration are not yet known. We develop efficient Hamiltonian certification and changepoint detection protocols in the autonomous setting, where we cannot rely on an external noiseless device and use only single-qubit gates and measurements, making the protocols robust to the calibration issues for multi-qubit operations they aim to detect. For unknown nnn-qubit Hamiltonians HHH and H0H_0H0​ with operator norm bounded by MMM, our certification protocol distinguishes whether ∥H−H0∥F≥ε\|H-H_0\|_F\geqε∥H−H0​∥F​≥ε or ∥H−H0∥F≤O(ε/n)\|H-H_0\|_F\leq O(ε/\sqrt{n})∥H−H0​∥F​≤O(ε/n​) with sample complexity O(nM2ln⁡(1/δ)/ε2)O(nM^2\ln(1/δ)/ε^2)O(nM2ln(1/δ)/ε2) and total evolution time O(nMln⁡(1/δ)/ε2)O(nM\ln(1/δ)/ε^2)O(nMln(1/δ)/ε2). We achieve this by evolving random stabilizer product states and performing adaptive single-qubit measurements based on a classically simulable hypothesis state. Extending this to continuous monitoring, we develop an online changepoint detection algorithm using the CUSUM procedure that achieves a detection delay time bound of O(nMln⁡(ME∞[T])/ε2)O(nM\ln(M\mathbb{E}_\infty[T])/ε^2)O(nMln(ME∞​[T])/ε2), matching the known asymptotically optimal scaling with respect to false alarm run time E∞[T]\mathbb{E}_\infty[T]E∞​[T]. Our approach enables quantum devices to autonomously monitor their own calibration status without requiring ancillary systems, entangling operations, or a trusted reference device, offering a practical solution for robust quantum computing with contemporary noisy devices.
Detecting abrupt changes in data streams is crucial because they are often triggered by events that have important consequences if left unattended. Quickest change-point detection has become a vital sequential analysis primitive that aims at designing procedures that minimize the expected detection delay of a change subject to a bounded expected false alarm time. We put forward the quantum counterpart of this fundamental primitive on streams of quantum data. We give a lower bound on the mean minimum delay when the expected time of a false alarm is asymptotically large, under the most general quantum detection strategy, which is given by a sequence of adaptive collective (potentially weak) measurements on the growing string of quantum data. In addition, we give particular strategies based on repeated measurements on independent blocks of samples that asymptotically attain the lower bound and thereby establish the ultimate quantum limit for quickest change-point detection. Finally, we discuss online change-point detection in quantum channels.
This paper investigates the quickest change detection of quantum states in a universal setting: specifically, where the post-change quantum state is not known a priori. We establish the asymptotic optimality of a two-stage approach in terms of worst average delay to detection. The first stage employs block POVMs with classical outputs that preserve quantum relative entropy to arbitrary precision. The second stage leverages a recently proposed windowed-CUSUM algorithm that is known to be asymptotically optimal for quickest change detection with an unknown post-change distribution in the classical setting.
Standard quantum verification and certification protocols often assume that experimental sources emit independent and identically distributed (i.i.d.) states. In realistic scenarios, however, temporal drift, memory effects, feedback, and correlated noise can violate this assumption, causing standard analyses to underestimate uncertainty and overestimate device performance. Here, we introduce a general framework for quantum verification and certification in which the state produced in each round may depend arbitrarily on the preceding experimental history. Our method provides rigorous confidence intervals for observable expectation values averaged over the experimental trajectory. The framework covers both full verification, in which every state is measured, and spot-checking certification, in which a randomly selected subset is tested to certify the average observable value of the complementary, remaining systems. We apply the framework to importance-sampled Pauli measurements for direct fidelity estimation, energy estimation, and entanglement witnessing, and to classical shadows, allowing multiple observables to be certified simultaneously from the same test data. We illustrate the framework numerically and demonstrate it experimentally through Bell-state certification on a quantum processor.
Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this Letter, we introduce a method for this purpose based on performing a single joint measurement that can be implemented locally and whose marginals yield noisy (unsharp) versions of the target set of noncommuting Pauli observables. We derive bounds on the number of experimental repetitions required to estimate energies up to a certain precision. We compare this strategy to the classical shadow formalism and show that our method yields the same performance as the locally biased classical shadow protocol. We also highlight some general connections between the two approaches by showing that classical shadows can be used to construct joint measurements and vice versa. Finally, we adapt the joint measurement strategy to minimise the sample complexity when the implementation of measurements is assumed noisy. This can provide significant efficiency improvements compared to known generalizations of classical shadows to noisy scenarios.
Classical shadows use a single measurement snapshot to estimate many observables. These estimates are jointly distributed, and their covariance is not determined by their expectation values or individual variances. It also differs from physical correlations between observables because it depends on the measurement and reconstruction protocol. We study the covariance matrix for a fixed set of shadow estimates and its spectrum. For general shadow protocols, we give a finite-sample operator-norm bound for the empirical covariance computed using the sample mean. This bound also controls the eigenvalues and isolated spectral subspaces of the covariance matrix. For local product shadow protocols with fixed local dimension, observables supported on a bounded number of sites lead to bounds that do not depend on the total system size, provided that the number of selected observables and the relevant local reconstruction factors remain bounded. For biased local Pauli shadows, we obtain explicit finite-sample bounds and an exact covariance formula determined by Pauli compatibility and local basis probabilities. A comparison with global Clifford shadows shows that dimension-independent covariance estimation depends on the measurement protocol and does not follow from the general theory alone.