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:2303.15519 · Quantum

Randomized measurement protocols for lattice gauge theories

Jacob Bringewatt, Jonathan Kunjummen, Niklas Mueller

Published Mar 27, 2024• 11 citations
arXivHTMLPDF

Abstract

Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. This can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments. Crucially, unlike symmetry-blind randomized measurement protocols, these latter tasks can be performed without relearning symmetries via full reconstruction of the density matrix.

DOI
10.22331/q-2024-03-27-1300

Related papers

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

Jacob Bringewatt, Henry Froland, Andreas Elben +1 more

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 for $\mathbb{Z}_2$ lattice gauge theory, where a dual formulation enables a rigorous analysis of resource requirements, including both circuit depth and sample complexity. Our approaches can offer exponential improvements in sample complexity over symmetry-agnostic methods, albeit at the cost of increased circuit complexity. While our analysis is restricted to $\mathbb{Z}_2$ lattice gauge theory, our approach offers a blueprint for similar protocols for more general lattice gauge theory models which are currently at the forefront of quantum simulation efforts.

quant-pharXiv:2511.02904•Quantum•Nov 6, 2025•0 citations

Noise-mitigated randomized measurements and self-calibrating shadow estimation

Emilio Onorati, Jonas Kitzinger, Jonas Helsen +4 more

Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible measurements, serving as the building block of prominent schemes like shadow estimation. In the real world, however, the implementation of the random gates at the core of these schemes is susceptible to various sources of noise and imperfections, strongly limiting the applicability of protocols. To attenuate the impact of this shortcoming, in this work we introduce an error-mitigated method of randomized measurements, giving rise to a robust shadow estimation procedure. On the practical side, we show that error mitigation and shadow estimation can be carried out using the same session of quantum experiments, hence ensuring that we can address and mitigate the noise affecting the randomization measurements. Mathematically, we develop a picture derived from Fourier-transforms to connect randomized benchmarking and shadow estimation. We prove rigorous performance guarantees and show the functioning using comprehensive numerics. More conceptually, we demonstrate that, if properly used, easily accessible data from randomized benchmarking schemes already provide such valuable diagnostic information to inform about the noise dynamics and to assist in quantum learning procedures.

arXiv:2403.04751•Mar 7, 2024•3 citations

Quantum State Estimation via Randomized Benchmarking

Jincheng Zhang

Quantum state estimation is a fundamental task in quantum information processing, crucial for applications such as quantum metrology, quantum sensing, and quantum process tomography. However, conventional methods for estimating the state of a quantum system often suffer from significant computational complexity, particularly for large systems or when high precision is required. This work introduces a novel approach to quantum state estimation that leverages Randomized Benchmarking (RB) techniques. By adapting RB protocols specifically designed for quantum systems, we achieve efficient and accurate state estimation with a reduced number of measurements compared to traditional methods. The core idea is to use a series of carefully designed, randomized measurements to extract information about the unknown quantum state. The resulting estimation process avoids the need for exhaustive state tomography, dramatically reducing the computational burden. We detail the mathematical framework underlying this approach, including the formulation of the RB protocol, the estimation algorithm, and an analysis of the estimation error. The results demonstrate the effectiveness and potential of this method for various quantum state estimation scenarios.

•Sep 3, 2026•0 citations

Dual-frame optimization for informationally complete quantum measurements

Laurin E. Fischer, T. K. L. Dao, Ivano Tavernelli +1 more

Randomized measurement protocols such as classical shadows represent powerful resources for quantum technologies, with applications ranging from quantum state characterization and process tomography to machine learning and error mitigation. Recently, the notion of measurement dual frames, in which classical shadows are generalized to dual operators of positive operator-valued measure (POVM) effects, resurfaced in the literature. This brought attention to additional degrees of freedom in the postprocessing stage of randomized measurements that are often neglected by established techniques. In this work, we leverage dual frames to construct improved observable estimators from informationally complete measurement samples. We introduce novel classes of parametrized frame superoperators and optimization-free dual frames based on empirical frequencies, which offer advantages over their canonical counterparts while retaining computational efficiency. Remarkably, this comes at almost no quantum or classical cost, thus rendering dual frame optimization a valuable addition to the randomized measurement toolbox. Published by the American Physical Society 2024

arXiv:2401.18071•Physical Review A•Jun 11, 2024•19 citations

Every Benchmark All at Once

Ana Silva, Eliška Greplová

As quantum technology matures, the efficient benchmarking of quantum devices remains a key challenge. Although sample-efficient, information-theoretic benchmarking techniques have recently been proposed, there is still a gap in adapting these techniques to contemporary experiments. In this work, we re-formulate five of the most common randomized benchmarking techniques in the modern language of the gate-set shadow tomography. This reformulation brings along several concrete advantages over conventional formulations of randomized benchmarking. For standard and interleaved randomized benchmarking, we can reduce the required gate-set size and, using median-of-means estimators, also reduce the required experimental sample size. For simultaneous and correlated randomized benchmarking, we can additionally reconstruct the Pauli-terms of correlated noise channels using additional post-processing of only a single experimental dataset. We also present a minimal approach to extract leakage errors. Our work provides a clear avenue for comprehensive, reliable, and convenient benchmarking of quantum devices, with all methods formulated under a single umbrella technique that can be easily adapted to a range of experimental quantities and gate sets.

arXiv:2510.18453•Oct 21, 2025•0 citations

Global Entanglement Quantification via Classical Shadows

João P. Engster, Eduardo I. Duzzioni

Detecting and characterizing quantum correlations are tasks of great relevance in quantum information. More specifically, quantifying the amount of multipartite entanglement is a known difficult task, even for pure states. To this end, several entanglement measures have been proposed, although there is currently no universal manner to do so. In this work, we propose the classical shadows technique to measure the generalized global entanglement introduced in Phys. Rev. A 74, 022314. This particular multipartite entanglement quantifier $E_G^{(n)}$ relies on the linear entropies of all $n$-qubit partitions of a state. As the linear entropy can be written in terms of a complete set of observables of the subsystem, we employ classical shadows to estimate many observables with fewer measurements. We simulate the quantification of $E_G^{(n)}$ for well-known entangled states and for random states, comparing shadow estimations and grouping techniques. Our results show a clear advantage of classical shadows over direct estimation approaches, indicating that it can be a useful tool to quantify entanglement without the need to reconstruct the density operator of the whole system.

quant-pharXiv:2609.21579•Sep 21, 2026•0 citations
Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. This can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments. Crucially, unlike symmetry-blind randomized measurement protocols, these latter tasks can be performed without relearning symmetries via full reconstruction of the density matrix.
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 for Z2\mathbb{Z}_2Z2​ lattice gauge theory, where a dual formulation enables a rigorous analysis of resource requirements, including both circuit depth and sample complexity. Our approaches can offer exponential improvements in sample complexity over symmetry-agnostic methods, albeit at the cost of increased circuit complexity. While our analysis is restricted to Z2\mathbb{Z}_2Z2​ lattice gauge theory, our approach offers a blueprint for similar protocols for more general lattice gauge theory models which are currently at the forefront of quantum simulation efforts.
Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible measurements, serving as the building block of prominent schemes like shadow estimation. In the real world, however, the implementation of the random gates at the core of these schemes is susceptible to various sources of noise and imperfections, strongly limiting the applicability of protocols. To attenuate the impact of this shortcoming, in this work we introduce an error-mitigated method of randomized measurements, giving rise to a robust shadow estimation procedure. On the practical side, we show that error mitigation and shadow estimation can be carried out using the same session of quantum experiments, hence ensuring that we can address and mitigate the noise affecting the randomization measurements. Mathematically, we develop a picture derived from Fourier-transforms to connect randomized benchmarking and shadow estimation. We prove rigorous performance guarantees and show the functioning using comprehensive numerics. More conceptually, we demonstrate that, if properly used, easily accessible data from randomized benchmarking schemes already provide such valuable diagnostic information to inform about the noise dynamics and to assist in quantum learning procedures.
Quantum state estimation is a fundamental task in quantum information processing, crucial for applications such as quantum metrology, quantum sensing, and quantum process tomography. However, conventional methods for estimating the state of a quantum system often suffer from significant computational complexity, particularly for large systems or when high precision is required. This work introduces a novel approach to quantum state estimation that leverages Randomized Benchmarking (RB) techniques. By adapting RB protocols specifically designed for quantum systems, we achieve efficient and accurate state estimation with a reduced number of measurements compared to traditional methods. The core idea is to use a series of carefully designed, randomized measurements to extract information about the unknown quantum state. The resulting estimation process avoids the need for exhaustive state tomography, dramatically reducing the computational burden. We detail the mathematical framework underlying this approach, including the formulation of the RB protocol, the estimation algorithm, and an analysis of the estimation error. The results demonstrate the effectiveness and potential of this method for various quantum state estimation scenarios.
Randomized measurement protocols such as classical shadows represent powerful resources for quantum technologies, with applications ranging from quantum state characterization and process tomography to machine learning and error mitigation. Recently, the notion of measurement dual frames, in which classical shadows are generalized to dual operators of positive operator-valued measure (POVM) effects, resurfaced in the literature. This brought attention to additional degrees of freedom in the postprocessing stage of randomized measurements that are often neglected by established techniques. In this work, we leverage dual frames to construct improved observable estimators from informationally complete measurement samples. We introduce novel classes of parametrized frame superoperators and optimization-free dual frames based on empirical frequencies, which offer advantages over their canonical counterparts while retaining computational efficiency. Remarkably, this comes at almost no quantum or classical cost, thus rendering dual frame optimization a valuable addition to the randomized measurement toolbox. Published by the American Physical Society 2024
As quantum technology matures, the efficient benchmarking of quantum devices remains a key challenge. Although sample-efficient, information-theoretic benchmarking techniques have recently been proposed, there is still a gap in adapting these techniques to contemporary experiments. In this work, we re-formulate five of the most common randomized benchmarking techniques in the modern language of the gate-set shadow tomography. This reformulation brings along several concrete advantages over conventional formulations of randomized benchmarking. For standard and interleaved randomized benchmarking, we can reduce the required gate-set size and, using median-of-means estimators, also reduce the required experimental sample size. For simultaneous and correlated randomized benchmarking, we can additionally reconstruct the Pauli-terms of correlated noise channels using additional post-processing of only a single experimental dataset. We also present a minimal approach to extract leakage errors. Our work provides a clear avenue for comprehensive, reliable, and convenient benchmarking of quantum devices, with all methods formulated under a single umbrella technique that can be easily adapted to a range of experimental quantities and gate sets.
Detecting and characterizing quantum correlations are tasks of great relevance in quantum information. More specifically, quantifying the amount of multipartite entanglement is a known difficult task, even for pure states. To this end, several entanglement measures have been proposed, although there is currently no universal manner to do so. In this work, we propose the classical shadows technique to measure the generalized global entanglement introduced in Phys. Rev. A 74, 022314. This particular multipartite entanglement quantifier EG(n)E_G^{(n)}EG(n)​ relies on the linear entropies of all nnn-qubit partitions of a state. As the linear entropy can be written in terms of a complete set of observables of the subsystem, we employ classical shadows to estimate many observables with fewer measurements. We simulate the quantification of EG(n)E_G^{(n)}EG(n)​ for well-known entangled states and for random states, comparing shadow estimations and grouping techniques. Our results show a clear advantage of classical shadows over direct estimation approaches, indicating that it can be a useful tool to quantify entanglement without the need to reconstruct the density operator of the whole system.