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.
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.
Efficiently estimating properties of large and strongly coupled quantum systems is a central focus in many-body physics and quantum information theory.While quantum computers promise speedups for many of these tasks, near-term devices are prone to noise that will generally reduce the accuracy of such estimates.Here, we propose a sample-efficient and noise-resilient protocol for learning properties of quantum states building on the shadow estimation scheme [Huang et al., Nature Physics 16, 1050-1057(2020)].By introducing an experimentally friendly calibration procedure, our protocol can efficiently characterize and mitigate noises in the shadow estimation scheme, given only minimal assumptions on the experimental conditions.When the strength of noises can be bounded, our protocol approximately retains the same order of sample efficiency as the standard shadow estimation scheme, while also possessing a provable noise resilience.We give rigorous bounds on the sample complexity of our protocol and demonstrate its performance with several numerical experiments, including estimations of quantum fidelity, correlation functions and energy expectations, etc., which highlight a wide spectrum of potential applications of our protocol on near-term devices.
Efficiently estimating properties of large and strongly coupled quantum systems is a central focus in many-body physics and quantum information theory. While quantum computers promise speedups for many of these tasks, near-term devices are prone to noise that will generally reduce the accuracy of such estimates. Here, we propose a sample-efficient and noise-resilient protocol for learning properties of quantum states building on the shadow estimation scheme [Huang et al., Nature Physics 16, 1050-1057 (2020)]. By introducing an experimentally friendly calibration procedure, our protocol can efficiently characterize and mitigate noises in the shadow estimation scheme, given only minimal assumptions on the experimental conditions. When the strength of noises can be bounded, our protocol approximately retains the same order of sample efficiency as the standard shadow estimation scheme, while also possessing a provable noise resilience. We give rigorous bounds on the sample complexity of our protocol and demonstrate its performance with several numerical experiments, including estimations of quantum fidelity, correlation functions and energy expectations, etc., which highlight a wide spectrum of potential applications of our protocol on near-term devices.
With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations. However, current quantum devices are only capable of short unstructured gate sequences followed by native measurements. We accept this limitation and turn it into a new paradigm for characterizing quantum gate-sets. A single experiment-random sequence estimation-solves a wealth of estimation problems, with all complexity moved to classical post-processing. We derive robust channel variants of shadow estimation with close-to-optimal performance guarantees and use these as a primitive for partial, compressive and full process tomography as well as the learning of Pauli noise. We discuss applications to the quantum gate engineering cycle, and propose novel methods for the optimization of quantum gates and diagnosing cross-talk.
With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations. However, current quantum devices are only capable of short unstructured gate sequences followed by native measurements. We accept this limitation and turn it into a new paradigm for characterizing quantum gate-sets. A single experiment—random sequence estimation—solves a wealth of estimation problems, with all complexity moved to classical post-processing. We derive robust channel variants of shadow estimation with close-to-optimal performance guarantees and use these as a primitive for partial, compressive and full process tomography as well as the learning of Pauli noise. We discuss applications to the quantum gate engineering cycle, and propose novel methods for the optimization of quantum gates and diagnosing cross-talk.
Measurement overhead and hardware noise present fundamental obstacles to the practical realization of quantum algorithms on near-term quantum devices. In many quantum applications, the dominant computational cost arises from repeated measurements needed to extract accurate information and from handling noise effects. This dissertation develops a unified framework for efficient measurement and error mitigation in quantum algorithms.In this work, measurement is treated as a controllable and designable component across hardware, algorithmic, and statistical levels, rather than as a fixed final step. By tailoring measurement schemes and estimators, we show that substantial reductions in measurement cost can be achieved without sacrificing accuracy. This approach is developed and validated across multiple settings, from hardware-level randomized measurement implementations to algorithm-level molecular energy estimation.At the hardware level, we investigate randomized measurement schemes based on photonic metasurfaces. We find that the device itself naturally realizes the required family of measurement bases without repeated active optical reconfiguration, providing an efficient platform for randomized measurements. We analyze the effect of realistic measurement noise and develop calibration-based error mitigation techniques that suppress noise-induced bias. Numerical studies show that this approach enables accurate estimation of state properties under realistic measurement noise.At the algorithmic level, we investigate measurement-efficient quantum eigen solvers through the Non-Orthogonal Quantum Eigensolver (NOQE). We develop a detailed implementation framework for NOQE, including circuit construction and simplification, analysis of measurement complexity, and resource estimation. Building on this understanding, we incorporate randomized measurements as an alternative to standard Hadamard-test-based schemes and develop shadow-tomography-enhanced variants of NOQE that significantly reduce circuit complexity and qubit requirements while maintaining favorable sample complexity. Shadow-based error mitigation methods, including shadow distillation, further improve robustness against noise.Finally, we investigate a more fundamental redesign of the NOQE measurement task by reformulating matrix-element estimation as a quantum amplitude estimation problem. By integrating iterative quantum amplitude estimation into the NOQE framework, we replace the original incoherent sampling-based estimation with coherent information accumulation through amplitude amplification and achieve near-Heisenberg scaling in measurement complexity, improving on the standard sampling-based methods. Numerical results for molecular energy estimation demonstrate that this approach reaches chemical accuracy with fewer queries than the original NOQE.Overall, this dissertation shows that measurement overhead is not a fixed limitation, but a resource bottleneck that can be identified and reduced at multiple levels in quantum applications. Across the settings studied here, improvements are achieved at different layers, including hardware-aware randomized measurements, algorithm-level redesign of measurement protocols, estimator-level error mitigation, and statistical improvements based on coherent information accumulation. Taken together, these results provide a unified framework for understanding and reducing measurement cost under realistic noise, and offer practical guidance for the design of quantum algorithms on near-term quantum devices.
Randomized benchmarking refers to a collection of protocols that in the past decade have become central methods for characterizing quantum gates.These protocols aim at efficiently estimating the quality of a set of quantum gates in a way that is resistant to state preparation and measurement errors.Over the years many versions have been developed, however a comprehensive theoretical treatment of randomized benchmarking has been missing.In this work, we develop a rigorous framework of randomized benchmarking general enough to encompass virtually all known protocols as well as novel, more flexible extensions.Overcoming previous limitations on error models and gate sets, this framework allows us, for the first time, to formulate realistic conditions under which we can rigorously guarantee that the output of any randomized benchmarking experiment is well described by a linear combination of matrix exponential decays.We complement this with a detailed analysis of the fitting problem associated with randomized benchmarking data.We introduce modern signal processing techniques to randomized benchmarking, prove analytical sample complexity bounds, and numerically evaluate performance and limitations.In order to reduce the resource demands of this fitting problem, we introduce novel, scalable postprocessing techniques to isolate exponential decays, significantly improving the practical feasibility of a large set of randomized benchmarking protocols.These postprocessing techniques overcome shortcomings in efficiency of several previously proposed methods such as character benchmarking and linear-cross entropy benchmarking.Finally, we discuss, in full generality, how and when randomized benchmarking decay rates can be used to infer quality measures like the average fidelity.On the technical side, our work substantially extends the recently developed Fourier-theoretic perspective on randomized benchmarking by making use of the perturbation theory of invariant subspaces, as well as ideas from signal processing.