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:2312.04211 · Communications Physics

Readout error mitigated quantum state tomography tested on superconducting qubits

Adrian Skasberg Aasen, Andras Di Giovanni, Hannes Rotzinger, Alexey Vladimirovich Ustinov, Martin Gärttner

Published Sep 6, 2024• 15 citations
arXivHTMLPDF

Abstract

Abstract Quantum technologies rely heavily on accurate control and reliable readout of quantum systems. Current experiments are limited by numerous sources of noise that can only be partially captured by simple analytical models and additional characterization of the noise sources is required. We test the ability of readout error mitigation to correct noise found in systems composed of quantum two-level objects (qubits). To probe the limit of such methods, we designed a beyond-classical readout error mitigation protocol based on quantum state tomography (QST), which estimates the density matrix of a quantum system, and quantum detector tomography (QDT), which characterizes the measurement procedure. By treating readout error mitigation in the context of state tomography the method becomes largely readout mode-, architecture-, noise source-, and quantum state-independent. We implement this method on a superconducting qubit and evaluate the increase in reconstruction fidelity for QST. We characterize the performance of the method by varying important noise sources, such as suboptimal readout signal amplification, insufficient resonator photon population, off-resonant qubit drive, and effectively shortened T1 and T2 coherence. As a result, we identified noise sources for which readout error mitigation worked well, and observed decreases in readout infidelity by a factor of up to 30.

DOI
10.1038/s42005-024-01790-8

Related papers

Benchmarking the quality of multiplexed qubit readout beyond assignment fidelity

Andras Di Giovanni, Adrian Skasberg Aasen, Jürgen Lisenfeld +3 more

The accurate measurement of quantum two-level objects (qubits) is crucial for developing quantum computers. Over the last decade, the measure of choice for benchmarking readout routines for superconducting qubits has been assignment fidelity; however, this method only focuses on the preparation of computational basis states and therefore does not provide a complete characterization of the readout. Here, we expand the focus to the use of detector tomography to fully characterize multiqubit readout of superconducting transmon qubits. The impact of different readout parameters on the rate of information extraction is studied using quantum-state reconstruction infidelity as a proxy. The results are then compared with assignment fidelities, showing good agreement for separable two-qubit states. We therefore propose the rate of infidelity convergence as a validation tool for assignment fidelity and a more comprehensive benchmark for single- and multiqubit readout optimization. To make the best use of experimental resources, we investigate the most efficient distribution of a limited shot budget between detector tomography and state reconstruction within the context of single- and two-qubit experiments. To address the growing interest in three-qubit gates and test the scalability of the validation tool, we perform three-qubit quantum-state tomography that goes beyond conventional readout-error-mitigation methods and find a factor-of-30 reduction in quantum infidelity. Our results demonstrate that qubit readout correlations are not induced by a significantly reduced state distinguishability. Consequently, correlation coefficients can serve as a valuable tool in qubit readout optimization.

arXiv:2502.08589•Physical Review Applied•Sep 15, 2025•4 citations

Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography

Filip B. Maciejewski, Zoltán Zimborás, Michał Oszmaniec

We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.

arXiv:1907.08518•Quantum•Apr 24, 2020•226 citations

Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography

Maciejewski, Filip, Zoltán Zimborás, Oszmaniec, Michal

We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.

•Jan 1, 2020•184 citations

Limitations for adaptive quantum state tomography in the presence of detector noise

Adrian Skasberg Aasen, Martin Gärttner

Assumption-free reconstruction of quantum states from measurements is essential for benchmarking and certifying quantum devices, but it remains difficult due to the extensive measurement statistics and experimental resources it demands. An approach to alleviating these demands is provided by adaptive measurement strategies, which can yield up to a quadratic improvement in reconstruction accuracy for pure states by dynamically optimizing measurement settings during data acquisition. A key open question is whether these asymptotic advantages remain in realistic experiments, where readout is inevitably noisy. In this work, we analyze the impact of readout noise on adaptive quantum state tomography with readout-error mitigation, focusing on the challenging regime of reconstructing pure states using mixed-state estimators. Using analytical arguments based on Fisher information optimization and extensive numerical simulations using Bayesian inference, we show that any nonzero readout noise eliminates the asymptotic quadratic scaling advantage of adaptive strategies. We numerically investigate the behavior for finite measurement statistics for single- and two-qubit systems with exact readout-error mitigation and find a gradual transition from ideal to sub-optimal scaling. We furthermore investigate realistic scenarios where detector tomography is performed with a limited number of state copies for calibration, showing that insufficient detector characterization leads to estimator bias and limited reconstruction accuracy. Although our result imposes an upper bound on the reconstruction accuracy that can be achieved with adaptive strategies, we nevertheless observe numerically a constant-factor gain in reconstruction accuracy, which becomes larger as the readout noise decreases. This indicates potential practical benefits in using adaptive measurement strategies in well-calibrated experiments.

quant-pharXiv:2601.04020•Physical Review A•Jan 8, 2026•0 citations

Extracting information from noisy quantum systems: Readout-error mitigation and adaptive measurement strategies

Adrian Skasberg Aasen

The field of quantum technologies has experienced explosive growth in the past decade. As hardware capabilities have advanced, quantum computing has exhibited a scaling trend analogous to Moore's law, often referred to as Rose's law, where the number of coherently controlled qubits roughly doubles every two years. Associated with such rapid growth is an equally growing need for benchmarking tools and error handling. While advancements in quantum hardware and software have mainly concentrated on enhancing gate fidelity and qubit connectivity, the progress in addressing readout errors has been relatively limited during the same period. This thesis tries to close this gap by advancing and developing new tools for information extraction in quantum systems. We do this in two different ways: In Part II, we focus on mitigating the effect of general readout errors in quantum systems. We developed a comprehensive protocol for readout-error-mitigated state tomography (REMST) and implemented it on a superconducting qubit system. The REMST protocol was designed to mitigate not only classical readout errors but also more challenging coherent and correlated readout errors. The protocol uses only a deterministic application of single-qubit readout, making it one of the most experimentally friendly approaches available. We developed a scalable version of the REMST protocol and showed numerically that it is suitable for systems with more than 100 qubits, matching the size of current state-of-the-art systems. The REMST protocol was applied to superconducting qubit experiments, where we saw an improvement in reconstruction accuracy by a factor of up to 30. In Part III, we move our focus to optimal measurement strategies. Adaptive measurement strategies promise a quadratic improvement in the statistical fluctuation of pure and close-to-pure state reconstruction by dynamically optimizing measurement settings during sampling. We investigated whether these adaptive measurement strategies were viable in realistic experimental settings. We demonstrated both analytically and in numerical simulations that going from ideal readout to noisy readout disproportionally deteriorates the quality of the adaptive measurement strategy, to a point where no asymptotic benefit exists for adaptive measurements. These results not only deepen our understanding of readout processes in superconducting qubits but also provide concrete implementations of more robust quantum measurement and tomography protocols, offering clearer insight into the interplay between readout noise and information extraction.

•Jan 1, 2026•0 citations

Mitigation of correlated readout errors without randomized measurements

Adrian Skasberg Aasen, Andras Di Giovanni, Hannes Rotzinger +2 more

Quantum simulation, the study of strongly correlated quantum matter using synthetic quantum systems, has been the most successful application of quantum computers to date. It often requires determining observables with high precision, for example when studying critical phenomena near quantum phase transitions. Thus, readout errors must be carefully characterized and mitigated in data postprocessing, using scalable and noise-model agnostic protocols. We present a readout error-mitigation protocol that uses only single-qubit Pauli measurements and avoids experimentally challenging randomized measurements. The proposed approach captures a very broad class of correlated noise models and is scalable to large qubit systems. It is based on a complete and efficient characterization of few-qubit correlated positive operator-valued measures, using overlapping detector tomography. To assess the effectiveness of the protocol, observables are extracted from simulations involving up to 100 qubits employing readout errors obtained from experiments with superconducting qubits.

arXiv:2503.24276•Physical Review A•Jul 14, 2025•2 citations
Abstract Quantum technologies rely heavily on accurate control and reliable readout of quantum systems. Current experiments are limited by numerous sources of noise that can only be partially captured by simple analytical models and additional characterization of the noise sources is required. We test the ability of readout error mitigation to correct noise found in systems composed of quantum two-level objects (qubits). To probe the limit of such methods, we designed a beyond-classical readout error mitigation protocol based on quantum state tomography (QST), which estimates the density matrix of a quantum system, and quantum detector tomography (QDT), which characterizes the measurement procedure. By treating readout error mitigation in the context of state tomography the method becomes largely readout mode-, architecture-, noise source-, and quantum state-independent. We implement this method on a superconducting qubit and evaluate the increase in reconstruction fidelity for QST. We characterize the performance of the method by varying important noise sources, such as suboptimal readout signal amplification, insufficient resonator photon population, off-resonant qubit drive, and effectively shortened T1 and T2 coherence. As a result, we identified noise sources for which readout error mitigation worked well, and observed decreases in readout infidelity by a factor of up to 30.
The accurate measurement of quantum two-level objects (qubits) is crucial for developing quantum computers. Over the last decade, the measure of choice for benchmarking readout routines for superconducting qubits has been assignment fidelity; however, this method only focuses on the preparation of computational basis states and therefore does not provide a complete characterization of the readout. Here, we expand the focus to the use of detector tomography to fully characterize multiqubit readout of superconducting transmon qubits. The impact of different readout parameters on the rate of information extraction is studied using quantum-state reconstruction infidelity as a proxy. The results are then compared with assignment fidelities, showing good agreement for separable two-qubit states. We therefore propose the rate of infidelity convergence as a validation tool for assignment fidelity and a more comprehensive benchmark for single- and multiqubit readout optimization. To make the best use of experimental resources, we investigate the most efficient distribution of a limited shot budget between detector tomography and state reconstruction within the context of single- and two-qubit experiments. To address the growing interest in three-qubit gates and test the scalability of the validation tool, we perform three-qubit quantum-state tomography that goes beyond conventional readout-error-mitigation methods and find a factor-of-30 reduction in quantum infidelity. Our results demonstrate that qubit readout correlations are not induced by a significantly reduced state distinguishability. Consequently, correlation coefficients can serve as a valuable tool in qubit readout optimization.
We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.
We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.
Assumption-free reconstruction of quantum states from measurements is essential for benchmarking and certifying quantum devices, but it remains difficult due to the extensive measurement statistics and experimental resources it demands. An approach to alleviating these demands is provided by adaptive measurement strategies, which can yield up to a quadratic improvement in reconstruction accuracy for pure states by dynamically optimizing measurement settings during data acquisition. A key open question is whether these asymptotic advantages remain in realistic experiments, where readout is inevitably noisy. In this work, we analyze the impact of readout noise on adaptive quantum state tomography with readout-error mitigation, focusing on the challenging regime of reconstructing pure states using mixed-state estimators. Using analytical arguments based on Fisher information optimization and extensive numerical simulations using Bayesian inference, we show that any nonzero readout noise eliminates the asymptotic quadratic scaling advantage of adaptive strategies. We numerically investigate the behavior for finite measurement statistics for single- and two-qubit systems with exact readout-error mitigation and find a gradual transition from ideal to sub-optimal scaling. We furthermore investigate realistic scenarios where detector tomography is performed with a limited number of state copies for calibration, showing that insufficient detector characterization leads to estimator bias and limited reconstruction accuracy. Although our result imposes an upper bound on the reconstruction accuracy that can be achieved with adaptive strategies, we nevertheless observe numerically a constant-factor gain in reconstruction accuracy, which becomes larger as the readout noise decreases. This indicates potential practical benefits in using adaptive measurement strategies in well-calibrated experiments.
The field of quantum technologies has experienced explosive growth in the past decade. As hardware capabilities have advanced, quantum computing has exhibited a scaling trend analogous to Moore's law, often referred to as Rose's law, where the number of coherently controlled qubits roughly doubles every two years. Associated with such rapid growth is an equally growing need for benchmarking tools and error handling. While advancements in quantum hardware and software have mainly concentrated on enhancing gate fidelity and qubit connectivity, the progress in addressing readout errors has been relatively limited during the same period. This thesis tries to close this gap by advancing and developing new tools for information extraction in quantum systems. We do this in two different ways: In Part II, we focus on mitigating the effect of general readout errors in quantum systems. We developed a comprehensive protocol for readout-error-mitigated state tomography (REMST) and implemented it on a superconducting qubit system. The REMST protocol was designed to mitigate not only classical readout errors but also more challenging coherent and correlated readout errors. The protocol uses only a deterministic application of single-qubit readout, making it one of the most experimentally friendly approaches available. We developed a scalable version of the REMST protocol and showed numerically that it is suitable for systems with more than 100 qubits, matching the size of current state-of-the-art systems. The REMST protocol was applied to superconducting qubit experiments, where we saw an improvement in reconstruction accuracy by a factor of up to 30. In Part III, we move our focus to optimal measurement strategies. Adaptive measurement strategies promise a quadratic improvement in the statistical fluctuation of pure and close-to-pure state reconstruction by dynamically optimizing measurement settings during sampling. We investigated whether these adaptive measurement strategies were viable in realistic experimental settings. We demonstrated both analytically and in numerical simulations that going from ideal readout to noisy readout disproportionally deteriorates the quality of the adaptive measurement strategy, to a point where no asymptotic benefit exists for adaptive measurements. These results not only deepen our understanding of readout processes in superconducting qubits but also provide concrete implementations of more robust quantum measurement and tomography protocols, offering clearer insight into the interplay between readout noise and information extraction.
Quantum simulation, the study of strongly correlated quantum matter using synthetic quantum systems, has been the most successful application of quantum computers to date. It often requires determining observables with high precision, for example when studying critical phenomena near quantum phase transitions. Thus, readout errors must be carefully characterized and mitigated in data postprocessing, using scalable and noise-model agnostic protocols. We present a readout error-mitigation protocol that uses only single-qubit Pauli measurements and avoids experimentally challenging randomized measurements. The proposed approach captures a very broad class of correlated noise models and is scalable to large qubit systems. It is based on a complete and efficient characterization of few-qubit correlated positive operator-valued measures, using overlapping detector tomography. To assess the effectiveness of the protocol, observables are extracted from simulations involving up to 100 qubits employing readout errors obtained from experiments with superconducting qubits.