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:2109.14329 · Physical Review A

Mitigating errors by quantum verification and postselection

Rawad Mezher, James K. Mills, Elham Kashefi

Published May 27, 2022• 14 citations
arXivHTMLPDF

Abstract

Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits efficiently classically simulable, thereby destroying any quantum advantage potentially offered by an ideal (noiseless) implementation of these circuits. Although the technique of quantum error correction (QEC) allows correcting these errors very accurately, QEC usually requires a large overhead of physical qubits which is not reachable with currently available quantum hardware. This has been the motivation behind the field of quantum error mitigation, which aims at developing techniques to correct an important part of the errors in quantum circuits, while also being compatible with current and near-term quantum hardware. In this work, we present a technique for quantum error mitigation which is based on a technique from quantum verification, the so-called accreditation protocol, together with postselection. Our technique allows for correcting the expectation value of an observable $O$, which is the output of multiple runs of noisy quantum circuits, where the noise in these circuits is at the level of preparations, gates, and measurements. We discuss the sample complexity of our procedure and provide rigorous guarantees of errors being mitigated under some realistic assumptions on the noise. Our technique is tailored to time-dependent behaviors, as we allow for the output states to be different between different runs of the accreditation protocol. We validate our findings by running our technique on currently available quantum hardware.

DOI
10.1103/physreva.105.052608

Related papers

Towards reliable quantum computation: mitigation and certification from NISQ to early fault-tolerance

James Alastair Casebourne Mills

The recent pace of experimental progress in quantum technologies suggests we may soon reach a time when quantum devices can be applied to solve problems of practical interest. Despite this, we are still far from being able to abstract away the effects of noise on quantum computation. The reliable execution of computations on current devices remains a significant challenge. This holds true both for computation with noisy physical qubits and for computation using the limited forms of error correction available on early fault-tolerant quantum devices. In this thesis, I propose methods for improving the reliability of quantum devices, as the field transitions from the regime of noisy intermediate-scale quantum (NISQ) devices to that of early fault-tolerance. These span the topics of quantum error mitigation, quantum error correction and quantum certification. In the first instance, I propose methods for improving the performance of quantum devices affected by limited amounts of noise. Specifically, I present a method for mitigating the effects of time-dependent noise. This adapts a computational certification protocol called accreditation into a method for postselecting on weaker time-dependent noise behaviours. The method is analytically shown to lead to a provable reduction in errors for the case of depolarising noise, and demonstrated in experiments on superconducting hardware. I also present a method for mitigating the effects of photon loss in photonic quantum devices. Through a combination of analytical and numerical analysis, it is shown that there are wide regimes of photon loss for which this method outperforms postselection, the standard method of handling loss in photonic devices. Additionally, evidence is provided that the method enhances the performance of a quantum machine learning model known as a Quantum Circuit Born Machine in the presence of photon loss. Next, I introduce a framework for certifying the correctness of computations run on encoded logical qubits. This is sensitive to considerably more general forms of noise than is usually considered in quantum error correction. It can be applied to efficiently certify the correctness of quantum computations for large system sizes, beyond the capabilities of methods relying on classical simulation. In numerical experiments, the framework was applied to certify the accuracy of instantaneous quantum polynomial (IQP) circuit sampling and Trotterised Hamiltonian simulation. It can be used to efficiently assess whether quantum error mitigation may be usefully applied to a computation, to upper-bound the infidelity of the encoded logical state, and to extend the method of entropy density benchmarking to logical computation. The methods presented in this thesis contribute to the wider effort of building towards reliable quantum computation: both in the sense of reducing the effects of noise on computational output, and in the sense of certifying the correctness of computation beyond the capabilities of classical simulators. Only with reliable quantum computation can the full potential of this technology be realised.

•May 7, 2026•0 citations

Efficiently improving the performance of noisy quantum computers

Samuele Ferracin, Akel Hashim, Jean-Loup Ville +7 more

Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named ``Noiseless Output Extrapolation" and ``Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.

arXiv:2201.10672•Quantum•Jul 15, 2024•34 citations

Quantum Error Mitigation at the pre-processing stage

Juan F. Martin, Giuseppe Cocco, Javier Fonollosa

The realization of fault-tolerant quantum computers remains a challenging endeavor, forcing state-of-the-art quantum hardware to rely heavily on noise mitigation techniques. Standard quantum error mitigation is typically based on post-processing strategies. In contrast, the present work explores a pre-processing approach, in which the effects of noise are mitigated before performing a measurement on the output state. The main idea is to find an observable $Y$ such that its expectation value on a noisy quantum state $\mathcal{E(ρ)}$ matches the expectation value of a target observable $X$ on the noiseless quantum state $ρ$. Our method requires the execution of a noisy quantum circuit, followed by the measurement of the surrogate observable $Y$. The main enablers of our method in practical scenarios are Tensor Networks. The proposed method improves over Tensor Error Mitigation (TEM) in terms of average error, circuit depth, and complexity, attaining a measurement overhead that approaches the theoretical lower bound. The improvement in terms of classical computation complexity is in the order of $\sim 10^6$ times when compared to the post-processing computational cost of TEM in practical scenarios. Such gain comes from eliminating the need to perform the set of informationally complete positive operator-valued measurements (IC-POVM) required by TEM, as well as any other tomographic strategy.

quant-pharXiv:2602.05916•Feb 6, 2026•0 citations

Error mitigation of BQP computations using measurement-based verification

Joseph P. Harris, Elham Kashefi

We present a modular error mitigation protocol for running bounded-error quantum polynomial time (BQP) computations on a quantum computer with time-dependent noise. Utilizing existing tools from quantum verification and measurement-based quantum computation, our protocol interleaves standard computation rounds alongside test rounds for noise sampling and inherits an exponential bound (in the number of circuit runs) on the probability that a returned classical output is correct. We introduce a postselection technique called to address time-dependent noise and reduce overhead. The result is an error mitigation protocol which requires minimal noise assumptions, making it straightforwardly implementable on existing, noisy intermediate-scale quantum devices. We perform a demonstration of the protocol using classical noisy simulation, presenting a universal measurement pattern which directly maps to (and can be tiled on) the heavy-hex layout of current IBM hardware.

Physical Review A•Feb 4, 2025•1 citation

Advanced Methods for Quasiprobabilistic Quantum Error Mitigation

Christophe Piveteau

Current quantum computers are plagued by prohibitive amounts of noise, which complicates the experimental realization of useful quantum algorithms that outperform classical computers.Quantum error mitigation techniques could constitute a potential avenue to demonstrate this feat without the need for fault-tolerant quantum error correction.One method in this family of mitigation techniques is the quasiprobability method introduced by Temme et al. [1].It simulates a noise-free quantum computer with a noisy one, with the caveat of only producing the correct expected values of measurement observables.The cost of a quasiprobability simulation manifests as a sampling overhead which scales exponentially in the number of error-mitigated gates in the circuit.In this thesis we aim to reduce the exponential basis of that overhead, which in turn allows the application of the quasiprobability method to deeper quantum circuits.A central result is the introduction of a novel scheme, which we call Stinespring algorithm, that aims to choose the quasiprobability decomposition in a noise-aware manner.Along the way, we introduce a generalization of the quasiprobability method, which we denote approximate quasiprobability method, that allows for a tradeoff between an approximation error and the sampling overhead.This method is already interesting on its own and we present a few potential applications.Finally, we present some ideas how quantum error correction can benefit from the quasiprobability method.This final part is separate to the other topics of the master thesis and gives a rough overview of a new research project that started towards the end of the thesis and that we will continue to pursue in the future.i Overview of ContributionsWe summarize the novel contributions from this thesis:• Many details in the presentation of Chapter 2 have not been stated in such precision in previous literature.However, we estimate that many of these contributions are evident for someone knowledgeable in the domain.• The channel difference decomposition (Section 2.6).• The approximate QPD and its applications (Chapter 3).• The Stinespring algorithm (Chapter 4).

•Sep 1, 2020•4 citations

Quantum error mitigation via quantum-noise-effect circuit groups

Yusuke Hama, Hirofumi Nishi

Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to perform quantum computation in good accuracy with these machines we need to develop alternative approaches for mitigating quantum computational errors. In this work, we propose quantum error mitigation (QEM) scheme for quantum computational errors which occur due to couplings with environments during gate operations, i.e., decoherence. To establish our QEM scheme, first we estimate the quantum noise effects on single-qubit states and represent them as groups of quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM scheme is conducted by subtracting expectation values generated by the quantum-noise-effect circuit groups from those obtained by the quantum circuits for the quantum algorithms under consideration. As a result, the quantum noise effects are reduced, and we obtain approximately the ideal expectation values via the quantum-noise-effect circuit groups and the numbers of elementary quantum circuits composing them scale polynomial with respect to the products of the depths of quantum algorithms and the numbers of register bits. To numerically demonstrate the validity of our QEM scheme, we run noisy quantum simulations of qubits under amplitude damping effects for four types of quantum algorithms. Furthermore, we implement our QEM scheme on IBM Q Experience processors and examine its efficacy. Consequently, the validity of our scheme is verified via both the quantum simulations and the quantum computations on the real quantum devices. Our QEM scheme is solely composed of quantum-computational operations (quantum gates and measurements), and thus, it can be conducted by any type of quantum device. In addition, it can be applied to error mitigation for many other types of quantum noise effects as well as noisy quantum computing of long-depth quantum algorithms.

arXiv:2205.13907•Scientific Reports•Mar 13, 2024•9 citations
Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits efficiently classically simulable, thereby destroying any quantum advantage potentially offered by an ideal (noiseless) implementation of these circuits. Although the technique of quantum error correction (QEC) allows correcting these errors very accurately, QEC usually requires a large overhead of physical qubits which is not reachable with currently available quantum hardware. This has been the motivation behind the field of quantum error mitigation, which aims at developing techniques to correct an important part of the errors in quantum circuits, while also being compatible with current and near-term quantum hardware. In this work, we present a technique for quantum error mitigation which is based on a technique from quantum verification, the so-called accreditation protocol, together with postselection. Our technique allows for correcting the expectation value of an observable OOO, which is the output of multiple runs of noisy quantum circuits, where the noise in these circuits is at the level of preparations, gates, and measurements. We discuss the sample complexity of our procedure and provide rigorous guarantees of errors being mitigated under some realistic assumptions on the noise. Our technique is tailored to time-dependent behaviors, as we allow for the output states to be different between different runs of the accreditation protocol. We validate our findings by running our technique on currently available quantum hardware.
The recent pace of experimental progress in quantum technologies suggests we may soon reach a time when quantum devices can be applied to solve problems of practical interest. Despite this, we are still far from being able to abstract away the effects of noise on quantum computation. The reliable execution of computations on current devices remains a significant challenge. This holds true both for computation with noisy physical qubits and for computation using the limited forms of error correction available on early fault-tolerant quantum devices. In this thesis, I propose methods for improving the reliability of quantum devices, as the field transitions from the regime of noisy intermediate-scale quantum (NISQ) devices to that of early fault-tolerance. These span the topics of quantum error mitigation, quantum error correction and quantum certification. In the first instance, I propose methods for improving the performance of quantum devices affected by limited amounts of noise. Specifically, I present a method for mitigating the effects of time-dependent noise. This adapts a computational certification protocol called accreditation into a method for postselecting on weaker time-dependent noise behaviours. The method is analytically shown to lead to a provable reduction in errors for the case of depolarising noise, and demonstrated in experiments on superconducting hardware. I also present a method for mitigating the effects of photon loss in photonic quantum devices. Through a combination of analytical and numerical analysis, it is shown that there are wide regimes of photon loss for which this method outperforms postselection, the standard method of handling loss in photonic devices. Additionally, evidence is provided that the method enhances the performance of a quantum machine learning model known as a Quantum Circuit Born Machine in the presence of photon loss. Next, I introduce a framework for certifying the correctness of computations run on encoded logical qubits. This is sensitive to considerably more general forms of noise than is usually considered in quantum error correction. It can be applied to efficiently certify the correctness of quantum computations for large system sizes, beyond the capabilities of methods relying on classical simulation. In numerical experiments, the framework was applied to certify the accuracy of instantaneous quantum polynomial (IQP) circuit sampling and Trotterised Hamiltonian simulation. It can be used to efficiently assess whether quantum error mitigation may be usefully applied to a computation, to upper-bound the infidelity of the encoded logical state, and to extend the method of entropy density benchmarking to logical computation. The methods presented in this thesis contribute to the wider effort of building towards reliable quantum computation: both in the sense of reducing the effects of noise on computational output, and in the sense of certifying the correctness of computation beyond the capabilities of classical simulators. Only with reliable quantum computation can the full potential of this technology be realised.
Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named ``Noiseless Output Extrapolation" and ``Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.
The realization of fault-tolerant quantum computers remains a challenging endeavor, forcing state-of-the-art quantum hardware to rely heavily on noise mitigation techniques. Standard quantum error mitigation is typically based on post-processing strategies. In contrast, the present work explores a pre-processing approach, in which the effects of noise are mitigated before performing a measurement on the output state. The main idea is to find an observable YYY such that its expectation value on a noisy quantum state E(ρ)\mathcal{E(ρ)}E(ρ) matches the expectation value of a target observable XXX on the noiseless quantum state ρρρ. Our method requires the execution of a noisy quantum circuit, followed by the measurement of the surrogate observable YYY. The main enablers of our method in practical scenarios are Tensor Networks. The proposed method improves over Tensor Error Mitigation (TEM) in terms of average error, circuit depth, and complexity, attaining a measurement overhead that approaches the theoretical lower bound. The improvement in terms of classical computation complexity is in the order of ∼106\sim 10^6∼106 times when compared to the post-processing computational cost of TEM in practical scenarios. Such gain comes from eliminating the need to perform the set of informationally complete positive operator-valued measurements (IC-POVM) required by TEM, as well as any other tomographic strategy.
We present a modular error mitigation protocol for running bounded-error quantum polynomial time (BQP) computations on a quantum computer with time-dependent noise. Utilizing existing tools from quantum verification and measurement-based quantum computation, our protocol interleaves standard computation rounds alongside test rounds for noise sampling and inherits an exponential bound (in the number of circuit runs) on the probability that a returned classical output is correct. We introduce a postselection technique called to address time-dependent noise and reduce overhead. The result is an error mitigation protocol which requires minimal noise assumptions, making it straightforwardly implementable on existing, noisy intermediate-scale quantum devices. We perform a demonstration of the protocol using classical noisy simulation, presenting a universal measurement pattern which directly maps to (and can be tiled on) the heavy-hex layout of current IBM hardware.
Current quantum computers are plagued by prohibitive amounts of noise, which complicates the experimental realization of useful quantum algorithms that outperform classical computers.Quantum error mitigation techniques could constitute a potential avenue to demonstrate this feat without the need for fault-tolerant quantum error correction.One method in this family of mitigation techniques is the quasiprobability method introduced by Temme et al. [1].It simulates a noise-free quantum computer with a noisy one, with the caveat of only producing the correct expected values of measurement observables.The cost of a quasiprobability simulation manifests as a sampling overhead which scales exponentially in the number of error-mitigated gates in the circuit.In this thesis we aim to reduce the exponential basis of that overhead, which in turn allows the application of the quasiprobability method to deeper quantum circuits.A central result is the introduction of a novel scheme, which we call Stinespring algorithm, that aims to choose the quasiprobability decomposition in a noise-aware manner.Along the way, we introduce a generalization of the quasiprobability method, which we denote approximate quasiprobability method, that allows for a tradeoff between an approximation error and the sampling overhead.This method is already interesting on its own and we present a few potential applications.Finally, we present some ideas how quantum error correction can benefit from the quasiprobability method.This final part is separate to the other topics of the master thesis and gives a rough overview of a new research project that started towards the end of the thesis and that we will continue to pursue in the future.i Overview of ContributionsWe summarize the novel contributions from this thesis:• Many details in the presentation of Chapter 2 have not been stated in such precision in previous literature.However, we estimate that many of these contributions are evident for someone knowledgeable in the domain.• The channel difference decomposition (Section 2.6).• The approximate QPD and its applications (Chapter 3).• The Stinespring algorithm (Chapter 4).
Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to perform quantum computation in good accuracy with these machines we need to develop alternative approaches for mitigating quantum computational errors. In this work, we propose quantum error mitigation (QEM) scheme for quantum computational errors which occur due to couplings with environments during gate operations, i.e., decoherence. To establish our QEM scheme, first we estimate the quantum noise effects on single-qubit states and represent them as groups of quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM scheme is conducted by subtracting expectation values generated by the quantum-noise-effect circuit groups from those obtained by the quantum circuits for the quantum algorithms under consideration. As a result, the quantum noise effects are reduced, and we obtain approximately the ideal expectation values via the quantum-noise-effect circuit groups and the numbers of elementary quantum circuits composing them scale polynomial with respect to the products of the depths of quantum algorithms and the numbers of register bits. To numerically demonstrate the validity of our QEM scheme, we run noisy quantum simulations of qubits under amplitude damping effects for four types of quantum algorithms. Furthermore, we implement our QEM scheme on IBM Q Experience processors and examine its efficacy. Consequently, the validity of our scheme is verified via both the quantum simulations and the quantum computations on the real quantum devices. Our QEM scheme is solely composed of quantum-computational operations (quantum gates and measurements), and thus, it can be conducted by any type of quantum device. In addition, it can be applied to error mitigation for many other types of quantum noise effects as well as noisy quantum computing of long-depth quantum algorithms.