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:1712.04954

Measuring and Suppressing Error Correlations in Quantum Circuits

Claire Edmunds, Cornelius Hempel, R. Harris, Harrison Ball, Virginia Frey, Thomas M. Stace, Michael J. Biercuk

Published Dec 13, 2017• 5 citations
arXivHTMLPDF

Abstract

Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of independent errors in quantum logic operations is at odds with realistic environments where error-sources may exhibit strong temporal correlations. We present experiments enabling the identification of error correlations between operations in quantum circuits, using only projective measurements at the end of the circuit. Using a single trapped ion qubit and engineered noise with tunable temporal correlations, we identify a clear signature of error correlations between sequential gates in randomly composed quantum circuits, and extract quantitative measures linked to the underlying noise correlation length. By replacing all gates in these circuits with "virtual" dynamically corrected gates (DCGs), we demonstrate that even in the presence of strongly correlated noise the signatures of error correlations between sequential gates appear similar to standard gates exposed to uncorrelated noise. A theoretical model applied to our experiments reveals that common DCGs suppress the correlated error component by over $270\times$ with $95\%$ confidence. Using block-correlated noise, we explore the scaling of the effective error correlation length at the virtual level, and show that DCGs exhibit error correlations indistinguishable from those arising from uncorrelated noise.

DOI
10.48550/arxiv.1712.04954

Related papers

Experimental quantum verification in the presence of temporally correlated noise

Sandeep Mavadia, Claire Edmunds, Cornelius Hempel +4 more

Abstract Growth in the capabilities of quantum information hardware mandates access to techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). Our analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped 171Yb+ ion-qubit and inject engineered noise $$\left( { \propto \hat \sigma _z} \right)$$ ∝ σ ^ z to probe protocol performance. Experiments on RB validate predictions that measured fidelities over sequences are described by a gamma distribution varying between approximately Gaussian, and a broad, highly skewed distribution for rapidly and slowly varying noise, respectively. Similarly we find a strong gate set dependence of default experimental GST procedures in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlated $$\hat \sigma _z$$ σ ^ z errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlated $$\hat \sigma _x$$ σ ^ x or $$\hat \sigma _y$$ σ ^ y errors or depolarising noise processes, highlighting the impact of the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments.

arXiv:1706.03787•npj Quantum Information•Jan 23, 2018•57 citations

Suppressing Correlated Noise in Quantum Computers via Context-Aware Compiling

Alireza Seif, Haoran Liao, Vinay Tripathi +5 more

Coherent errors, and especially those that occur in correlation among a set of qubits, are detrimental for large-scale quantum computing. Correlations in noise can occur as a result of spatial and temporal configurations of instructions executing on the quantum processor. In this paper, we perform a detailed experimental characterization of many of these error sources, and theoretically connect them to the physics of superconducting qubits and gate operations. Equipped with this knowledge, we devise compiler strategies to suppress these errors using dynamical decoupling or error compensation into the rest of the circuit. Importantly, these strategies are successful when the context at each layer of computation is taken into account: how qubits are connected, what crosstalk terms exist on the device, and what gates or idle periods occur in that layer. Our context-aware compiler thus suppresses some dominant sources of error, making further error mitigation or error correction substantially less expensive. For example, our experiments show an increase of $\mathbf{1 8. 5 \%}$ in layer fidelity for a candidate 10 -qubit circuit layer compared to context-unaware suppression. Owing to the exponential nature of error mitigation, these improvements due to error suppression translate to several orders of magnitude reduction of sampling overhead for a circuit consisting of a moderate number of layers.

arXiv:2403.06852•Proceedings - International Symposium on Computer Architecture/Proceedings•Jun 29, 2024•18 citations

Robust Quantum Gates against Correlated Noise in Integrated Quantum Chips

Kangyuan Yi, Yong-Ju Hai, Kai Luo +9 more

As quantum circuits become more integrated and complex, additional error sources that were previously insignificant start to emerge. Consequently, the fidelity of quantum gates benchmarked under pristine conditions falls short of predicting their performance in realistic circuits. To overcome this problem, we must improve their robustness against pertinent error models besides isolated fidelity. Here, we report the experimental realization of robust quantum gates in superconducting quantum circuits based on a geometric framework for diagnosing and correcting various gate errors. Using quantum process tomography and randomized benchmarking, we demonstrate robust single-qubit gates against quasistatic noise and spatially correlated noise in a broad range of strengths, which are common sources of coherent errors in large-scale quantum circuits. We also apply our method to nonstatic noises and to realize robust two-qubit gates. Our Letter provides a versatile toolbox for achieving noise-resilient complex quantum circuits.

arXiv:2401.01810•Physical Review Letters•Jun 20, 2024•23 citations

Dynamically corrected gates suppressing spatiotemporal error correlations as measured by randomized benchmarking

Claire Edmunds, Cornelius Hempel, R. J. Harris +3 more

This work introduces a method to measure error correlations in quantum circuits, both temporally between gates and spatially between qubits. The authors demonstrate that using appropriately tailored dynamically corrected gates can not only reduce the likelihood of errors, but also correlations between them, and can hence be used to precondition a circuit for quantum error correction.

arXiv:1909.10727•Physical Review Research•Feb 13, 2020•28 citations

Measuring Correlated Qubit Errors on Quantum Computers

Peyton Schales

Abstract Quantum computing is an emerging technology that, with its exponential computational speedup, will allow us to solve a new level of hard problems. From rapid vaccine development, efficient discovery of exotic materials, and complex AI models, to quickly cracking RSA encryption, quantum computers have the potential to revolutionize science. However, for quantum computing to solve these problems, quantum error correction methods are needed to eliminate qubit errors. An underlying assumption of current quantum error correction is that qubit errors are not correlated. If correlated qubit errors are prevalent, quantum error correction will be difficult, if not impossible. In this work, I developed a method to identify correlated errors between pairs of qubits and used this method to determine if correlations exist on current small-scale quantum computers. My method uses independence of error probabilities P(qa) ⨉ P(qb) = P(qaqb) to determine correlation. After running 40 million experiments to collect error probabilities by varying the quantum gates, number of gates, and pairs of qubits on multiple quantum computers, I found that these computers have a high occurrence of correlated qubit errors when qubits are topological neighbors. For example, I found that Hadamard gate operations can cause correlated errors, supported by a p-value of 0.0160. My work shows that the assumption that qubit errors are not correlated is incorrect for current quantum computers. In the future, scientists can use these methods to test for correlated errors as they develop new quantum computers, enabling quantum computing to achieve its full potential.

•Nov 3, 2021•1 citation

Fault-tolerant threshold of quantum circuit under correlated noise

Zhan-Yun Wang

Abstract We investigate the impact of the correlation between error gates on the fault-tolerant threshold in quantum circuits under three typical noise models. In the fault-tolerant encoding schemes for two fundamental quantum logical operations, we extend the conventional error injection method by simultaneously applying error gates to both control and target qubits after two-qubit gate operations, with a quantitative characterization of the correlation strength between these error gates. The results show that the fault-tolerant error threshold can be noticeably enhanced by the presence of correlations between error gates, resulting in more robust quantum circuit implementations. We further apply fault-tolerant encoding to the single-qubit teleportation circuit and investigate the effect of correlated noise on its error threshold. The results show that the threshold varies non-monotonically with the correlation strength and that the system’s fault-tolerance differs significantly across noise models.

Communications in Theoretical Physics•Feb 27, 2026•0 citations
Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of independent errors in quantum logic operations is at odds with realistic environments where error-sources may exhibit strong temporal correlations. We present experiments enabling the identification of error correlations between operations in quantum circuits, using only projective measurements at the end of the circuit. Using a single trapped ion qubit and engineered noise with tunable temporal correlations, we identify a clear signature of error correlations between sequential gates in randomly composed quantum circuits, and extract quantitative measures linked to the underlying noise correlation length. By replacing all gates in these circuits with "virtual" dynamically corrected gates (DCGs), we demonstrate that even in the presence of strongly correlated noise the signatures of error correlations between sequential gates appear similar to standard gates exposed to uncorrelated noise. A theoretical model applied to our experiments reveals that common DCGs suppress the correlated error component by over 270×270\times270× with 95%95\%95% confidence. Using block-correlated noise, we explore the scaling of the effective error correlation length at the virtual level, and show that DCGs exhibit error correlations indistinguishable from those arising from uncorrelated noise.
Abstract Growth in the capabilities of quantum information hardware mandates access to techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). Our analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped 171Yb+ ion-qubit and inject engineered noise (∝σ^z)\left( { \propto \hat \sigma _z} \right)(∝σ^z​) ∝ σ ^ z to probe protocol performance. Experiments on RB validate predictions that measured fidelities over sequences are described by a gamma distribution varying between approximately Gaussian, and a broad, highly skewed distribution for rapidly and slowly varying noise, respectively. Similarly we find a strong gate set dependence of default experimental GST procedures in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlated σ^z\hat \sigma _zσ^z​ σ ^ z errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlated σ^x\hat \sigma _xσ^x​ σ ^ x or σ^y\hat \sigma _yσ^y​ σ ^ y errors or depolarising noise processes, highlighting the impact of the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments.
Coherent errors, and especially those that occur in correlation among a set of qubits, are detrimental for large-scale quantum computing. Correlations in noise can occur as a result of spatial and temporal configurations of instructions executing on the quantum processor. In this paper, we perform a detailed experimental characterization of many of these error sources, and theoretically connect them to the physics of superconducting qubits and gate operations. Equipped with this knowledge, we devise compiler strategies to suppress these errors using dynamical decoupling or error compensation into the rest of the circuit. Importantly, these strategies are successful when the context at each layer of computation is taken into account: how qubits are connected, what crosstalk terms exist on the device, and what gates or idle periods occur in that layer. Our context-aware compiler thus suppresses some dominant sources of error, making further error mitigation or error correction substantially less expensive. For example, our experiments show an increase of 18.5%\mathbf{1 8. 5 \%}18.5% in layer fidelity for a candidate 10 -qubit circuit layer compared to context-unaware suppression. Owing to the exponential nature of error mitigation, these improvements due to error suppression translate to several orders of magnitude reduction of sampling overhead for a circuit consisting of a moderate number of layers.
As quantum circuits become more integrated and complex, additional error sources that were previously insignificant start to emerge. Consequently, the fidelity of quantum gates benchmarked under pristine conditions falls short of predicting their performance in realistic circuits. To overcome this problem, we must improve their robustness against pertinent error models besides isolated fidelity. Here, we report the experimental realization of robust quantum gates in superconducting quantum circuits based on a geometric framework for diagnosing and correcting various gate errors. Using quantum process tomography and randomized benchmarking, we demonstrate robust single-qubit gates against quasistatic noise and spatially correlated noise in a broad range of strengths, which are common sources of coherent errors in large-scale quantum circuits. We also apply our method to nonstatic noises and to realize robust two-qubit gates. Our Letter provides a versatile toolbox for achieving noise-resilient complex quantum circuits.
Abstract Quantum computing is an emerging technology that, with its exponential computational speedup, will allow us to solve a new level of hard problems. From rapid vaccine development, efficient discovery of exotic materials, and complex AI models, to quickly cracking RSA encryption, quantum computers have the potential to revolutionize science. However, for quantum computing to solve these problems, quantum error correction methods are needed to eliminate qubit errors. An underlying assumption of current quantum error correction is that qubit errors are not correlated. If correlated qubit errors are prevalent, quantum error correction will be difficult, if not impossible. In this work, I developed a method to identify correlated errors between pairs of qubits and used this method to determine if correlations exist on current small-scale quantum computers. My method uses independence of error probabilities P(qa) ⨉ P(qb) = P(qaqb) to determine correlation. After running 40 million experiments to collect error probabilities by varying the quantum gates, number of gates, and pairs of qubits on multiple quantum computers, I found that these computers have a high occurrence of correlated qubit errors when qubits are topological neighbors. For example, I found that Hadamard gate operations can cause correlated errors, supported by a p-value of 0.0160. My work shows that the assumption that qubit errors are not correlated is incorrect for current quantum computers. In the future, scientists can use these methods to test for correlated errors as they develop new quantum computers, enabling quantum computing to achieve its full potential.
Abstract We investigate the impact of the correlation between error gates on the fault-tolerant threshold in quantum circuits under three typical noise models. In the fault-tolerant encoding schemes for two fundamental quantum logical operations, we extend the conventional error injection method by simultaneously applying error gates to both control and target qubits after two-qubit gate operations, with a quantitative characterization of the correlation strength between these error gates. The results show that the fault-tolerant error threshold can be noticeably enhanced by the presence of correlations between error gates, resulting in more robust quantum circuit implementations. We further apply fault-tolerant encoding to the single-qubit teleportation circuit and investigate the effect of correlated noise on its error threshold. The results show that the threshold varies non-monotonically with the correlation strength and that the system’s fault-tolerance differs significantly across noise models.