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:1205.1836 · Physical Review A

Simplified quantum error detection and correction for superconducting qubits

Kyle Keane, Alexander N. Korotkov

Published Jul 27, 2012• 16 citations
arXivHTMLPDF

Abstract

We analyze simple quantum error detection and quantum error correction protocols relevant to current experiments with superconducting qubits. We show that for qubits with energy relaxation the repetitive $N$-qubit codes cannot be used for quantum error correction, but can be used for quantum error detection. In the latter case it is sufficient to use only two qubits for the encoding. In the analysis we demonstrate a useful technique of unraveling the qubit energy relaxation into ``relaxation'' and ``no relaxation'' scenarios. Also, we propose and numerically analyze several two-qubit algorithms for quantum error detection and correction, which can be readily realized at the present-day level of the phase qubit technology.

DOI
10.1103/physreva.86.012333

Related papers

Quantum State Protection and Transfer Using Superconducting Qubits

Kyle Keane

This dissertation presents a theoretical analysis of protocols relevant for quantum information processing with superconducting qubits. The purpose of these protocols is decoherence suppression and quantum information transfer. Our analysis makes use of the standard density matrix formalism and Kraus operator (operator-sum) representation of quantum operations. We also use the mathematical trick of unravelling continuous evolution into discrete scenarios with corresponding probabilities.We show that decoherence due to zero-temperature energy relaxation can be almost completely suppressed, probabilistically, by weak measurement reversal (also known as quantum uncollapsing). To protect a qubit, a weak (partial) quantum measurement moves it towards the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength.We also analyze several simple quantum error correction (QEC) and quantum error detection (QED) protocols, relevant to superconducting qubits. We show that for energy relaxation the repetitive N-qubit quantum codes cannot be used for QEC, but can be used for QED (also known as probabilistic error correction). Moreover, the repetitive code with only two qubits is sufficient for QED. We also present several other two-qubit algorithms realizable with the current technology of superconducting phase qubits; these algorithms can demonstrate QEC for intentional errors and QED for real decoherence.We also analyze a procedure designed to transfer the state of a microwave qubit from one superconducting resonator to another resonator via a transmission line; the emission and capture of the microwave energy is achieved using tunable couplers. The procedure is shown to be robust against experimental imperfections of required pulse shapes. Our results also indicate that a successful state transfer requires nearly equal resonator frequencies for the entire duration of the procedure.

•Jan 1, 2012•0 citations

Implementation of the three-qubit phase-flip error correction code with superconducting qubits

Lars Tornberg, Margareta Wallquist, Göran Johansson +2 more

We investigate the performance of a three-qubit error correcting code in the framework of superconducting qubit implementations. Such a code can recover a quantum state perfectly in the case of dephasing errors but only in situations where the dephasing rate is low. Numerical studies in previous work have however shown that the code does increase the fidelity of the encoded state even in the presence of high error probability, during both storage and processing. In this work we give analytical expressions for the fidelity of such a code. We consider two specific schemes for qubit-qubit interaction realizable in superconducting systems; one ${\ensuremath{\sigma}}_{z}{\ensuremath{\sigma}}_{z}$ coupling and one cavity-mediated coupling. With these realizations in mind, and considering errors during storing as well as processing, we calculate the maximum operation time allowed in order to still benefit from the code. We show that this limit can be reached with current technology.

arXiv:0803.1747•Physical Review B•Jun 27, 2008•13 citations

Exponential suppression of bit or phase flip errors with repetitive quantum error correction

Zijun Chen, Kevin J. Satzinger, Juan Atalaya +88 more

Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than $100\times$ when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing.

•Feb 11, 2021•8 citations

Efficient Quantum Error Correction of Dephasing Induced by a Common Fluctuator

David Layden, Mo Chen, Paola Cappellaro

Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on n qubits corrects errors to order t^{O(n)}, with t the time between recoveries, our codes correct to order t^{O(2^{n})}. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.

arXiv:1903.01046•Physical Review Letters•Jan 17, 2020•21 citations

Reducing the impact of intrinsic dissipation in a superconducting circuit by quantum error detection

Youpeng Zhong, Zongli Wang, Haohua Wang +3 more

A fundamental challenge for quantum information processing is reducing the impact of environmentally induced errors. Here we demonstrate a quantum error detection and rejection protocol based on the idea of quantum uncollapsing, using this protocol to reduce the impact of energy relaxation owing to the environment in a three-qubit superconducting circuit. We encode quantum information in a target qubit, and use the other two qubits to detect and reject errors caused by energy relaxation. This protocol improves the storage time of a quantum state by a factor of roughly three, at the cost of a reduced probability of success. This constitutes the first experimental demonstration of the algorithm-based improvement in the lifetime of a quantum state stored in a qubit. © 2014 Macmillan Publishers Limited. All rights reserved.

Bulletin of the American Physical Society•Mar 3, 2014•0 citations

Exponential suppression of bit or phase errors with cyclic error correction

Google Quantum AI, Zijun Chen, Kevin J. Satzinger +94 more

Abstract Realizing the potential of quantum computing requires sufficiently low logical error rates 1 . Many applications call for error rates as low as 10 −15 (refs. 2–9 ), but state-of-the-art quantum platforms typically have physical error rates near 10 −3 (refs. 10–14 ). Quantum error correction 15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device 18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

arXiv:2102.06132•Nature•Jul 14, 2021•385 citations
We analyze simple quantum error detection and quantum error correction protocols relevant to current experiments with superconducting qubits. We show that for qubits with energy relaxation the repetitive NNN-qubit codes cannot be used for quantum error correction, but can be used for quantum error detection. In the latter case it is sufficient to use only two qubits for the encoding. In the analysis we demonstrate a useful technique of unraveling the qubit energy relaxation into relaxation'' and no relaxation'' scenarios. Also, we propose and numerically analyze several two-qubit algorithms for quantum error detection and correction, which can be readily realized at the present-day level of the phase qubit technology.
This dissertation presents a theoretical analysis of protocols relevant for quantum information processing with superconducting qubits. The purpose of these protocols is decoherence suppression and quantum information transfer. Our analysis makes use of the standard density matrix formalism and Kraus operator (operator-sum) representation of quantum operations. We also use the mathematical trick of unravelling continuous evolution into discrete scenarios with corresponding probabilities.We show that decoherence due to zero-temperature energy relaxation can be almost completely suppressed, probabilistically, by weak measurement reversal (also known as quantum uncollapsing). To protect a qubit, a weak (partial) quantum measurement moves it towards the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength.We also analyze several simple quantum error correction (QEC) and quantum error detection (QED) protocols, relevant to superconducting qubits. We show that for energy relaxation the repetitive N-qubit quantum codes cannot be used for QEC, but can be used for QED (also known as probabilistic error correction). Moreover, the repetitive code with only two qubits is sufficient for QED. We also present several other two-qubit algorithms realizable with the current technology of superconducting phase qubits; these algorithms can demonstrate QEC for intentional errors and QED for real decoherence.We also analyze a procedure designed to transfer the state of a microwave qubit from one superconducting resonator to another resonator via a transmission line; the emission and capture of the microwave energy is achieved using tunable couplers. The procedure is shown to be robust against experimental imperfections of required pulse shapes. Our results also indicate that a successful state transfer requires nearly equal resonator frequencies for the entire duration of the procedure.
We investigate the performance of a three-qubit error correcting code in the framework of superconducting qubit implementations. Such a code can recover a quantum state perfectly in the case of dephasing errors but only in situations where the dephasing rate is low. Numerical studies in previous work have however shown that the code does increase the fidelity of the encoded state even in the presence of high error probability, during both storage and processing. In this work we give analytical expressions for the fidelity of such a code. We consider two specific schemes for qubit-qubit interaction realizable in superconducting systems; one ${\ensuremath{\sigma}}_{z}{\ensuremath{\sigma}}_{z}$ coupling and one cavity-mediated coupling. With these realizations in mind, and considering errors during storing as well as processing, we calculate the maximum operation time allowed in order to still benefit from the code. We show that this limit can be reached with current technology.
Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the 10−1510^{-15}10−15 regime, but state-of-the-art quantum platforms typically have physical error rates near 10−310^{-3}10−3. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than 100×100\times100× when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing.
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on n qubits corrects errors to order t^{O(n)}, with t the time between recoveries, our codes correct to order t^{O(2^{n})}. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.
A fundamental challenge for quantum information processing is reducing the impact of environmentally induced errors. Here we demonstrate a quantum error detection and rejection protocol based on the idea of quantum uncollapsing, using this protocol to reduce the impact of energy relaxation owing to the environment in a three-qubit superconducting circuit. We encode quantum information in a target qubit, and use the other two qubits to detect and reject errors caused by energy relaxation. This protocol improves the storage time of a quantum state by a factor of roughly three, at the cost of a reduced probability of success. This constitutes the first experimental demonstration of the algorithm-based improvement in the lifetime of a quantum state stored in a qubit. © 2014 Macmillan Publishers Limited. All rights reserved.
Abstract Realizing the potential of quantum computing requires sufficiently low logical error rates 1 . Many applications call for error rates as low as 10 −15 (refs. 2–9 ), but state-of-the-art quantum platforms typically have physical error rates near 10 −3 (refs. 10–14 ). Quantum error correction 15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device 18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.