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:0906.0525 · Physical Review A

Dynamical quantum error correction of unitary operations with bounded controls

Kaveh Khodjasteh, Lorenza Viola

Published Sep 14, 2009• 107 citations
arXivHTMLPDF

Abstract

Dynamically corrected gates were recently introduced [K. Khodjasteh and L. Viola, Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected quantum gates based on open-loop Hamiltonian engineering. Here, we further expand the framework of dynamical quantum error correction, with emphasis on elucidating under what conditions decoherence suppression can be ensured while performing a generic target quantum gate, using only available bounded-strength control resources. Explicit constructions for physically relevant error models are detailed, including arbitrary linear decoherence and pure dephasing on qubits. The effectiveness of dynamically corrected gates in an illustrative non-Markovian spin-bath setting is investigated numerically, confirming the expected fidelity performance in a wide parameter range. Robustness against a class of systematic control errors is automatically incorporated in the perturbative error regime.

DOI
10.1103/physreva.80.032314

Related papers

Automated synthesis of dynamically corrected quantum gates

Kaveh Khodjasteh, Hendrik Bluhm, Lorenza Viola

Dynamically corrected gates are extended to non-Markovian open quantum systems where limitations on the available controls and/or the presence of control noise make existing analytical approaches unfeasible. A computational framework for the synthesis of dynamically corrected gates is formalized that allows sensitivity against non-Markovian decoherence and control errors to be perturbatively minimized via numerical search, resulting in robust gate implementations. Explicit sequences for achieving universal high-fidelity control in a singlet-triplet spin qubit subject to realistic system and control constraint are provided, which simultaneously cancel to the leading order the dephasing due to non-Markovian nuclear-bath dynamics and voltage noise affecting the control fields. Substantially improved gate fidelities are predicted for current laboratory devices.

arXiv:1205.0217•Physical Review A•Oct 22, 2012•59 citations

Arbitrarily Accurate Dynamical Control in Open Quantum Systems

Kaveh Khodjasteh, Daniel A. Lidar, Lorenza Viola

We show that open-loop dynamical control techniques may be used to synthesize unitary transformations in open quantum systems in such a way that decoherence is perturbatively compensated for to a desired (in principle arbitrarily high) level of accuracy, which depends only on the strength of the relevant errors and the achievable rate of control modulation. Our constructive and fully analytical solution employs concatenated dynamically corrected gates, and is applicable independently of detailed knowledge of the system-environment interactions and environment dynamics. Explicit implications for boosting quantum gate fidelities in realistic scenarios are addressed.

arXiv:0908.1526•Physical Review Letters•Mar 4, 2010•174 citations

Dynamically Error-Corrected Gates for Universal Quantum Computation

Kaveh Khodjasteh, Lorenza Viola

Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary gates on an open quantum system without encoding or measurement overhead. Our results allow for a low-level error correction strategy solely based on Hamiltonian engineering using realistic bounded-strength controls and may substantially reduce implementation requirements for fault-tolerant quantum computing architectures.

arXiv:0810.0698•Physical Review Letters•Feb 26, 2009•256 citations

Hamiltonian quantum simulation with bounded-strength controls

Adam D. Bookatz, Paweł Wocjan, Lorenza Viola

We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians . Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an 'Eulerian decoupling cycle,' that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation . We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls . In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaevʼs honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed.

arXiv:1310.4153•New Journal of Physics•Apr 25, 2014•14 citations

High-fidelity and robust controlled-Z gates for superconducting transmon qubits. II. System-parameter uncertainties and overall errors

Chia-Hsien Huang, Hsi-Sheng Goan

In the companion paper (Part I), we developed an optimal-control framework to suppress intrinsic and decoherence-induced errors in controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons. Here, we extend this framework to incorporate uncertainties in coupling strength, anharmonicities, and zero-flux qubit frequencies, enabling the design of high-fidelity gates robust against noise and parameter uncertainties. We classify these uncertainties by whether they perturb the off-diagonal coupling strengths or the diagonal detunings of the Hamiltonian, and we identify distinct suppression mechanisms for each class. Coupling errors are mitigated through dynamical decoupling induced by strong detuning modulation. For a 30-ns gate, this strategy reduces the coupling error to $6.21\times10^{-7}$ and tolerates coupling-strength uncertainties up to $2π\times4$ MHz while keeping total gate infidelity below $10^{-3}$. Detuning errors are minimized near a symmetric-detuning operating point that balances the two dominant leakage-mediated interactions. A 24-ns gate operated near this point tolerates individual uncertainties of up to $2π\times5$ MHz in each relevant diagonal parameter under the same infidelity threshold. We further optimize gate performance under realistic conditions where intrinsic errors, decoherence, and parameter uncertainties coexist across six representative stages of progressively improving hardware performance. The resulting stage-specific controls achieve lower infidelity and greater robustness. Together with the companion study (Part I), this framework offers a practical approach to balance speed, fidelity, and robustness while reducing the need for exhaustive characterization and frequent recalibration in large-scale superconducting quantum processors.

quant-pharXiv:2610.30681•Oct 23, 2026•0 citations

Continuous quantum error correction for non-Markovian decoherence

Ognyan Oreshkov, Todd A. Brun

We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics.

arXiv:0705.2342•Physical Review A•Aug 20, 2007•47 citations
Dynamically corrected gates were recently introduced [K. Khodjasteh and L. Viola, Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected quantum gates based on open-loop Hamiltonian engineering. Here, we further expand the framework of dynamical quantum error correction, with emphasis on elucidating under what conditions decoherence suppression can be ensured while performing a generic target quantum gate, using only available bounded-strength control resources. Explicit constructions for physically relevant error models are detailed, including arbitrary linear decoherence and pure dephasing on qubits. The effectiveness of dynamically corrected gates in an illustrative non-Markovian spin-bath setting is investigated numerically, confirming the expected fidelity performance in a wide parameter range. Robustness against a class of systematic control errors is automatically incorporated in the perturbative error regime.
Dynamically corrected gates are extended to non-Markovian open quantum systems where limitations on the available controls and/or the presence of control noise make existing analytical approaches unfeasible. A computational framework for the synthesis of dynamically corrected gates is formalized that allows sensitivity against non-Markovian decoherence and control errors to be perturbatively minimized via numerical search, resulting in robust gate implementations. Explicit sequences for achieving universal high-fidelity control in a singlet-triplet spin qubit subject to realistic system and control constraint are provided, which simultaneously cancel to the leading order the dephasing due to non-Markovian nuclear-bath dynamics and voltage noise affecting the control fields. Substantially improved gate fidelities are predicted for current laboratory devices.
We show that open-loop dynamical control techniques may be used to synthesize unitary transformations in open quantum systems in such a way that decoherence is perturbatively compensated for to a desired (in principle arbitrarily high) level of accuracy, which depends only on the strength of the relevant errors and the achievable rate of control modulation. Our constructive and fully analytical solution employs concatenated dynamically corrected gates, and is applicable independently of detailed knowledge of the system-environment interactions and environment dynamics. Explicit implications for boosting quantum gate fidelities in realistic scenarios are addressed.
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary gates on an open quantum system without encoding or measurement overhead. Our results allow for a low-level error correction strategy solely based on Hamiltonian engineering using realistic bounded-strength controls and may substantially reduce implementation requirements for fault-tolerant quantum computing architectures.
We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians . Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an 'Eulerian decoupling cycle,' that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation . We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls . In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaevʼs honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed.
In the companion paper (Part I), we developed an optimal-control framework to suppress intrinsic and decoherence-induced errors in controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons. Here, we extend this framework to incorporate uncertainties in coupling strength, anharmonicities, and zero-flux qubit frequencies, enabling the design of high-fidelity gates robust against noise and parameter uncertainties. We classify these uncertainties by whether they perturb the off-diagonal coupling strengths or the diagonal detunings of the Hamiltonian, and we identify distinct suppression mechanisms for each class. Coupling errors are mitigated through dynamical decoupling induced by strong detuning modulation. For a 30-ns gate, this strategy reduces the coupling error to 6.21×10−76.21\times10^{-7}6.21×10−7 and tolerates coupling-strength uncertainties up to 2π×42π\times42π×4 MHz while keeping total gate infidelity below 10−310^{-3}10−3. Detuning errors are minimized near a symmetric-detuning operating point that balances the two dominant leakage-mediated interactions. A 24-ns gate operated near this point tolerates individual uncertainties of up to 2π×52π\times52π×5 MHz in each relevant diagonal parameter under the same infidelity threshold. We further optimize gate performance under realistic conditions where intrinsic errors, decoherence, and parameter uncertainties coexist across six representative stages of progressively improving hardware performance. The resulting stage-specific controls achieve lower infidelity and greater robustness. Together with the companion study (Part I), this framework offers a practical approach to balance speed, fidelity, and robustness while reducing the need for exhaustive characterization and frequent recalibration in large-scale superconducting quantum processors.
We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics.