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:2504.00279 · Quantum Science and Technology

Noise-aware time-optimal quantum control

Minjun Jeon, Zhenyu Cai

Published Jun 3, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract Quantum optimal control plays a vital role in many quantum technologies, including quantum computation. One of the most important control parameters to optimise for is the evolution time (pulse duration). However, most existing works focus on finding the shortest evolution time theoretically possible without offering explicit pulse constructions under practical constraints like noise in the system. This paper addresses these limitations by introducing an efficient method to perform the chopped random basis optimisation in the presence of noise, specifically when the noise commutes with the gate Hamiltonian, i.e. when the unitary and dissipative parts of the Liouvillian commute. This noise-aware approach allows for direct optimisation of the evolution time alongside other control parameters, significantly reducing the computational cost compared to full noisy simulations. The protocol is demonstrated through numerical simulations on state-to-state transfer and gate compilation problems under several noise models. Results show that the optimised fidelity has a strong dependence on evolution time due to noise, drift Hamiltonian, and local traps in optimisation, highlighting the necessity of optimising evolution time in practical settings that can lead to a substantial gain in the fidelity. Our pulse optimisation protocol can consistently escape from many local minima in all of our examples. We hope that our protocol can be the start of many more works on the crucial topic of control pulse time optimisation in practical settings.

DOI
10.1088/2058-9565/ae7750

Related papers

Optimized pulses for the control of uncertain qubits

Matthew Grace, Jason Dominy, Wayne M. Witzel +1 more

Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, postfacto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.

arXiv:1105.2358•Physical Review A•May 18, 2012•28 citations

Control optimization for parametric Hamiltonians by pulse reconstruction

Piero Luchi, Francesco Turro, Sofia Quaglioni +5 more

Abstract Optimal control techniques provide a means to tailor the control pulses required to generate customized quantum gates, which helps to improve the resilience of quantum simulations to gate errors and device noise. However, the significant amount of (classical) computation required to generate customized gates can quickly undermine the effectiveness of this approach, especially when pulse optimization needs to be iterated. We propose a method to reduce the computational time required to generate the control pulse for a Hamiltonian that is parametrically dependent on a time-varying quantity. We use simple interpolation schemes to accurately reconstruct the control pulses from a set of pulses obtained in advance for a discrete set of predetermined parameter values. We obtain a reconstruction with very high fidelity and a significant reduction in computational effort. We report the results of the application of the proposed method to device-level quantum simulations of the unitary (real) time evolution of two interacting neutrons based on superconducting qubits.

arXiv:2102.12316•The European Physical Journal A•Sep 1, 2023•6 citations

Control of noisy quantum systems: Field-theory approach to error mitigation

Rafael Hipolito, Paul M. Goldbart

We consider the basic quantum-control task of obtaining a target unitary operation (i.e., a quantum gate) via control fields that couple to the quantum system and are chosen to best mitigate errors resulting from time-dependent noise, which frustrate this task. We allow for two sources of noise: fluctuations in the control fields and fluctuations arising from the environment. We address the issue of control-error mitigation by means of a formulation rooted in the Martin-Siggia-Rose (MSR) approach to noisy, classical statistical-mechanical systems. To do this, we express the noisy control problem in terms of a path integral, and integrate out the noise to arrive at an effective, noise-free description. We characterize the degree of success in error mitigation via a fidelity metric, which characterizes the proximity of the sought-after evolution to ones that are achievable in the presence of noise. Error mitigation is then best accomplished by applying the optimal control fields, i.e., those that maximize the fidelity subject to any constraints obeyed by the control fields. To make connection with MSR, we reformulate the fidelity in terms of a Schwinger-Keldysh (SK) path integral, with the added twist that the ``forward'' and ``backward'' branches of the time contour are inequivalent with respect to the noise. The present approach naturally and readily allows the incorporation of constraints on the control fields---a useful feature in practice, given that constraints feature in all real experiments. In addition to addressing the noise average of the fidelity, we consider its full probability distribution. The information content present in this distribution allows one to address more complex questions regarding error mitigation, including, in principle, questions of extreme value statistics, i.e., the likelihood and impact of rare instances of the fidelity and how to harness or cope with their influence. We illustrate this MSR-SK reformulation by considering a model system consisting of a single spin-$s$ freedom (with $s$ arbitrary), focusing on the case of $1/f$ noise in the weak-noise limit. We discover that optimal error mitigation is accomplished via a universal control field protocol that is valid for all $s$, from the qubit (i.e., $s=1/2$) case to the classical (i.e., $s\ensuremath{\rightarrow}\ensuremath{\infty}$) limit. In principle, this MSR-SK approach provides a transparent framework for addressing quantum control in the presence of noise for systems of arbitrary complexity.

arXiv:1512.05477•Physical Review A•Apr 12, 2016•0 citations

Multiple classical noise mitigation by multiobjective robust quantum optimal control

Bowen Shao, Xiaodong Yang, Ran Liu +4 more

High-quality control is a fundamental requirement for quantum computation, but practically it is often hampered by the presence of various types of noises, which can be static or time dependent. In many realistic scenarios, multiple noise sources coexist, and their resulting noise effects need to be corrected to a sufficient order, posing significant challenges for the design of effective robust control methods. Here, we explore the method of robust quantum optimal control to generally tackle the problem of resisting multiple noises from a complicated noise environment. Specifically, we confine our analysis to classical stochastic noises that can be described by classical noise models. This method employs a gradient-based multiobjective optimization algorithm to maximize the control figure of merit, and meanwhile to minimize the perturbative effects of the noises that are allowed for. To verify its effectiveness, we apply this method to a number of examples, including robust entangling gate in a trapped-ion system and robust controlled-$Z$ gate in superconducting qubits, under commonly encountered static and time-dependent noises. Our simulation results reveal that robust optimal control can find smooth, robust pulses that can simultaneously resist several noises and thus achieve high-fidelity gates. Therefore, we expect that this method will find wide applications on current noisy quantum computing devices.

arXiv:2403.00298•Physical Review Applied•Mar 20, 2024•4 citations

Pulse Quality Optimisation in Quantum Optimal Control

Dylan Lewis, Roeland Wiersema

Quantum optimal control methods are widely used to design experimental control pulses such as laser amplitudes, phases, or detunings, that implement a target unitary evolution. In practice, what makes a pulse "good" depends not only on its fidelity, but also on the experimental setting and the relevant hardware constraints. Here, we introduce geometric quantum control with kernel optimisation (GECKO), a model-agnostic method for improving control pulses after a high-fidelity solution has been found. GECKO uses the Riemannian geometry of the special unitary group to identify directions in pulse space that leave the implemented unitary unchanged to first order, allowing one to traverse level sets of the control landscape while optimising a chosen differentiable pulse-quality function. We demonstrate GECKO on a transverse-field Ising Hamiltonian implementing CZ and CNOT gates, optimising pulse properties including spectral filtering, smoothness, robustness to parameter deviations, and pulse duration. In all cases, GECKO finds substantially improved pulse solutions.

quant-pharXiv:2604.25768•Apr 29, 2026•0 citations

Quantum control for time-dependent noise

Chingiz Kabytayev

The main obstacles to implementing ideal quantum operations are unwanted interactions of quantum systems with the environment and noise in control fields. This problem can be tackled by methods of quantum control. Among these methods are \ncomposite pulse (CP) sequences which have long been employed in nuclear magnetic resonance (NMR) to mitigate the effects of systematic errors in the control. CP sequences have been initially developed to correct for static but otherwise unknown \nerrors in the amplitude or frequency of the driving field. One of the challenges to the systematic incorporation of these control protocols into practical quantum information systems remains the limited understanding of CP performance in the presence \nof time-dependent noise. Treating the influence of time-dependent noise processes on quantum control operations has been facilitated by recent advances in dynamical \nerror suppression based on open-loop Hamiltonian engineering. These approaches provide a general framework for understanding and mitigating non-Markovian time- \ndependent noise in a finite-dimensional open quantum system. Particularly, arbitrary single-qubit control characteristics may be captured quantitatively in filter-transfer \nfunctions (FF) using methods of spectral overlap in the frequency domain. In this thesis work, we present a systematic study of control pulse sequences in the presence of time-dependent noise. We use a combination of analytic formulations based on FFs and numerical simulations to demonstrate that CPs are able to effectively suppress control errors caused by time-dependent processes possessing realistic noise \npower spectra. We provide a geometric interpretation of CP performance under time-dependent amplitude noise, further linking the FF formalism with known techniques in CP construction. We also develop new optimized pulse sequences that act as notch filters for time-dependent noise. These high-fidelity control protocols effectively sup- \npress errors from the noise sources with sharp features in spectral densities and can be used practically on various quantum architectures. We also present our work \non simulation of randomized benchmarking protocols and CPs that have been used experimentally by our collaborators to measure gate errors.

•May 15, 2015•2 citations
Abstract Quantum optimal control plays a vital role in many quantum technologies, including quantum computation. One of the most important control parameters to optimise for is the evolution time (pulse duration). However, most existing works focus on finding the shortest evolution time theoretically possible without offering explicit pulse constructions under practical constraints like noise in the system. This paper addresses these limitations by introducing an efficient method to perform the chopped random basis optimisation in the presence of noise, specifically when the noise commutes with the gate Hamiltonian, i.e. when the unitary and dissipative parts of the Liouvillian commute. This noise-aware approach allows for direct optimisation of the evolution time alongside other control parameters, significantly reducing the computational cost compared to full noisy simulations. The protocol is demonstrated through numerical simulations on state-to-state transfer and gate compilation problems under several noise models. Results show that the optimised fidelity has a strong dependence on evolution time due to noise, drift Hamiltonian, and local traps in optimisation, highlighting the necessity of optimising evolution time in practical settings that can lead to a substantial gain in the fidelity. Our pulse optimisation protocol can consistently escape from many local minima in all of our examples. We hope that our protocol can be the start of many more works on the crucial topic of control pulse time optimisation in practical settings.
Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, postfacto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.
Abstract Optimal control techniques provide a means to tailor the control pulses required to generate customized quantum gates, which helps to improve the resilience of quantum simulations to gate errors and device noise. However, the significant amount of (classical) computation required to generate customized gates can quickly undermine the effectiveness of this approach, especially when pulse optimization needs to be iterated. We propose a method to reduce the computational time required to generate the control pulse for a Hamiltonian that is parametrically dependent on a time-varying quantity. We use simple interpolation schemes to accurately reconstruct the control pulses from a set of pulses obtained in advance for a discrete set of predetermined parameter values. We obtain a reconstruction with very high fidelity and a significant reduction in computational effort. We report the results of the application of the proposed method to device-level quantum simulations of the unitary (real) time evolution of two interacting neutrons based on superconducting qubits.
We consider the basic quantum-control task of obtaining a target unitary operation (i.e., a quantum gate) via control fields that couple to the quantum system and are chosen to best mitigate errors resulting from time-dependent noise, which frustrate this task. We allow for two sources of noise: fluctuations in the control fields and fluctuations arising from the environment. We address the issue of control-error mitigation by means of a formulation rooted in the Martin-Siggia-Rose (MSR) approach to noisy, classical statistical-mechanical systems. To do this, we express the noisy control problem in terms of a path integral, and integrate out the noise to arrive at an effective, noise-free description. We characterize the degree of success in error mitigation via a fidelity metric, which characterizes the proximity of the sought-after evolution to ones that are achievable in the presence of noise. Error mitigation is then best accomplished by applying the optimal control fields, i.e., those that maximize the fidelity subject to any constraints obeyed by the control fields. To make connection with MSR, we reformulate the fidelity in terms of a Schwinger-Keldysh (SK) path integral, with the added twist that the ``forward'' and ``backward'' branches of the time contour are inequivalent with respect to the noise. The present approach naturally and readily allows the incorporation of constraints on the control fields---a useful feature in practice, given that constraints feature in all real experiments. In addition to addressing the noise average of the fidelity, we consider its full probability distribution. The information content present in this distribution allows one to address more complex questions regarding error mitigation, including, in principle, questions of extreme value statistics, i.e., the likelihood and impact of rare instances of the fidelity and how to harness or cope with their influence. We illustrate this MSR-SK reformulation by considering a model system consisting of a single spin-sss freedom (with sss arbitrary), focusing on the case of 1/f1/f1/f noise in the weak-noise limit. We discover that optimal error mitigation is accomplished via a universal control field protocol that is valid for all sss, from the qubit (i.e., s=1/2s=1/2s=1/2) case to the classical (i.e., $s\ensuremath{\rightarrow}\ensuremath{\infty}$) limit. In principle, this MSR-SK approach provides a transparent framework for addressing quantum control in the presence of noise for systems of arbitrary complexity.
High-quality control is a fundamental requirement for quantum computation, but practically it is often hampered by the presence of various types of noises, which can be static or time dependent. In many realistic scenarios, multiple noise sources coexist, and their resulting noise effects need to be corrected to a sufficient order, posing significant challenges for the design of effective robust control methods. Here, we explore the method of robust quantum optimal control to generally tackle the problem of resisting multiple noises from a complicated noise environment. Specifically, we confine our analysis to classical stochastic noises that can be described by classical noise models. This method employs a gradient-based multiobjective optimization algorithm to maximize the control figure of merit, and meanwhile to minimize the perturbative effects of the noises that are allowed for. To verify its effectiveness, we apply this method to a number of examples, including robust entangling gate in a trapped-ion system and robust controlled-ZZZ gate in superconducting qubits, under commonly encountered static and time-dependent noises. Our simulation results reveal that robust optimal control can find smooth, robust pulses that can simultaneously resist several noises and thus achieve high-fidelity gates. Therefore, we expect that this method will find wide applications on current noisy quantum computing devices.
Quantum optimal control methods are widely used to design experimental control pulses such as laser amplitudes, phases, or detunings, that implement a target unitary evolution. In practice, what makes a pulse "good" depends not only on its fidelity, but also on the experimental setting and the relevant hardware constraints. Here, we introduce geometric quantum control with kernel optimisation (GECKO), a model-agnostic method for improving control pulses after a high-fidelity solution has been found. GECKO uses the Riemannian geometry of the special unitary group to identify directions in pulse space that leave the implemented unitary unchanged to first order, allowing one to traverse level sets of the control landscape while optimising a chosen differentiable pulse-quality function. We demonstrate GECKO on a transverse-field Ising Hamiltonian implementing CZ and CNOT gates, optimising pulse properties including spectral filtering, smoothness, robustness to parameter deviations, and pulse duration. In all cases, GECKO finds substantially improved pulse solutions.
The main obstacles to implementing ideal quantum operations are unwanted interactions of quantum systems with the environment and noise in control fields. This problem can be tackled by methods of quantum control. Among these methods are \ncomposite pulse (CP) sequences which have long been employed in nuclear magnetic resonance (NMR) to mitigate the effects of systematic errors in the control. CP sequences have been initially developed to correct for static but otherwise unknown \nerrors in the amplitude or frequency of the driving field. One of the challenges to the systematic incorporation of these control protocols into practical quantum information systems remains the limited understanding of CP performance in the presence \nof time-dependent noise. Treating the influence of time-dependent noise processes on quantum control operations has been facilitated by recent advances in dynamical \nerror suppression based on open-loop Hamiltonian engineering. These approaches provide a general framework for understanding and mitigating non-Markovian time- \ndependent noise in a finite-dimensional open quantum system. Particularly, arbitrary single-qubit control characteristics may be captured quantitatively in filter-transfer \nfunctions (FF) using methods of spectral overlap in the frequency domain. In this thesis work, we present a systematic study of control pulse sequences in the presence of time-dependent noise. We use a combination of analytic formulations based on FFs and numerical simulations to demonstrate that CPs are able to effectively suppress control errors caused by time-dependent processes possessing realistic noise \npower spectra. We provide a geometric interpretation of CP performance under time-dependent amplitude noise, further linking the FF formalism with known techniques in CP construction. We also develop new optimized pulse sequences that act as notch filters for time-dependent noise. These high-fidelity control protocols effectively sup- \npress errors from the noise sources with sharp features in spectral densities and can be used practically on various quantum architectures. We also present our work \non simulation of randomized benchmarking protocols and CPs that have been used experimentally by our collaborators to measure gate errors.