We examine the effectiveness and resilience of achieving quantum gates employing three approaches stemming from quantum control methods: counterdiabatic driving, Floquet engineering, and inverse engineering. We critically analyze their performance in terms of the gate infidelity, the associated resource overhead based on energetic cost, the susceptibility to timekeeping errors, and the degradation under environmental noise. Despite significant differences in the dynamical path taken, we find a broadly consistent behavior across the three approaches in terms of the efficacy of implementing the target gate and the resource overhead. Furthermore, we establish that the functional form of the control fields plays a crucial role in determining how faithfully a gate operation is achieved. Our results are demonstrated for single-qubit gates, with particular focus on the Hadamard gate, and we discuss the extension to $N$ -qubit operations.We examine the effectiveness and resilience of achieving quantum gates employing three approaches stemming from quantum control methods: counterdiabatic driving, Floquet engineering, and inverse engineering. We critically analyze their performance in terms of the gate infidelity, the associated resource overhead based on energetic cost, the susceptibility to timekeeping errors, and the degradation under environmental noise. Despite significant differences in the dynamical path taken, we find a broadly consistent behavior across the three approaches in terms of the efficacy of implementing the target gate and the resource overhead. Furthermore, we establish that the functional form of the control fields plays a crucial role in determining how faithfully a gate operation is achieved. Our results are demonstrated for single-qubit gates, with particular focus on the Hadamard gate, and we discuss the extension to $N$-qubit operations.

Physical Review AAug 25, 20239 citations

Quantum gates by inverse engineering of a Hamiltonian

Alan C. Santos

Abstract Inverse engineering of a Hamiltonian (IEH) from an evolution operator is a useful technique for the protocol of quantum control with potential applications in quantum information processing. In this paper we introduce a particular protocol to perform IEH and we show how this scheme can be used to implement a set of quantum gates by using minimal quantum resources (such as entanglement, interactions between more than two qubits or auxiliary qubits). Remarkably, while previous protocols request three-qubit interactions and/or auxiliary qubits to implement such gates, our protocol requires just two-qubit interactions and no auxiliary qubits. By using this approach we can obtain a large class of Hamiltonians that allow us to implement single and two-qubit gates necessary for quantum computation. To conclude this article we analyze the performance of our scheme against systematic errors related to amplitude noise, where we show that the free parameters introduced in our scheme can be useful for enhancing the robustness of the protocol against such errors.Abstract Inverse engineering of a Hamiltonian (IEH) from an evolution operator is a useful technique for the protocol of quantum control with potential applications in quantum information processing. In this paper we introduce a particular protocol to perform IEH and we show how this scheme can be used to implement a set of quantum gates by using minimal quantum resources (such as entanglement, interactions between more than two qubits or auxiliary qubits). Remarkably, while previous protocols request three-qubit interactions and/or auxiliary qubits to implement such gates, our protocol requires just two-qubit interactions and no auxiliary qubits. By using this approach we can obtain a large class of Hamiltonians that allow us to implement single and two-qubit gates necessary for quantum computation. To conclude this article we analyze the performance of our scheme against systematic errors related to amplitude noise, where we show that the free parameters introduced in our scheme can be useful for enhancing the robustness of the protocol against such errors.

arXiv:1701.01848Journal of Physics B Atomic Molecular and Optical PhysicsNov 6, 201719 citations

Traversing Quantum Control Robustness Landscapes: A New Paradigm for Quantum Gate Engineering

Huiqi Xue, Xiu–Hao Deng

The optimization of robust quantum control is often tailored to specific tasks and suffers from inefficiencies due to the complexity of cost functions. Our recent findings indicate a highly effective methodology for the engineering of quantum gates by initiating the process with a robust control configuration of any arbitrary gate. We first introduce the Quantum Control Robustness Landscape (QCRL), a conceptual framework that maps control parameters to noise susceptibility. This framework facilitates a systematic investigation of equally robust controls for diverse quantum operations. By navigating through the level sets of the QCRL, our Robustness-Invariant Pulse Variation (RIPV) algorithm allows for the variation of control pulses while preserving robustness. Numerical simulations demonstrate that our single- and two-qubit gates exceed the quantum error correction threshold even with substantial noise. This methodology opens up a new paradigm for quantum gate engineering capable of effectively suppressing generic noise.The optimization of robust quantum control is often tailored to specific tasks and suffers from inefficiencies due to the complexity of cost functions. Our recent findings indicate a highly effective methodology for the engineering of quantum gates by initiating the process with a robust control configuration of any arbitrary gate. We first introduce the Quantum Control Robustness Landscape (QCRL), a conceptual framework that maps control parameters to noise susceptibility. This framework facilitates a systematic investigation of equally robust controls for diverse quantum operations. By navigating through the level sets of the QCRL, our Robustness-Invariant Pulse Variation (RIPV) algorithm allows for the variation of control pulses while preserving robustness. Numerical simulations demonstrate that our single- and two-qubit gates exceed the quantum error correction threshold even with substantial noise. This methodology opens up a new paradigm for quantum gate engineering capable of effectively suppressing generic noise.

arXiv:2412.19473Dec 27, 20240 citations

Dynamical quantum error correction of unitary operations with bounded controls

Kaveh Khodjasteh, Lorenza Viola

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 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.

arXiv:0906.0525Physical Review ASep 14, 2009107 citations

Engineered Robustness for Nonadiabatic Geometric Quantum Gates

Xuan Zhang, XIao-le Li, Jingjing Niu +2 more

While geometric quantum gates are often theorized to possess intrinsic resilience to control errors by exploiting the global properties of evolution paths, this promise has not consistently translated into practical robustness. We present a streamlined framework for nonadiabatic geometric quantum gates (NGQGs) that incorporates additional auxiliary constraints to suppress dynamical contamination and achieve super-robust performance. Within this framework, we also design NGQGs using noncyclic paths, offering enhanced design flexibility. Implemented on superconducting transmon qubits, our scheme realizes high-fidelity single-qubit gates that are robust against Rabi amplitude error $ε$ , with infidelity scaling as $\mathcal{O}(ε^4)$ , in contrast to the $\mathcal{O}(ε^2)$ behavior of conventional dynamical gates. We further analyze two-qubit NGQGs under parametric driving. Our results identify subtle limitations that compromise performance in two-qubit scenarios, underscoring the importance of phase compensation and waveform calibration. The demonstrated simplicity and generality of our super-robust NGQG scheme make it applicable across diverse quantum platforms.While geometric quantum gates are often theorized to possess intrinsic resilience to control errors by exploiting the global properties of evolution paths, this promise has not consistently translated into practical robustness. We present a streamlined framework for nonadiabatic geometric quantum gates (NGQGs) that incorporates additional auxiliary constraints to suppress dynamical contamination and achieve super-robust performance. Within this framework, we also design NGQGs using noncyclic paths, offering enhanced design flexibility. Implemented on superconducting transmon qubits, our scheme realizes high-fidelity single-qubit gates that are robust against Rabi amplitude error $ε$, with infidelity scaling as $\mathcal{O}(ε^4)$, in contrast to the $\mathcal{O}(ε^2)$ behavior of conventional dynamical gates. We further analyze two-qubit NGQGs under parametric driving. Our results identify subtle limitations that compromise performance in two-qubit scenarios, underscoring the importance of phase compensation and waveform calibration. The demonstrated simplicity and generality of our super-robust NGQG scheme make it applicable across diverse quantum platforms.

quant-pharXiv:2511.04225Physical Review AppliedNov 7, 20250 citations

Low-Weight Pauli Hamiltonian Sequences for Noise-Resilient Quantum Gates

R. J. Epstein

A simple protocol based on low-weight Pauli Hamiltonians is introduced for performing quantum gates that are robust to control noise. Gates are implemented by an adiabatic sequence of single-qubit fields and two-qubit interactions with a single ancillary qubit, whereas related techniques require three-qubit interactions, perturbation gadgets, higher dimensional subsystems, and/or more ancilla qubits. Low-weight interactions and low qubit overhead open a viable path to experimental investigation, while operation in a degenerate ground space allows for physical qubit designs that are immune to energy relaxation. Simulations indicate that two-qubit gate error due to control noise can be as low as $10^{-5}$ , for realizable coupling strengths and time-scales, with low-frequency noise that is as high as 15% of the control pulse amplitude.A simple protocol based on low-weight Pauli Hamiltonians is introduced for performing quantum gates that are robust to control noise. Gates are implemented by an adiabatic sequence of single-qubit fields and two-qubit interactions with a single ancillary qubit, whereas related techniques require three-qubit interactions, perturbation gadgets, higher dimensional subsystems, and/or more ancilla qubits. Low-weight interactions and low qubit overhead open a viable path to experimental investigation, while operation in a degenerate ground space allows for physical qubit designs that are immune to energy relaxation. Simulations indicate that two-qubit gate error due to control noise can be as low as $10^{-5}$, for realizable coupling strengths and time-scales, with low-frequency noise that is as high as 15% of the control pulse amplitude.

arXiv:1711.00570Nov 2, 20170 citations

N

-qubit operations.

ε

, with infidelity scaling as

\mathcal{O}(ε^4)

, in contrast to the

\mathcal{O}(ε^2)

behavior of conventional dynamical gates. We further analyze two-qubit NGQGs under parametric driving. Our results identify subtle limitations that compromise performance in two-qubit scenarios, underscoring the importance of phase compensation and waveform calibration. The demonstrated simplicity and generality of our super-robust NGQG scheme make it applicable across diverse quantum platforms.

10^{-5}

, for realizable coupling strengths and time-scales, with low-frequency noise that is as high as 15% of the control pulse amplitude.