Error suppression to the experimental imperfections is a central challenge for useful quantum computing. Recent studies have shown the advantages of using single-modulated pulses based on optimal control, which can realize high-fidelity two-qubit gates in neutral-atom arrays. However, typical optimization minimizes only the ideal gate error in the absence of any decay, which allows the gate to be passively influenced by all error sources leading to an exponential increase of the insensitivity when error becomes larger. In the present work, we propose the realization of two-qubit ${C}_{Z}$ gates with active robustness against two-photon detuning errors. Our method depends on a modified cost function in numerical optimization for shaping gate pulses, which minimizes, not only the ideal gate error but also the fluctuations of gate infidelity over a wide error range. We introduce a family of Rydberg blockade gates with active robustness towards the impacts of versatile noise sources such as Doppler dephasing and ac Stark shifts. The resulting gates with robust pulses can significantly increase the insensitivity to any type of errors acting on the two-photon detuning, benefiting from a relaxed requirement of colder atomic temperatures or more stable lasers for current experimental technology.Error suppression to the experimental imperfections is a central challenge for useful quantum computing. Recent studies have shown the advantages of using single-modulated pulses based on optimal control, which can realize high-fidelity two-qubit gates in neutral-atom arrays. However, typical optimization minimizes only the ideal gate error in the absence of any decay, which allows the gate to be passively influenced by all error sources leading to an exponential increase of the insensitivity when error becomes larger. In the present work, we propose the realization of two-qubit ${C}_{Z}$ gates with active robustness against two-photon detuning errors. Our method depends on a modified cost function in numerical optimization for shaping gate pulses, which minimizes, not only the ideal gate error but also the fluctuations of gate infidelity over a wide error range. We introduce a family of Rydberg blockade gates with active robustness towards the impacts of versatile noise sources such as Doppler dephasing and ac Stark shifts. The resulting gates with robust pulses can significantly increase the insensitivity to any type of errors acting on the two-photon detuning, benefiting from a relaxed requirement of colder atomic temperatures or more stable lasers for current experimental technology.

Physical Review AppliedSep 24, 20246 citations

Detuning-robust Rydberg entangling gates from echoed pulses

Zhubing Jia, Yichao Yu, Xiye Hu +4 more

Rydberg-based two-qubit gate fidelities in neutral atom arrays are limited chiefly by laser intensity inhomogeneity and by detuning errors from frequency miscalibration, background-field drift, intermediate state light shift and Doppler shifts. Quantum optimal control can suppress the former, but no pulse can render a controlled-Z gate first-order insensitive to detuning. Here we show that this obstruction can be circumvented by designing Rydberg gate pulses with every leading-order detuning error relegated to single-qubit Z-rotations, which an echoed sequence removes. The resulting maximally-entangling ZZ gate has no leading-order response to arbitrary detunings on either atom, maintaining an infidelity below $10^{-3}$ within a much wider range of single-atom detunings than the time-optimal gates. We further show that a large fraction of residual error is dominated by population outside the computational subspace, which can be converted into heralded erasures. Our results significantly reduce the requirements on laser frequency stability and intensity homogeneity, field calibration and atomic temperature toward practical fault-tolerant quantum computing with neutral atoms.Rydberg-based two-qubit gate fidelities in neutral atom arrays are limited chiefly by laser intensity inhomogeneity and by detuning errors from frequency miscalibration, background-field drift, intermediate state light shift and Doppler shifts. Quantum optimal control can suppress the former, but no pulse can render a controlled-Z gate first-order insensitive to detuning. Here we show that this obstruction can be circumvented by designing Rydberg gate pulses with every leading-order detuning error relegated to single-qubit Z-rotations, which an echoed sequence removes. The resulting maximally-entangling ZZ gate has no leading-order response to arbitrary detunings on either atom, maintaining an infidelity below $10^{-3}$ within a much wider range of single-atom detunings than the time-optimal gates. We further show that a large fraction of residual error is dominated by population outside the computational subspace, which can be converted into heralded erasures. Our results significantly reduce the requirements on laser frequency stability and intensity homogeneity, field calibration and atomic temperature toward practical fault-tolerant quantum computing with neutral atoms.

quant-pharXiv:2608.26446Aug 28, 20260 citations

Optimized ancillary drive for fast Rydberg entangling gates

Rui Li, Min-Hua Zhang, Jing Qian

Reaching fast and robust two-qubit gates with low infidelities has been an outstanding challenge for the long-term goal of useful quantum computers. Typically, optimizing the pulse shapes can minimize the gate infidelity and improve its robustness to certain types of errors; yet it remains incapable of speeding up the gate execution time which is fundamentally restricted by the attainable Rabi frequency in a realistic setup. In this work, we develop a fast implementation of two-qubit CZ gates using optimized ancillary drive to enhance the two-photon Rabi frequency between the ground and Rydberg states.This ancillary drive can work in an error-robustness framework without increasing the original gate infidelity in the absence of the drive. Considering the experimentally feasible parameters for $^{87}$ Rb atoms, we demonstrate that the execution time required for such CZ gates can be shortened by more than 30 $\%$ as compared to standard two-photon protocols arising the gate fidelity above 0.9954 by taking account of all relevant error sources. Our results reduce the high-power laser requirement and unlock the potential toward fast, high-fidelity quantum operations for large-scale quantum computation with neutral atoms.Reaching fast and robust two-qubit gates with low infidelities has been an outstanding challenge for the long-term goal of useful quantum computers. Typically, optimizing the pulse shapes can minimize the gate infidelity and improve its robustness to certain types of errors; yet it remains incapable of speeding up the gate execution time which is fundamentally restricted by the attainable Rabi frequency in a realistic setup. In this work, we develop a fast implementation of two-qubit CZ gates using optimized ancillary drive to enhance the two-photon Rabi frequency between the ground and Rydberg states.This ancillary drive can work in an error-robustness framework without increasing the original gate infidelity in the absence of the drive. Considering the experimentally feasible parameters for $^{87}$Rb atoms, we demonstrate that the execution time required for such CZ gates can be shortened by more than 30$\%$ as compared to standard two-photon protocols arising the gate fidelity above 0.9954 by taking account of all relevant error sources. Our results reduce the high-power laser requirement and unlock the potential toward fast, high-fidelity quantum operations for large-scale quantum computation with neutral atoms.

quant-pharXiv:2602.21512Feb 26, 20260 citations

Robust control and optimal Rydberg states for neutral atom two-qubit gates

Madhav Mohan, Robert de Keijzer, S. J. J. M. F. Kokkelmans

We investigate the robustness of two-qubit gates to deviations of experimental controls on a neutral atom platform utilizing Rydberg states. We construct robust controlled-Z gates---employing techniques from quantum optimal control---that retain high Bell-state fidelity $F>0.999$ in the presence of significant deviations of the coupling strength to the Rydberg state. Such deviations can arise from laser intensity noise and atomic motion in an inhomogeneous coupling field. We also discuss methods to mitigate errors due to deviations of the laser detuning. The designed pulses operate on timescales that are short compared to the fundamental decay timescale set by spontaneous emission and blackbody radiation. We account for the finite lifetime of the Rydberg state in both the optimization and fidelity calculations---this makes the gates conducive to noisy intermediate-scale quantum experiments, meaning that our protocols can reduce infidelity on near-term quantum computing devices. We calculate physical properties associated with infidelity for strontium-88 atoms---including lifetimes, polarizabilities, and blockade strengths---and use these calculations to identify optimal Rydberg states for our protocols, which allows for further minimization of infidelity.We investigate the robustness of two-qubit gates to deviations of experimental controls on a neutral atom platform utilizing Rydberg states. We construct robust controlled-Z gates---employing techniques from quantum optimal control---that retain high Bell-state fidelity $F>0.999$ in the presence of significant deviations of the coupling strength to the Rydberg state. Such deviations can arise from laser intensity noise and atomic motion in an inhomogeneous coupling field. We also discuss methods to mitigate errors due to deviations of the laser detuning. The designed pulses operate on timescales that are short compared to the fundamental decay timescale set by spontaneous emission and blackbody radiation. We account for the finite lifetime of the Rydberg state in both the optimization and fidelity calculations---this makes the gates conducive to noisy intermediate-scale quantum experiments, meaning that our protocols can reduce infidelity on near-term quantum computing devices. We calculate physical properties associated with infidelity for strontium-88 atoms---including lifetimes, polarizabilities, and blockade strengths---and use these calculations to identify optimal Rydberg states for our protocols, which allows for further minimization of infidelity.

arXiv:2212.10159Physical Review ResearchJul 25, 202340 citations

Erasing Doppler dephasing error in Rydberg quantum gates

Rui Li, Jing Qian, Weiping Zhang

Abstract The Doppler dephasing error due to residual thermal motion of atoms is a major cause of infidelity in neutral-atom quantum gates. Besides cooling and trapping advancements, few effective methods exist to mitigate this error. In the present work, we first propose an error-erasing strategy that utilizes a pair of off-resonant fields to continuously dress the protected Rydberg state with an auxiliary state, which can induce an opposite but enhanced sensitivity to the same source of Doppler dephasing error. Combining with the optimal control of laser pulses, we have realized a family of Rydberg two-qubit controlled-NOT gates in Rb and Cs atoms that are fully immune to the Doppler dephasing error. We numerically simulate this gate operation with fidelity F ≈ 0.9906 at any temperature for a lower-excited auxiliary state, and a higher fidelity of F ≈ 0.9960 can be attained for a ground auxiliary state even at a temperature of 500 µK. Finally, we predict a super-high fidelity of F > 0.9999 for 50 μ K is possible by using the robust pulses with a larger amplitude. Our results significantly reduce atomic temperature requirements for high-fidelity quantum gates, and may provide fundamental guidance to practical fault-tolerant quantum computing with neutral atoms.Abstract The Doppler dephasing error due to residual thermal motion of atoms is a major cause of infidelity in neutral-atom quantum gates. Besides cooling and trapping advancements, few effective methods exist to mitigate this error. In the present work, we first propose an error-erasing strategy that utilizes a pair of off-resonant fields to continuously dress the protected Rydberg state with an auxiliary state, which can induce an opposite but enhanced sensitivity to the same source of Doppler dephasing error. Combining with the optimal control of laser pulses, we have realized a family of Rydberg two-qubit controlled-NOT gates in Rb and Cs atoms that are fully immune to the Doppler dephasing error. We numerically simulate this gate operation with fidelity F ≈ 0.9906 at any temperature for a lower-excited auxiliary state, and a higher fidelity of F ≈ 0.9960 can be attained for a ground auxiliary state even at a temperature of 500 µK. Finally, we predict a super-high fidelity of F > 0.9999 for 50 μ K is possible by using the robust pulses with a larger amplitude. Our results significantly reduce atomic temperature requirements for high-fidelity quantum gates, and may provide fundamental guidance to practical fault-tolerant quantum computing with neutral atoms.

arXiv:2407.06517New Journal of PhysicsApr 23, 20252 citations

Time-Optimal Two- and Three-Qubit Gates for Rydberg Atoms

Sven Jandura, Guido Pupillo

We identify time-optimal laser pulses to implement the controlled-Z gate and its three qubit generalization, the C 2 Z gate, for Rydberg atoms in the blockade regime. Pulses are optimized using a combination of numerical and semi-analytical quantum optimal control techniques that result in smooth Ansätze with just a few variational parameters. For the CZ gate, the time-optimal implementation corresponds to a global laser pulse that does not require single site addressability of the atoms, simplifying experimental implementation of the gate. We employ quantum optimal control techniques to mitigate errors arising due to the finite lifetime of Rydberg states and finite blockade strengths, while several other types of errors affecting the gates are directly mitigated by the short gate duration. For the considered error sources, we achieve theoretical gate fidelities compatible with error correction using reasonable experimental parameters for CZ and C 2 Z gates.We identify time-optimal laser pulses to implement the controlled-Z gate and its three qubit generalization, the C 2 Z gate, for Rydberg atoms in the blockade regime. Pulses are optimized using a combination of numerical and semi-analytical quantum optimal control techniques that result in smooth Ansätze with just a few variational parameters. For the CZ gate, the time-optimal implementation corresponds to a global laser pulse that does not require single site addressability of the atoms, simplifying experimental implementation of the gate. We employ quantum optimal control techniques to mitigate errors arising due to the finite lifetime of Rydberg states and finite blockade strengths, while several other types of errors affecting the gates are directly mitigated by the short gate duration. For the considered error sources, we achieve theoretical gate fidelities compatible with error correction using reasonable experimental parameters for CZ and C 2 Z gates.

arXiv:2202.00903QuantumMay 13, 2022151 citations

{C}_{Z}

gates with active robustness against two-photon detuning errors. Our method depends on a modified cost function in numerical optimization for shaping gate pulses, which minimizes, not only the ideal gate error but also the fluctuations of gate infidelity over a wide error range. We introduce a family of Rydberg blockade gates with active robustness towards the impacts of versatile noise sources such as Doppler dephasing and ac Stark shifts. The resulting gates with robust pulses can significantly increase the insensitivity to any type of errors acting on the two-photon detuning, benefiting from a relaxed requirement of colder atomic temperatures or more stable lasers for current experimental technology.

10^{-3}

within a much wider range of single-atom detunings than the time-optimal gates. We further show that a large fraction of residual error is dominated by population outside the computational subspace, which can be converted into heralded erasures. Our results significantly reduce the requirements on laser frequency stability and intensity homogeneity, field calibration and atomic temperature toward practical fault-tolerant quantum computing with neutral atoms.

^{87}

Rb atoms, we demonstrate that the execution time required for such CZ gates can be shortened by more than 30

\%

as compared to standard two-photon protocols arising the gate fidelity above 0.9954 by taking account of all relevant error sources. Our results reduce the high-power laser requirement and unlock the potential toward fast, high-fidelity quantum operations for large-scale quantum computation with neutral atoms.

F>0.999

in the presence of significant deviations of the coupling strength to the Rydberg state. Such deviations can arise from laser intensity noise and atomic motion in an inhomogeneous coupling field. We also discuss methods to mitigate errors due to deviations of the laser detuning. The designed pulses operate on timescales that are short compared to the fundamental decay timescale set by spontaneous emission and blackbody radiation. We account for the finite lifetime of the Rydberg state in both the optimization and fidelity calculations---this makes the gates conducive to noisy intermediate-scale quantum experiments, meaning that our protocols can reduce infidelity on near-term quantum computing devices. We calculate physical properties associated with infidelity for strontium-88 atoms---including lifetimes, polarizabilities, and blockade strengths---and use these calculations to identify optimal Rydberg states for our protocols, which allows for further minimization of infidelity.