Quantum computing algorithms can be decomposed into a universal set of elementary one- and two-qubit gates. Different physical implementations of quantum computing, however, employ interactions that permit direct conditional dynamics on multiple qubits in a single step. In this work, we leverage quantum optimal control techniques to design single continuous laser pulses that implement multi-qubit controlled-phase, -NOT and -swap (Fredkin) gates on Rydberg atom quantum processors. The identification of robust multi-qubit operations leads to reduced operation time and less decoherence, and the control field provides continuous protection of the atoms from environmental noise. Notably, we find that the controlled-swap (Fredkin) gate, implemented using this approach achieves 99.74\% fidelity while accounting for imperfections such as spontaneous emission, laser fluctuations, and Doppler dephasing.Quantum computing algorithms can be decomposed into a universal set of elementary one- and two-qubit gates. Different physical implementations of quantum computing, however, employ interactions that permit direct conditional dynamics on multiple qubits in a single step. In this work, we leverage quantum optimal control techniques to design single continuous laser pulses that implement multi-qubit controlled-phase, -NOT and -swap (Fredkin) gates on Rydberg atom quantum processors. The identification of robust multi-qubit operations leads to reduced operation time and less decoherence, and the control field provides continuous protection of the atoms from environmental noise. Notably, we find that the controlled-swap (Fredkin) gate, implemented using this approach achieves 99.74\% fidelity while accounting for imperfections such as spontaneous emission, laser fluctuations, and Doppler dephasing.

quant-pharXiv:2511.22202Nov 28, 20250 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

Multiple-qubit controlled unitary quantum gate for Rydberg atoms using shortcut to adiabaticity and optimized geometric quantum operations

Meng Li, F.-Q. Guo, Z. Jin +3 more

Multiple-qubit quantum logic gates are an important element in the implementation of quantum computers. The direct construction of multiple-qubit quantum logic gates in an efficient way has important values compared to the construction of multiple-qubit gates using a series of two-qubit and single-qubit gates. We propose a scheme to construct a multiple-qubit ${\mathrm{C}}_{k}\mathrm{U}$ gate ( $k$ denotes the number of control qubits and U means the arbitrary universal operation performed on the target qubit) in a neutral atom platform through the Rydberg blockade effect by successively exciting them to Rydberg states. This scheme takes advantage of the shortcut to adiabaticity of inverse engineering, geometric quantum operations, as well as optimized control theory. The geometric quantum computation considered in this manuscript guarantees the robustness to operational errors. Meanwhile, inverse engineering-based shortcut to adiabaticity provides a further advantage in terms of the speed of the system evolution compared to adiabatic processes. An additional feature of our multiple-qubit quantum logic gate is that arbitrary operation on the target atom can be realized by adjusting the amplitude and phase of the laser fields. Numerical simulation of the master equation based on the full Hamiltonian demonstrates the high fidelity of the proposed scheme and its robustness to operational errors and spontaneous emission.Multiple-qubit quantum logic gates are an important element in the implementation of quantum computers. The direct construction of multiple-qubit quantum logic gates in an efficient way has important values compared to the construction of multiple-qubit gates using a series of two-qubit and single-qubit gates. We propose a scheme to construct a multiple-qubit ${\mathrm{C}}_{k}\mathrm{U}$ gate ($k$ denotes the number of control qubits and U means the arbitrary universal operation performed on the target qubit) in a neutral atom platform through the Rydberg blockade effect by successively exciting them to Rydberg states. This scheme takes advantage of the shortcut to adiabaticity of inverse engineering, geometric quantum operations, as well as optimized control theory. The geometric quantum computation considered in this manuscript guarantees the robustness to operational errors. Meanwhile, inverse engineering-based shortcut to adiabaticity provides a further advantage in terms of the speed of the system evolution compared to adiabatic processes. An additional feature of our multiple-qubit quantum logic gate is that arbitrary operation on the target atom can be realized by adjusting the amplitude and phase of the laser fields. Numerical simulation of the master equation based on the full Hamiltonian demonstrates the high fidelity of the proposed scheme and its robustness to operational errors and spontaneous emission.

Physical Review AJun 15, 202143 citations

Optimal quantum gates \nfor Rydberg atoms quantum computer

Pagano, Alice

Arrays of identical neutral atoms trapped in optical tweezers are a promising candidate for use in quantum computing. These platforms are highly scalable to large numbers of qubits and neutral atoms boost several attractive features as long coherence times and the possibility to be entangled via strong dipole-dipole interactions by driving them to highly excited Rydberg states. \nThe Thesis work is developed inside the framework of the QRydDemo project, whose aim in the next few years is to realize a neutral atom quantum processor with several hundred qubits. The smallest building blocks for the quantum computer are one and two-qubit gates: to entangle two atoms in the quantum register, a controlled-phase (CZ) gate will be implemented by shining fine-tuned laser pulses onto them. In this work, after giving a theoretical description of the Hamiltonian of two neutral atoms in the quantum register, a numerical simulation of this system is exploited to reproduce the behavior of the two-qubit CZ gate. Realistic effects are taken into account as finite temperature, imperfect Rydberg blockade, or decay out of the Rydberg state. A protocol with constant pulses is analyzed and its optimal parameters are found through classical optimizers. Then, time-dependent pulses are introduced and the optimal pulses are found through the optimal control algorithm dCRAB in an open-loop optimization. For the experimental realization of the gate, this analysis is of pivotal importance to know in which aspect more effort has to be put to maximize the experimental precision of the operation and thus improving the performance of the whole device \nArrays of identical neutral atoms trapped in optical tweezers are a promising candidate for use in quantum computing. These platforms are highly scalable to large numbers of qubits and neutral atoms boost several attractive features as long coherence times and the possibility to be entangled via strong dipole-dipole interactions by driving them to highly excited Rydberg states. \nThe Thesis work is developed inside the framework of the QRydDemo project, whose aim in the next few years is to realize a neutral atom quantum processor with several hundred qubits. The smallest building blocks for the quantum computer are one and two-qubit gates: to entangle two atoms in the quantum register, a controlled-phase (CZ) gate will be implemented by shining fine-tuned laser pulses onto them. In this work, after giving a theoretical description of the Hamiltonian of two neutral atoms in the quantum register, a numerical simulation of this system is exploited to reproduce the behavior of the two-qubit CZ gate. Realistic effects are taken into account as finite temperature, imperfect Rydberg blockade, or decay out of the Rydberg state. A protocol with constant pulses is analyzed and its optimal parameters are found through classical optimizers. Then, time-dependent pulses are introduced and the optimal pulses are found through the optimal control algorithm dCRAB in an open-loop optimization. For the experimental realization of the gate, this analysis is of pivotal importance to know in which aspect more effort has to be put to maximize the experimental precision of the operation and thus improving the performance of the whole device \n

Sep 1, 20210 citations

Multiqubit parity gates for Rydberg atoms in various configurations

Javad Kazemi, Michael Schuler, Christian Ertler +1 more

We present a native approach for realizing multiqubit parity phase gates in neutral-atom systems through global phase modulation of a Rydberg excitation laser. By shaping the temporal profile of the laser’s phase, we enable high-fidelity, time efficient entangling operations between multiple qubits without requiring individual qubit addressing. To mitigate intrinsic noise sources including spontaneous decay and motional effects, we develop a noise-aware optimal control framework that reduces gate errors under the presence of noise while maintaining smooth pulse profiles suitable for experimental implementation. In addition to equidistant qubit arrangements, we explore the impact of nonequidistant atomic configurations, where interaction inhomogeneity becomes significant. In these cases, the flexibility of our control approach helps to compensate for such variations, supporting reliable gate performance across different spatial layouts. These results facilitate the practical implementation of complex, multiqubit quantum operations in near-term neutral-atom quantum processors.We present a native approach for realizing multiqubit parity phase gates in neutral-atom systems through global phase modulation of a Rydberg excitation laser. By shaping the temporal profile of the laser’s phase, we enable high-fidelity, time efficient entangling operations between multiple qubits without requiring individual qubit addressing. To mitigate intrinsic noise sources including spontaneous decay and motional effects, we develop a noise-aware optimal control framework that reduces gate errors under the presence of noise while maintaining smooth pulse profiles suitable for experimental implementation. In addition to equidistant qubit arrangements, we explore the impact of nonequidistant atomic configurations, where interaction inhomogeneity becomes significant. In these cases, the flexibility of our control approach helps to compensate for such variations, supporting reliable gate performance across different spatial layouts. These results facilitate the practical implementation of complex, multiqubit quantum operations in near-term neutral-atom quantum processors.

arXiv:2506.09686Physical Review ResearchAug 20, 20254 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

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.

{\mathrm{C}}_{k}\mathrm{U}

gate (

k

denotes the number of control qubits and U means the arbitrary universal operation performed on the target qubit) in a neutral atom platform through the Rydberg blockade effect by successively exciting them to Rydberg states. This scheme takes advantage of the shortcut to adiabaticity of inverse engineering, geometric quantum operations, as well as optimized control theory. The geometric quantum computation considered in this manuscript guarantees the robustness to operational errors. Meanwhile, inverse engineering-based shortcut to adiabaticity provides a further advantage in terms of the speed of the system evolution compared to adiabatic processes. An additional feature of our multiple-qubit quantum logic gate is that arbitrary operation on the target atom can be realized by adjusting the amplitude and phase of the laser fields. Numerical simulation of the master equation based on the full Hamiltonian demonstrates the high fidelity of the proposed scheme and its robustness to operational errors and spontaneous emission.

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.