). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls

-

laser pulses to excite an atom to Rydberg states

-

that implement phase gates with one and two controls, the

\mathrm{C_1P}

and

\mathrm{C_2P}

gates respectively, on neutral atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. Further, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral atom hardware.

DOI: 10.48550/arxiv.2411.19785

Related papers

Parametrized multiqubit gates for neutral-atom quantum platforms

Madhav Mohan, Julius de Hond, S. J. J. M. F. Kokkelmans

A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer from various sources of error that propagate with the circuit depth. Parametrized gates in particular have found use in both near-term algorithms and circuit compilation. The one- and two-qubit versions of these gates have been demonstrated on various computing architectures. The neutral-atom platform has the capability to implement native $N$ -qubit gates (for $N\ensuremath{\ge}2$). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls---laser pulses to excite an atom to Rydberg states---that implement phase gates with one and two controls, the ${\mathrm{C}}_{1}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}$ and ${\mathrm{C}}_{2}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}$ gates, respectively, on neutral-atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. In addition, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral-atom hardware.A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer from various sources of error that propagate with the circuit depth. Parametrized gates in particular have found use in both near-term algorithms and circuit compilation. The one- and two-qubit versions of these gates have been demonstrated on various computing architectures. The neutral-atom platform has the capability to implement native $N$-qubit gates (for $N\ensuremath{\ge}2$). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls---laser pulses to excite an atom to Rydberg states---that implement phase gates with one and two controls, the ${\mathrm{C}}_{1}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}$ and ${\mathrm{C}}_{2}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}$ gates, respectively, on neutral-atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. In addition, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral-atom hardware.

Physical Review AppliedMay 27, 20254 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

Multiqubit Rydberg Gates for Quantum Error Correction

David F. Locher, Josias Old, Katharina Brechtelsbauer +4 more

Multiqubit gates that involve three or more qubits are usually thought to be of little significance for fault-tolerant quantum error correction because single gate faults can lead to errors of high Pauli weight. However, recent works have shown that multiqubit gates can be beneficial for measurement-free fault-tolerant quantum error correction and for fault-tolerant stabilizer readout in unrotated surface codes. In this work, we investigate multiqubit Rydberg gates that are useful for fault-tolerant quantum error correction in single-species neutral-atom platforms and can be implemented with global laser pulses that do not individually address atomic sites. We develop an open-source Python package to generate analytical, few-parameter pulses that implement the desired gates while minimizing gate errors due to Rydberg-state decay. The tool also allows us to identify parameter-optimal pulses, characterized by a minimal parameter count for the pulse ansatz. Measurement-free quantum error correction protocols require CCZ gates, which we analyze for atoms arranged in symmetric and asymmetric configurations. We investigate the performance of these schemes for various single-, two-, and three-qubit gate error rates, showing that break-even performance of measurement-free QEC is within reach of current hardware. Moreover, we study Floquet quantum error correction protocols that comprise two-body stabilizer measurements. Those can be realized using global three-qubit gates, and we show that this can lead to a significant reduction in shuttling operations. Simulations with realistic circuit-level noise indicate that applying three-qubit gates for stabilizer measurements in Floquet codes can yield competitive logical qubit performance in experimentally relevant error regimes.Multiqubit gates that involve three or more qubits are usually thought to be of little significance for fault-tolerant quantum error correction because single gate faults can lead to errors of high Pauli weight. However, recent works have shown that multiqubit gates can be beneficial for measurement-free fault-tolerant quantum error correction and for fault-tolerant stabilizer readout in unrotated surface codes. In this work, we investigate multiqubit Rydberg gates that are useful for fault-tolerant quantum error correction in single-species neutral-atom platforms and can be implemented with global laser pulses that do not individually address atomic sites. We develop an open-source Python package to generate analytical, few-parameter pulses that implement the desired gates while minimizing gate errors due to Rydberg-state decay. The tool also allows us to identify parameter-optimal pulses, characterized by a minimal parameter count for the pulse ansatz. Measurement-free quantum error correction protocols require CCZ gates, which we analyze for atoms arranged in symmetric and asymmetric configurations. We investigate the performance of these schemes for various single-, two-, and three-qubit gate error rates, showing that break-even performance of measurement-free QEC is within reach of current hardware. Moreover, we study Floquet quantum error correction protocols that comprise two-body stabilizer measurements. Those can be realized using global three-qubit gates, and we show that this can lead to a significant reduction in shuttling operations. Simulations with realistic circuit-level noise indicate that applying three-qubit gates for stabilizer measurements in Floquet codes can yield competitive logical qubit performance in experimentally relevant error regimes.

quant-pharXiv:2512.00843PRX QuantumDec 2, 20251 citation

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

Proposal for practical Rydberg quantum gates using a native two-photon excitation

Rui Li, Jing Qian, Weiping Zhang

Abstract Rydberg quantum gate serving as an indispensable computing unit for neutral-atom quantum computation, has attracted intense research efforts for the last decade. However, the state-of-the-art experiments have not reached the high gate fidelity as predicted by most theories due to the unexpected large loss remaining in Rydberg and intermediate states. In this paper, we report our findings in constructing a native two-qubit controlled-NOT gate based on pulse optimization. We focus on the method of commonly-used two-photon Rydberg excitation with smooth Gaussian-shaped pulses which is straightforward for experimental demonstration. By utilizing optimized pulse shapes the scheme reveals a remarkable reduction in the decays from Rydberg and intermediate states, as well as a high-tolerance to the residual thermal motion of atoms. We extract a conservative lower bound for the gate fidelity >0.9921 after taking into account the experimental imperfections. Our results not only reduce the gap between experimental and theoretical prediction because of the optimal control, but also facilitate the connectivity of distant atomic qubits in a larger atom array by reducing the requirement of strong blockade, which is promising for developing multiqubit quantum computation in large-scale atomic arrays.Abstract Rydberg quantum gate serving as an indispensable computing unit for neutral-atom quantum computation, has attracted intense research efforts for the last decade. However, the state-of-the-art experiments have not reached the high gate fidelity as predicted by most theories due to the unexpected large loss remaining in Rydberg and intermediate states. In this paper, we report our findings in constructing a native two-qubit controlled-NOT gate based on pulse optimization. We focus on the method of commonly-used two-photon Rydberg excitation with smooth Gaussian-shaped pulses which is straightforward for experimental demonstration. By utilizing optimized pulse shapes the scheme reveals a remarkable reduction in the decays from Rydberg and intermediate states, as well as a high-tolerance to the residual thermal motion of atoms. We extract a conservative lower bound for the gate fidelity >0.9921 after taking into account the experimental imperfections. Our results not only reduce the gap between experimental and theoretical prediction because of the optimal control, but also facilitate the connectivity of distant atomic qubits in a larger atom array by reducing the requirement of strong blockade, which is promising for developing multiqubit quantum computation in large-scale atomic arrays.

arXiv:2303.16605Quantum Science and TechnologyJun 24, 202314 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

N

-qubit gates (for

N \geq 2

). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls

-

laser pulses to excite an atom to Rydberg states

-

that implement phase gates with one and two controls, the

\mathrm{C_1P}

and

\mathrm{C_2P}

N

-qubit gates (for $N\ensuremath{\ge}2$). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls---laser pulses to excite an atom to Rydberg states---that implement phase gates with one and two controls, the

{\mathrm{C}}_{1}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}

and

{\mathrm{C}}_{2}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}

gates, respectively, on neutral-atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. In addition, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral-atom hardware.

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.