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arXiv:2305.06409

Spatiotemporal control of entangling gates on atomic N-qubit systems

Ignacio R. Solá, Seokmin Shin, Bo Y. Chang

Published May 10, 2023• 0 citations
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Abstract

We use a novel optimization procedure that includes the temporal and spatial parameters of the pulses acting on arrays of trapped neutral atoms, to prepare entangling gates in N-qubits systems. The spatio-temporal control allows treating a denser array of atoms, where each pulse acts on a subset of the qubits, potentially allowing to speed the gate operation by two orders of magnitude by boosting the dipole-blockade between the Rydberg states. Studying the rate of success of the algorithm under different constraints, we evaluate the impact of the proximity of the atoms and, indirectly, the role of the geometry of the arrays in 3 and 4-qubit systems, as well as the minimal energy requirements and how this energy is used among the different qubits. Finally, we characterize and classify all optimal protocols according to the mechanism of the gate, using a quantum pathways analysis.

DOI
10.48550/arxiv.2305.06409

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We use a novel optimization procedure that includes the temporal and spatial parameters of the pulses acting on arrays of trapped neutral atoms, to prepare entangling gates in N-qubits systems. The spatio-temporal control allows treating a denser array of atoms, where each pulse acts on a subset of the qubits, potentially allowing to speed the gate operation by two orders of magnitude by boosting the dipole-blockade between the Rydberg states. Studying the rate of success of the algorithm under different constraints, we evaluate the impact of the proximity of the atoms and, indirectly, the role of the geometry of the arrays in 3 and 4-qubit systems, as well as the minimal energy requirements and how this energy is used among the different qubits. Finally, we characterize and classify all optimal protocols according to the mechanism of the gate, using a quantum pathways analysis.
We use a novel optimization procedure that includes the temporal and spatial parameters of the pulses acting on arrays of trapped neutral atoms to prepare entangling gates in N-qubit systems. The spatiotemporal control allows treating a denser array of atoms, where each pulse acts on a subset of the qubits, potentially allowing to speed up the gate operation by two orders of magnitude by boosting the dipole-blockade between the Rydberg states. Studying the rate of success of the algorithm under different constraints, we evaluate the impact of the proximity of the atoms and, indirectly, the role of the geometry of the arrays in three and four-qubit systems, as well as the minimal energy requirements and how this energy is used among the different qubits. Finally, we characterize and classify all optimal protocols according to the mechanism of the gate using a quantum pathway analysis.
We characterize the set of optimal protocols for two-qubit entangling gates through a mechanism analysis based on quantum pathways, which allows us to compare and rank the different solutions. As an example of a flexible platform with a rich landscape of protocols, we consider trapped neutral atoms excited to Rydberg states by different pulse sequences that extend over several atomic sites, optimizing both the temporal and the spatial features of the pulses. Studying the rate of success of the algorithm under different constraints, we analyze the impact of the proximity of the atoms on the nature and quality of the optimal protocols. We characterize in detail the features of the solutions in parameter space, showing some striking correlations among the set of parameters. Together with the mechanism analysis, the spatiotemporal control allows us to select protocols that operate under mechanisms by design, like finding needles in a haystack.
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 \n
Arrays of qubits encoded in the ground-state manifold of neutral atoms trapped in optical (or magnetic) lattices appear to be a promising platform for the realization of a scalable quantum computer. Two-qubit conditional gates between nearest-neighbor qubits in the array can be implemented by exploiting the Rydberg blockade mechanism, as was shown by D. Jaksch et al. [Phys. Rev. Lett. 85, 2208 (2000)]. However, the energy shift due to dipole-dipole interactions causing the blockade falls off rapidly with the interatomic distance, and protocols based on direct Rydberg blockade typically fail to operate between atoms separated by more than one lattice site. In this work, we propose an extension of the protocol of Jaksch et al. for controlled-ZZZ and controlled-not gates which works in the general case where the qubits are not nearest neighbors in the array. Our proposal relies on the Rydberg excitation hopping along a chain of ancilla noncoding atoms connecting the qubits on which the gate is to be applied. The dependence of the gate fidelity on the number of ancilla atoms, the blockade strength, and the decay rates of the Rydberg states is investigated. A comparison between our implementation of a distant controlled-not gate and one based on a sequence of nearest-neighbor two-qubit gates is also provided.
Arrays of optically trapped neutral atoms are an emerging platform for scalable quantum computing, where achieving high-fidelity entangling gates remains a central challenge. We present a systematic analysis of the two-qubit controlled-Z (cz) gate under finite Rydberg blockade, paying particular attention to the influence of near-degenerate Rydberg pair states and resonant dipole-dipole interactions. Using the global two-pulse excitation protocol, we model the full gate dynamics, explicitly capturing population leakage into noncomputational states. By analyzing the interplay between the control parameters such as Rabi frequency, detuning, the F\"orster defect, and interaction strength, we identify conditions that enable fast, high-fidelity gate operation while minimizing leakage. We also quantify the impact of finite Rydberg-state lifetimes on gate error and further demonstrate that the optimal parameter regimes identified here are accessible in current rubidium-based tweezer experiments. These results provide practical guidance for optimizing two-qubit gate protocols in neutral-atom quantum processors with experimentally accessible conditions.