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arXiv:2203.14302 · Physical Review Applied

Multiqubit Toffoli Gates and Optimal Geometry with Rydberg Atoms

Dongmin Yu, Han Wang, Jin‐Ming Liu, Shi‐Lei Su, Jing Qian, Weiping Zhang

Published Sep 27, 2022• 14 citations
arXivHTMLPDF

Abstract

Due to its potential for implementing a scalable quantum computer, the multiqubit Toffoli gate lies in the heart of quantum information processing. In this paper, we demonstrate a multiqubit blockade gate with atoms arranged in a three-dimensional spheroidal array. The gate performance is greatly improved by the method of optimizing control-qubit distributions on the spherical surface via evolutionary algorithm, which leads to an enhanced asymmetric Rydberg blockade. This spheroidal configuration, not only preserves the dipole blockade energy well between arbitrary control-target pairs, which keeps the asymmetric blockade error at a very low level, but also manifests an unprecedented robustness to the spatial position variations, leading to a negligible position error. Taking account of intrinsic errors and using typical experimental parameters, we numerically show that a c${}_{6}$not Rydberg gate can be created with a fidelity of 0.992, which is only limited by the Rydberg state decays. Our protocol opens up a platform of higher-dimensional atomic arrays for achieving multiqubit neutral-atom quantum computation.

DOI
10.1103/physrevapplied.18.034072

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•Sep 1, 2021•0 citations
Due to its potential for implementing a scalable quantum computer, the multiqubit Toffoli gate lies in the heart of quantum information processing. In this paper, we demonstrate a multiqubit blockade gate with atoms arranged in a three-dimensional spheroidal array. The gate performance is greatly improved by the method of optimizing control-qubit distributions on the spherical surface via evolutionary algorithm, which leads to an enhanced asymmetric Rydberg blockade. This spheroidal configuration, not only preserves the dipole blockade energy well between arbitrary control-target pairs, which keeps the asymmetric blockade error at a very low level, but also manifests an unprecedented robustness to the spatial position variations, leading to a negligible position error. Taking account of intrinsic errors and using typical experimental parameters, we numerically show that a c6{}_{6}6​not Rydberg gate can be created with a fidelity of 0.992, which is only limited by the Rydberg state decays. Our protocol opens up a platform of higher-dimensional atomic arrays for achieving multiqubit neutral-atom quantum computation.
We propose an exotic multi-qubit Toffoli gate protocol via asymmetric Rydberg blockade, benefiting from the use of a spheroidal configuration to optimize the gate performance. The merit of a spheroidal structure lies in a well preservation of strong blocked energies between all control-target atom pairs within the sphere, which can persistently keep the blockade error at a low level. On the basis of optimization for three different types of (2+1)(2+1)(2+1)-qubitqubitqubit gate units to minimize the antiblockade error, the gate fidelity of an optimal (6+1)(6+1)(6+1)-qubitqubitqubit configuration can attain as high as 0.98410.98410.9841 mainly contributed by the decay error. And the extension with much more control atoms is also discussed. Our findings may shed light on scalable neutral-atom quantum computation in special high-dimensional arrays.
Scalability and high-efficiency of an (n+1)(n+1)(n+1)-qubit Toffoli gate sphere via blockaded Rydberg atoms
The Toffoli gate serving as a basic building block for reversible quantum computation, has manifested its great potentials in improving the error-tolerant rate in quantum communication. While current route to the creation of Toffoli gate requires implementing sequential single- and two-qubit gates, limited by longer operation time and lower average fidelity. We develop a new theoretical protocol to construct a universal (n+1)(n+1)(n+1)-qubit Toffoli gate sphere based on the Rydberg blockade mechanism, by constraining the behavior of one central target atom with nnn surrounding control atoms. Its merit lies in the use of only five πππ pulses independent of the control atom number nnn which leads to the overall gate time as fast as $\sim125125125n$s and the average fidelity closing to 0.999. The maximal filling number of control atoms can be up to n=46n=46n=46, determined by the spherical diameter which is equal to the blockade radius, as well as by the nearest neighbor spacing between two trapped-atom lattices. Taking n=2,3,4n=2,3,4n=2,3,4 as examples we comparably show the gate performance with experimentally accessible parameters, and confirm that the gate errors mainly attribute to the imperfect blockade strength, the spontaneous atomic loss and the imperfect ground-state preparation. In contrast to an one-dimensional-array configuration it is remarkable that the spherical atomic sample preserves a high-fidelity output against the increasing of nnn, shedding light on the study of scalable quantum simulation and entanglement with multiple neutral atoms.
Multitarget gates offer the potential to reduce gate depth in syndrome extraction for quantum error correction. Although neutral-atom quantum computers have demonstrated native multiqubit gates, existing approaches that avoid additional control or multiple atomic species have been limited to single-target gates. We propose single-control multitarget C ( Z ⊗ N ) gates on a single-species neutral-atom platform that requires no extra control and has gate durations comparable to standard C Z gates. Our approach leverages tailored interatomic distances to create an asymmetric blockade between the control and target atoms. Using a graphics processing unit-accelerated pulse synthesis protocol, we design smooth control pulses for C Z Z and C Z Z Z gates, achieving fidelities of up to 99.55 % and 99.24 % , respectively, even in the presence of simulated atom-placement errors and Rydberg-state decay. Our approach is most effective for N = 2 ( C Z Z ) and N = 3 targets ( C Z Z Z ) ; for larger , increasing spatial crowding of the targets introduces significant challenges for maintaining the required blockade asymmetry. This work presents a practical path to implementing low-overhead multitarget gates in single-species neutral-atom systems, significantly reducing the resource overhead for syndrome extraction. To motivate the impact of these gates, we apply a greedy scheduling algorithm and we demonstrate that our proposed gates can reduce the number of atom reconfiguration costs by up to 50% for color code syndrome extraction of code distances greater than 5.
Because of their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multiqubit Rydberg-blockade gates that involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multiqubit gates can drastically simplify both quantum algorithms and state preparation. To illustrate this, we show that a 25-atom Greenberger-Horne-Zeilinger state can be created using only three gates with an error of 5.8%.
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.
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