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Entropy

Implementation of Quantum Algorithms via Fast Three-Rydberg-Atom CCZ Gates

Shi-Qing Tang, Chong Yang, Dongxiao Li, Xiao‐Qiang Shao

Published Sep 27, 2022• 4 citations
Publisher

Abstract

Multiqubit CCZ gates form one of the building blocks of quantum algorithms and have been involved in achieving many theoretical and experimental triumphs. Designing a simple and efficient multiqubit gate for quantum algorithms is still by no means trivial as the number of qubits increases. Here, by virtue of the Rydberg blockade effect, we propose a scheme to rapidly implement a three-Rydberg-atom CCZ gate via a single Rydberg pulse, and successfully apply the gate to realize the three-qubit refined Deutsch-Jozsa algorithm and three-qubit Grover search. The logical states of the three-qubit gate are encoded to the same ground states to avoid an adverse effect of the atomic spontaneous emission. Furthermore, there is no requirement for individual addressing of atoms in our protocol.

DOI
10.3390/e24101371

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Multiqubit CCZ gates form one of the building blocks of quantum algorithms and have been involved in achieving many theoretical and experimental triumphs. Designing a simple and efficient multiqubit gate for quantum algorithms is still by no means trivial as the number of qubits increases. Here, by virtue of the Rydberg blockade effect, we propose a scheme to rapidly implement a three-Rydberg-atom CCZ gate via a single Rydberg pulse, and successfully apply the gate to realize the three-qubit refined Deutsch-Jozsa algorithm and three-qubit Grover search. The logical states of the three-qubit gate are encoded to the same ground states to avoid an adverse effect of the atomic spontaneous emission. Furthermore, there is no requirement for individual addressing of atoms in our protocol.
Abstract In this paper, we propose a one-step scheme for generating a multiqubit controlled–controlled-Z (CCZ) gate based on Rydberg atoms where an amplitude-modulated field is employed to induce Rydberg antiblockade. The Rydberg atoms can form a Rabi oscillation between the ground state and the collective excited state effectively, so a one-step three-qubit CCZ gate can be easily achieved through a Rabi cycle. Numerical simulation results show that the scheme has a high fidelity and robustness against errors which are caused by parameter errors, intrinsic errors, and atomic decays. Therefore, we hope that this scheme will enable fast and robust quantum computing in the near future.
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.
We present efficient methods to implement the quantum computing Grover search algorithm using the Rydberg blockade interaction. We show that simple π-pulse excitation sequences between ground and Rydberg excited states readily produce the key conditional phase shift and inversion-about-the-mean unitary operations for the Grover search. Multi-qubit implementation schemes suitable for different properties of the atomic interactions are identified and the error scaling of the protocols with system size is found to be promising for experimental investigation.
We present a theoretical study of finite-blockade dynamics in a symmetric three-neutral-atom system, providing a framework for understanding high-fidelity multiqubit quantum operations. The transition from the finite- to the strong-blockade regime is systematically investigated to examine the effects of finite Rydberg blockade. Using a single Gaussian laser pulse, we analyze the complete gate dynamics while explicitly accounting for population leakage into non-computational Rydberg states. By exploiting the permutation symmetry of the system, we construct a symmetry-adapted Hamiltonian that reduces the computational complexity while preserving the exact dynamics. This enables a systematic investigation of the interplay among the Rabi frequency, laser detuning, and Rydberg blockade strength, leading to the identification of optimal operating regimes with high fidelity, fast gate operation, and suppressed leakage. We further quantify the dominant error mechanisms, including phase errors, population leakage, and finite Rydberg-state lifetimes, and evaluate their impact on the gate fidelity. Our results demonstrate experimentally accessible high-fidelity gate operation and provide practical guidelines for multi-qubit quantum computing.
One can implement fast two-qubit entangling gates by exploiting the Rydberg blockade. Although various theoretical schemes have been proposed, experimenters have not yet been able to demonstrate two-atom gates of high fidelity due to experimental constraints. We propose a novel scheme, which only uses a single Rydberg pulse illuminating both atoms, for the construction of neutral-atom controlled-phase gates. In contrast to the existing schemes, our approach is simpler to implement and requires neither individual addressing of atoms nor adiabatic procedures. With parameters estimated based on actual experimental scenarios, a gate fidelity higher than 0.99 is achievable.