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Physical Review Research

High-efficiency realization of the super-robust Rydberg Deutsch gate

Aofei Li, B.-B. Liu, L.-L. Yan, Shi‐Lei Su, Gang Chen, Mang Feng

Published Jun 3, 2024• 2 citations
Publisher

Abstract

Quantum logic gates are the essential components of quantum computation and have broad practical applications, especially for the multiple-qubit logic gates. Compared with appliying a series of single- and two-qubit gates, constrcuting quantum computation with multiple-qubit logic gates can be more efficient and high-fidelity. As a three-qubit logic gate, Deutsch gate enables the realization of any feasible quantum computations. Based on neutral atoms, we present a scheme of super-robust Deutsch gate via optimal control technique. Utilizing the Rydberg blockade effect of neutral atoms, we design an implementable D ( β ) based on the three-step program. One of the notable advantages of this function is that β can be achieved arbitrarily between 0 and π with the operation of target atom. In addition, we give an analytical solution agreed very well with numerical simulations for the residual blocking effect between next-neighbor atoms that affects the performance quality of Deutsch gate. The fidelity of our proposed scheme is demonstrated by numerical simulation of the master equation based on the full Hamiltonian, and the robustness of our scheme with control errors is also illustrated. Our proposal offers an alternative promising scheme for fault-tolerant quantum computation. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023231

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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 CkU{\mathrm{C}}_{k}\mathrm{U}Ck​U gate (kkk 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.
We propose a one-step scheme to implement the time-optimal nonadiabatic holonomic three-qubit controlled gates in Rydberg atoms by modulating Rabi frequencies of driving fields on the target atom. We perform the time-optimal operations following the brachistochrone curve, after which the scheme manifests completely different characteristics in contrast to the conventional nonadiabatic holonomic quantum computation (NHQC) that all operations require exactly the same evolution time, even for small angular rotations. Since the present three-qubit controlled-gate scheme significantly reduces the evolution time, the influence of decoherence can be greatly reduced. On the other hand, the robustness on the systematic error can also be guaranteed by the feature of geometric phase. The simulation through master equation verifies the high fidelity and robustness of our scheme. Although we use the Rydberg-atom system to verify the feasibility of our scheme, any quantum platforms capable of achieving the same form of effective Hamiltonian is feasible, which means the proposed three-qubit time-optimal-control nonadiabatic holonomic gates is independent of the particular physical platform and may have the potential for wider application.
Abstract Quantum computation (QC) and digital quantum simulation (DQS) essentially require two- or multi-qubit controlled-NOT (CNOT) or -phase gates. We propose an alternative pathway for QC and DQS using a multi-qubit parity gate in a one- or two-dimensional Rydberg atom array. The basic principle of the Rydberg parity gate (RPG) is that the operation on the target qubit is controlled by the parity of the control qubits. First, we discuss how to construct a three-qubit RPG in a one-dimensional atom array, based on dark state resonances. We optimize the gate parameters by numerically analyzing the time evolution of the computational basis states to maximize the gate fidelity. We also show that our proposed RPG is extremely robust against the Rydberg blockade error. Then to scale up, we propose multi-control RPG in a two-dimensional array of atoms. We show how these multiqubit parity gates can replace a long sequence of two-qubit gates in a quantum circuit. To demonstrate the efficiency of our proposed parity gates over the conventional CNOT or CZ gate in QC and DQS, we implement the Deutsch–Jozsa algorithm and simulate the Ising Hamiltonian. The results show that RPG can be a better substitute of the CNOT gate to yield better results, as it decreases the circuit noise by reducing circuit depth.
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
Quantum devices comprised of elementary components with more than two stable levels—so-called qudits—enrich the accessible Hilbert space, enabling applications ranging from fault-tolerant quantum computing to simulating complex many-body models. While several quantum platforms are built from local elements that are equipped with a rich spectrum of stable energy levels, schemes for the efficient control and entanglement of qudits are scarce. Importantly, no experimental demonstration of multiqudit control has been achieved to date in neutral atom arrays. Here, we propose a general scheme for controlling and entangling qudits and perform a full analysis for the case of qutrits, encoded in ground and metastable states of alkaline earth atoms. We find an efficient implementation of single-qudit gates via the simultaneous driving of multiple transition frequencies. For entangling operations, we provide a concrete and intuitive recipe for the controlled- Z ( C Z ) gate for any local dimension d , realized through alternating single qudit and entangling pulses that simultaneously drive up to two Rydberg transitions. We further prove that two simultaneous Rydberg tones are, in general, the minimum necessary for implementing the C Z gate with a global drive. The pulses we use are optimally controlled, smooth, and robust to realistic experimental imperfections, as we demonstrate using extensive noise simulations. This amounts to a minimal, resource-efficient, and practical protocol for realizing a universal set of gates. Our scheme for the native control of qudits in a neutral atom array provides a high-fidelity route toward qudit-based quantum computation, ready for implementation on near-term devices.
Abstract Due to the limitation of quantum resources, direct synthesis of a multiqubit logic gate can significantly improve the efficiency of practical quantum information processing. In this article, an enhanced‐robustness gate scheme is proposed to implement three‐qubit controlled gates, i.e., and , by using resonant dipole–dipole exchange interaction‐induced adiabatic evolutions along with the dark state dynamics and super‐robust pulse sequences in Rydberg atoms. Such a gate scheme can execute arbitrary single‐qubit operations on the target qubit with pure geometric phase and is especially suitable for the case where the decoherence is not very obvious. Taking and as typical examples, various experimental imperfections are studied, including the Doppler effect, spontaneous emission of the intermediate state, laser phase noise, and fluctuations of interaction and external fields. Therefore, with the increasing demand for multiqubit gates, the proposal provides a more promising alternative for future fault‐tolerant and scalable quantum computation.