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Journal of Experimental and Theoretical Physics

Optimization of Entangling Logic Gates Based on the Rydberg Blockade Effect

L. V. Gerasimov, Dmitriy V. Kupriyanov, Stanislav S. Straupe

Published Aug 1, 2023• 1 citation
Publisher

Abstract

Abstract The implementation of a quantum logic gate in a system of cold atoms in optical microtraps is analyzed. The dynamics of two spin qubits is simulated, and a number of processes that limit the efficiency of entanglement based on the Rydberg blockade effect are considered. A geometry of two-photon excitation of Rydberg states of atoms is proposed that makes it possible to increase the robustness of the system to variations in a number of parameters and to reduce losses associated with the incoherent scattering of the driving field.

DOI
10.1134/s1063776123080113

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Journal of the Optical Society of America B•Nov 20, 2023•2 citations
Abstract The implementation of a quantum logic gate in a system of cold atoms in optical microtraps is analyzed. The dynamics of two spin qubits is simulated, and a number of processes that limit the efficiency of entanglement based on the Rydberg blockade effect are considered. A geometry of two-photon excitation of Rydberg states of atoms is proposed that makes it possible to increase the robustness of the system to variations in a number of parameters and to reduce losses associated with the incoherent scattering of the driving field.
The implementation of a quantum logic gate in a system of cold atoms in optical microtraps is analyzed. The dynamics of two spin qubits is simulated, and a number of processes that limit the efficiency of entanglement based on the Rydberg blockade effect are considered. A geometry of two-photon excitation of Rydberg states of atoms is proposed that makes it possible to increase the robustness of the system to variations in a number of parameters and to reduce losses associated with the incoherent scattering of the driving field.
Single atoms in dipole microtraps or optical tweezers have recently become a promising platform for quantum computing and simulation. Here we report a detailed theoretical analysis of the physics underlying an implementation of a Rydberg two-qubit gate in such a system---a cornerstone protocol in quantum computing with single atoms. We focus on a blockade-type entangling gate and consider various decoherence processes limiting its performance in a real system. We provide numerical estimates for the limits on fidelity of the maximally entangled states and predict the full process matrix corresponding to the noisy two-qubit gate. We consider different excitation geometries and show certain advantages for the gate realization with linearly polarized driving beams. Our methods and results may find implementation in numerical models for simulation and optimization of neutral atom based quantum processors.
Single atoms in dipole microtraps or optical tweezers have recently become a promising platform for quantum computing and simulation. Here we report a detailed theoretical analysis of the physics underlying an implementation of a Rydberg two-qubit gate in such a system -- a cornerstone protocol in quantum computing with single atoms. We focus on a blockade-type entangling gate and consider various decoherence processes limiting its performance in a real system. We provide numerical estimates for the limits on fidelity of the maximally entangled states and predict the full process matrix corresponding to the noisy two-qubit gate. Our methods and results may find implementation in numerical models for simulation and optimization of neutral atom based quantum processors.
The Rydberg dipole blockade has emerged as the standard mechanism to induce entanglement between neutral-atom qubits. In these protocols, laser fields that couple qubit states to Rydberg states are modulated to implement entangling gates. Here we present an alternative protocol to implement entangling gates via Rydberg dressing and a microwave-field-driven spin-flip blockade [Y.-Y. Jau et al., Nat. Phys. 12, 71 (2016)]. We consider the specific example of qubits encoded in the clock states of cesium. An auxiliary hyperfine state is optically dressed so that it acquires partial Rydberg character. It thus acts as a proxy Rydberg state, with a nonlinear light shift that plays the role of blockade strength. A microwave-frequency field coupling a qubit state to this dressed auxiliary state can be modulated to implement entangling gates. Logic gate protocols designed for the optical regime can be imported to this microwave regime, for which experimental control methods are more robust. We show that unlike the strong dipole-blockade regime usually employed in Rydberg experiments, going to a moderate-spin-flip-blockade regime results in faster gates and smaller Rydberg decay. We study various regimes of operations that can yield high-fidelity two-qubit entangling gates and characterize their analytical behavior. In addition to the inherent robustness of microwave control, we can design these gates to be more robust to laser amplitude and frequency noises at the cost of a small increase in Rydberg decay.
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
We present a comparative analysis of physical constraints limiting the quality of spin entanglement created using the Rydberg blockade technique in an ensemble of trapped neutral 87 Rb atoms. Based on the approach developed earlier in Phys. Rev. A 106 , 042410 ( 2022 ) PLRAAN 1050-2947 10.1103/PhysRevA.106.042410 , we consider the complete multilevel Zeeman structure of the interacting atoms and apply our simulations to two excitation geometries featured by different transition types, both feasible for experimental verification. We demonstrate that the blockade shift strongly depends not only on the interatomic separation but also on the angular position of the atom pair with respect to the quantization axis determined by polarization of the driving fields. As an example, we have estimated fidelity for a promising design of a CZ gate, recently proposed by Levine et al . [ Phys. Rev. Lett. 123 , 230501 ( 2019 ) PRLTAO 0031-9007 10.1103/PhysRevLett.123.230501 ] for various possible experimental geometries. Anisotropic effects in entangling gates considered here are important for the optimal choice of proper geometry for quantum computing in two- and three-dimensional arrays of atomic qubits and are of considerable interest for quantum simulators, especially those that are designed for anisotropic physical models.