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Physica Scripta

Quantum computation and simulation using Rydberg parity gates

Sinchan Snigdha Rej, Snigdhadev Ray, Bimalendu Deb

Published Jun 5, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ae7912

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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.
Quantum computation (QC) and digital quantum simulation (DQS) essentially require two- or multi-qubit controlled-NOT or -phase gates. We propose an alternative pathway for QC and DQS using a three-qubit parity gate in a Rydberg atom array. The basic principle of the Rydberg atom 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 an RPG based on a dark state resonance. 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. To demonstrate the efficiency of the proposed RPG 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.
Abstract Multi-qubit quantum gates are the most important building blocks for quantum computation. In this article, we propose a scheme for realizing the Toffoli gate in a linear neutral atom array. Two ground-state hyperfine levels of the atoms are considered as qubit states. Our method relies on the strong and long-range interactions between atoms due to Rydberg excitations and the occurrence of dark states in the target qubit, with both control and target qubits being individually addressed with laser pulses. Our gate protocol enables precise control over the quantum states of individual qubits, effectively suppressing undesirable transitions to ensure high-fidelity gate performance. We also implement two-atom Rydberg antiblockade mechanism to avoid any unwanted population blockage in the control atoms to get the best fidelity. At zero temperature, the gate fidelity is estimated to be about 99.16% for realistic laser power omitting the motional state of the atoms when the interatomic distance ( l ) 6.55 μ m. We construct a C n NOT gate with n > 2 in a 2D atomic array by exploiting the n -atom Rydberg antiblockade (RAB) mechanism, which allows n atoms within the blockade radius to be simultaneously excited to the Rydberg states. In particular, we simulate C 3 NOT gate with about 98.37 % fidelity. We further analyze the gate error by decreasing the interatomic distance and find that gate fidelity improves more rapidly for larger n with increased interaction potential. We find that more than 99 % fidelity can be achieved for C 3 NOT gate for l < 6.2 μ m, implying that our proposed scheme promising and reliable for multi-qubit controlled NOT gates. For a finite temperature ( ∼ 30 μ K), including the Doppler dephasing, we simulate our gates to achieve 98.90% and 98.54 % fidelity for the Toffoli gate and C 3
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
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 experimental results on two-qubit Rydberg-blockade quantum gates and entanglement in a two-dimensional qubit array. Without postselection against atom loss we achieve a Bell state fidelity of $0.73\ifmmode\pm\else\textpm\fi{}0.05$. The experiments are performed in an array of single Cs atom qubits with a site to site spacing of $3.8\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$. Using the standard protocol for a Rydberg-blockade CZ{C}_{Z}CZ​ gate together with single qubit operations we create Bell states and measure their fidelity using parity oscillations. We analyze the role of ac Stark shifts that occur when using two-photon Rydberg excitation and show how to tune experimental conditions for optimal gate fidelity.
Digital-analog quantum computing (DAQC) combines digital gates with analog operations, offering an alternative paradigm for universal quantum computation. This approach leverages the higher fidelities of analog operations and the flexibility of local single-qubit gates. In this paper, we propose a quantum genetic algorithm within the DAQC framework using a Rydberg-atom emulator. The algorithm employs single-qubit operations in the digital domain and a global driving interaction based on the Rydberg Hamiltonian in the analog domain. We evaluate the algorithm performance by estimating the ground-state energy of Hamiltonians, with a focus on molecules such as H2,LiH{\mathrm{H}}_{2}, \mathrm{LiH}H2​,LiH, and BeH2{\mathrm{BeH}}_{2}BeH2​. Our results show energy estimations with less than 1% error and state overlaps nearing 1, with computation times ranging from a few minutes for H2{\mathrm{H}}_{2}H2​ (two-qubit circuits) to one to two days for LiH\mathrm{LiH}LiH and BeH2{\mathrm{BeH}}_{2}BeH2​ (six-qubit circuits). The gate fidelities of global analog operations further underscore DAQC as a promising quantum computing strategy in the noisy intermediate-scale quantum era.