Rydberg atom parity gate based on dark state resonances

TL;DR

This work introduces a three-qubit Rydberg parity gate (RPG) that relies on dark-state resonances to condition the target qubit on the parity of two control qubits. Even parity blocks target evolution via dark-state protection, while odd parity breaks the protection and enables a targeted flip through a parity-dependent Raman process, using a sequence of pi-pulses and Raman driving. Numerical optimization under master-equation dynamics yields a maximum fidelity around $0.9935$ (approximately $99.35\%$) at about $0.27\ \mu$s for realistic Cs-Rydberg parameters, with strong robustness to blockade errors. Demonstrations on the Deutsch–Jozsa algorithm and a two-qubit Ising Hamiltonian illustrate that RPG can outperform cascaded CNOT/CZ gates by reducing circuit depth and mitigating noise, offering a practical route to more efficient QC and DQS implementations.

Abstract

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.

Figures (5)

• Figure 1: (a) Three atoms are trapped in three different optical traps at a fixed inter-atom spacing $l$, and the pulse sequence to complete the gate protocol is shown. (b) and (c) show that any evolution in the target atom is forbidden when the parity of the control qubits is even. (d) and (e) show that the evolution $\ket A \longleftrightarrow \ket{B}$ happens in the target atom when the control qubits are in odd parity.
• Figure 2: (a) For even parity of the control qubits, population transfer in the target atom does not happen for $\Omega_c/\Omega_e>2$. (b) For odd parity($\ket{10}$), population transfer in the target qubit happens as $\delta$ increases. (c) For odd parity($\ket{01}$), population transfer in the target qubit happens for increasing $V$. (d) The variation of average gate fidelity is plotted as a function of total gate time.
• Figure 3: (a) For $V> 2.5\Omega_c$ more than 99% fidelity can be achieved, while we fix $\Omega_c=2.5\Omega_e$. (b) The vdW interaction strength is plotted as a function of inter-atomic distance.
• Figure 4: (a) an (b) are the circuits for simulating the Deutsch–Jozsa algorithm using CNOT gates and RPG, respectively, for the function $f(x_i)=x_1\oplus x_2$. (c) shows how the probability of getting $\ket {11}$ (i.e., detecting as a balanced function) changes with changing individual gate operation time.
• Figure 5: (a) and (b) are the circuits to simulate the Hamiltonian $H=hZ_1Z_2$ for a two-qubit system, with the initial state $\ket{\psi_i}=1/\sqrt{2}(\ket{00}+\ket{10})$ using CNOT gates and RPG, respectively. (c) The time evolution of the state $\ket{\psi_i}$ is plotted; the RPG-based result resembles the exact one more closely than the CNOT-based result.