Implementation of non-local arbitrary two-qubit controlled gates via geometric quantum computation with Rydberg anti-blockade

Abstract

In the context of Rydberg anti-blockade, this paper proposes a new scheme for a high-fidelity controlled-unitary gate based on non-adiabatic holonomic quantum computation. Under specific detuning and interaction conditions, the scheme achieves a suitable evolution path for non-adiabatic holonomic quantum computation through reverse engineering of pulse parameters. Numerical simulations show that the geometric gate maintains high fidelity even in the presence of spontaneous radiation and laser intensity errors. Finally,we extend our designed quantum gates to non-local gates and investigate their use in converting four-qubit entangled states. This finding indicates the potential applicability of our scheme to complex quantum information processing tasks.

Figures (6)

• Figure 1: Schematic diagram of three-level Rydberg atoms interacting with lasers.
• Figure 2: (a) The population dynamics in the evolution of the CNOT gate. (b) The average fidelity of the CNOT gate changes over time, and the final average fidelity obtained is 0.9975.
• Figure 3: (a) Schematic diagram of fidelity under laser error. (b) Fidelity under different decay rates.
• Figure 4: (a) Schematics of interaction between three Rydberg atoms and lasers. (b) Diagram illustrating the process of entanglement transfer.
• Figure 5: Quantum circuits for entanglement conversion: (a) $GHZ$ to cluster state, (b) $GHZ$ to $W$ state. $q_i(i=1,2,3,4)$ denotes the qubit index.