Parallel implementation of CNOT$^{N}$ and C$_2$NOT$^2$ gates via homonuclear and heteronuclear F\"{o}rster interactions of Rydberg atoms

TL;DR

This paper proposes optimized schemes for high-fidelity multiqubit CNOT and C2NOT gates using Rydberg atoms, leveraging heteronuclear F"{o}rster interactions to overcome previous fidelity limitations and achieve over 99% fidelity.

Contribution

It introduces a novel approach utilizing heteronuclear F"{o}rster resonances to enhance multiqubit gate fidelity in neutral atom quantum computing.

Findings

CNOT$^4$ gate fidelity up to 99.3%

C$_2$NOT$^2$ gate fidelity up to 99.7%

Optimized schemes feasible with current experimental setups

Abstract

We analyze schemes of high-fidelity multiqubit CNOT$^{N}$ and C$_{2}$NOT$^{2}$ gates for alkali-metal neutral atoms used as qubits. These schemes are based on the electromagnetically induced transparency and Rydberg blockade, as proposed by M. M\"{u}ller et al. [PRL 102, 170502 (2009)]. In the original paper, the fidelity of multi-qubit CNOT$^{\text{N}}$ gate based on Rydberg blockade was limited by the undesirable interaction between the target atoms, and by the coupling laser intensity. We propose overcoming these limits by using strong heteronuclear dipole-dipole interactions via F\"{o}rster resonances for control and target atoms, while the target atoms are coupled by weaker van der Waals interaction. We have optimized the gate performance in order to achieve higher fidelity, while keeping coupling laser intensity as small as possible in order to improve the experimental feasibility of the gate schemes. We also considered optimization of schemes of C$_{2}$NOT$^{2}$ gates, where the fidelity is affected by the relation between the control-control, control-target and target-target interaction energies. Our numeric simulations confirm that the fidelity of CNOT$^4$ gate (single control and four target atoms) can be up to $99.3\%$ and the fidelity of C$_2$NOT$^2$ (two control and two target atoms) is up to $99.7\%$ for the conditions which are experimentally feasible.