Parallel implementation of CNOT${}^N$ and C${}_2$NOT${}^2$ gates via homonuclear and heteronuclear Förster interactions of Rydberg atoms

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. Müller 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 Förster 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.

15 pages, 13 figures. Supplementary datasets are available from here: https://doi.org/10.5281/zenodo.8154008

References in corpus (19)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Strong quantum computational advantage using a superconducting quantum processor
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
• Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state
• High-fidelity parallel entangling gates on a neutral atom quantum computer
• Cooperative atom-light interaction in a blockaded Rydberg ensemble
• Creation of ultracold ${}^{87}$RbCs molecules in the rovibrational ground state
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Quantum simulation and computing with Rydberg-interacting qubits
• Consequences of Zeeman Degeneracy for van der Waals Blockade between Rydberg Atoms
• High fidelity entanglement of neutral atoms via a Rydberg-mediated single-modulated-pulse controlled-PHASE gate
• Defect-free arbitrary-geometry assembly of mixed-species atom arrays
• Demonstration of a Quantum Gate using Electromagnetically Induced Transparency
• A blueprint for fault-tolerant quantum computation with Rydberg atoms
• Observation of Rydberg blockade due to the charge-dipole interaction between an atom and a polar molecule
• Unselective ground-state blockade of Rydberg atoms for implementing quantum gates

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• Long-range $CC\Phi$ gates via radio-frequency-induced Förster resonances
• Generation of quantum phases of matter and finding a maximum-weight independent set of unit-disk graphs using Rydberg atoms
• Fast measurement-based generation of large-scale Greenberger-Horne-Zeilinger state with atomic nuclear-spin qubits