Quantum optimization via four-body Rydberg gates

TL;DR

This paper introduces a fast, high-fidelity four-body Rydberg gate that enables scalable quantum optimization on neutral atom arrays, facilitating efficient implementation of QAOA for complex problems.

Contribution

It proposes a novel four-body Rydberg parity gate that simplifies encoding of optimization problems and supports scalable, efficient quantum algorithms like QAOA.

Findings

Demonstrates a numerically simulated implementation of QAOA on a small problem.

Shows the gate's programmability via two hold-times during operation.

Enables execution of variational steps with constant system manipulations.

Abstract

There is a large ongoing research effort towards obtaining a quantum advantage in the solution of combinatorial optimization problems on near-term quantum devices. A particularly promising platform for testing and developing quantum optimization algorithms are arrays of trapped neutral atoms, laser-coupled to highly excited Rydberg states. However, encoding combinatorial optimization problems in atomic arrays is challenging due to the limited inter-qubit connectivity given by their native finite-range interactions. Here we propose and analyze a fast, high fidelity four-body Rydberg parity gate, enabling a direct and straightforward implementation of the Lechner-Hauke-Zoller (LHZ) scheme and its recent generalization, the parity architecture, a scalable architecture for encoding arbitrarily connected interaction graphs. Our gate relies on onetime-optimized adiabatic laser pulses and is fully programmable by adjusting two hold-times during operation. We numerically demonstrate an implementation of the quantum approximate optimization algorithm (QAOA) for a small scale test problem. Our approach allows for efficient execution of variational optimization steps with a constant number of system manipulations, independent of the system size, thus paving the way for experimental investigations of QAOA beyond the reach of numerical simulations.