Solving optimization problems with local light shift encoding on Rydberg quantum annealers

TL;DR

This paper introduces a novel method using local light shift encoding on Rydberg quantum annealers to efficiently solve combinatorial optimization problems like Max-Cut and MIS, leveraging spatial control and optimal protocols.

Contribution

It presents a non-unit disk framework for graph problem encoding on Rydberg systems with local control, enabling scalable and efficient quantum annealing solutions.

Findings

Solutions achieved within system lifetime for various graph sizes

Approximation ratios close to one for prototype graphs

Advantages over classical simulated annealing in system size and convergence

Abstract

We provide a non-unit disk framework to solve combinatorial optimization problems such as Maximum Cut (Max-Cut) and Maximum Independent Set (MIS) on a Rydberg quantum annealer. Our setup consists of a many-body interacting Rydberg system where locally controllable light shifts are applied to individual qubits in order to map the graph problem onto the Ising spin model. Exploiting the flexibility that optical tweezers offer in terms of spatial arrangement, our numerical simulations implement the local-detuning protocol while globally driving the Rydberg annealer to the desired many-body ground state, which is also the solution to the optimization problem. Using optimal control methods, these solutions are obtained for prototype graphs with varying sizes at time scales well within the system lifetime and with approximation ratios close to one. The non-blockade approach facilitates the encoding of graph problems with specific topologies that can be realized in two-dimensional Rydberg configurations and is applicable to both unweighted as well as weighted graphs. A comparative analysis with fast simulated annealing is provided which highlights the advantages of our scheme in terms of system size, hardness of the graph, and the number of iterations required to converge to the solution.