A quantum wire approach to weighted combinatorial graph optimisation problems

TL;DR

The study addresses embedding non-UDG combinatorial optimization problems into native MWIS problems on unit-disk graphs using a hardware-efficient scheme of quantum wires formed by chains of Rydberg-blockaded atoms. It introduces a practical encoding where wires preserve the problem spectrum and weights are implemented with local light shifts, enabling MWIS and QUBO on quasi-unit-disk connectivity with substantially reduced ancilla overhead. The authors demonstrate the approach experimentally on a programmable neutral-atom array and verify solutions for MWIS and QUBO instances, highlighting a scalable path toward near-term quantum optimization. This work broadens the operational toolkit of neutral-atom devices and enhances their potential for scalable quantum optimization on structured graphs.

Abstract

Neutral atom arrays provide a versatile platform to implement coherent quantum annealing as an approach to solving hard combinatorial optimization problems. Here we present and experimentally demonstrate an efficient encoding scheme based on chains of Rydberg-blockaded atoms, which we call quantum wires, to natively embed maximum weighted independent set (MWIS) and quadratic unconstrained binary optimization (QUBO) problems on a neutral atom architecture. For graphs with quasi-unit-disk connectivity, in which only a few long-range edges are required, our approach requires a significantly lower overhead in the number of ancilla qubits than previous proposals, facilitating the implementation on currently available hardware. To demonstrate the approach, we perform weighted-graph annealing on a programmable atom array using local light shifts to encode problem-specific weights across graphs of varying sizes. This approach successfully identifies the solutions to the original MWIS and QUBO graph instances. Our work expands the operational toolkit of near-term neutral atom arrays, enhancing their potential for scalable quantum optimization.

Figures (2)

• Figure 1: Quantum Wire Approach (a) An example MWIS problem defined on a graph with non-unit-disk connectivity imposed by a sparse number of long-range edges (left) can be efficiently embedded on neutral atom hardware by introducing weighted quantum wires (right) created from chains of ancilla atoms as indicated by red circles. (b) An MWIS problem is mapped to a UDG-MWIS and solved on the QPU, with the solution indicated by dashed grey circles. (c) This strategy can be extended to QUBO problems by transforming them into equivalent UDG-MWIS instances where weighted edges are embedded using quantum wires.
• Figure 2: Weighted Quantum Wires (a) Basic construction of a wire to connect two nodes with weights $\alpha$ and $\beta$ in MWIS and QUBO problems. The energy diagram shows the ordering of the eigenstates for an MWIS implementation. (b, c) Wire constructions to delocalise triangular and all-to-all square interactions between vertices in MWIS problems. (d) Generalization of the crossing gadget introduced in nguyen2023 to allow for arbitrary weights of the nodes.