Speaker
Description
Quadratic Unconstrained Binary Optimization problems (QUBOs) provide relevant testing grounds for quantum annealing platforms. However, mapping the logical QUBO onto a given quantum register is a known computational bottleneck. For Rydberg atom devices, the natural Unit-Disk topology arising from the Rydberg blockade mechanism limits the types of problems that can be naturally embedded on the hardware. Typical approaches to embedding include problem-based heuristics or general "gadget" reductions. The latter are graph-theoretic constructions that mediate interactions via ancillary qubits, typically incurring quadratic ancilla overhead. To address this scalability issue, we propose an approximate heuristic based on the spectral properties of the QUBO's adjacency matrix. By decomposing the QUBO into its singular modes, we use individual ancillas to mediate the structure of each relevant mode. We optimize for the position of the ancilla within a polygon defined by the logical qubits, while adjusting the local detuning of these ancillas to minimize the spectral distance between the QUBO and the physical Hamiltonian. Preliminary results suggest that this approach exhibits linear scaling with respect to the number of ancillary qubits. This work establishes a framework for developing further spectral embedding methods and provides an alternative for obtaining approximate solutions to larger problems.
| Keyword-1 | Neutral Atom Quantum Computing |
|---|---|
| Keyword-2 | Embedding Problem |
| Keyword-3 | Singular Value Decomposition |