Rydberg blockade based parity quantum optimization

We present a scalable architecture for solving higher-order constrained binary optimization problems on current neutral-atom hardware operating in the Rydberg blockade regime. In particular, we formulate the recently developed parity encoding of arbitrary connected higher-order optimization problems as a maximum-weight independent set (\textsf{MWIS}) problem on disk graphs, that are directly encodable on such devices. Our architecture builds from small \textsf{MWIS} modules in a problem-independent way, crucial for practical scalability.Comment: 10 pages, 7 figure

Modular Parity Quantum Approximate Optimization

The parity transformation encodes spin models in the low-energy subspace of a larger Hilbert-space with constraints on a planar lattice. Applying the Quantum Approximate Optimization Algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricting the dynamics to the low-energy subspace via the driver Hamiltonian. While the explicit approach allows for parallelization with a system-size-independent circuit depth, the implicit approach shows better QAOA performance. Here we combine the two approaches in order to improve the QAOA performance while keeping the circuit parallelizable. In particular, we introduce a modular parallelization method that partitions the circuit into clusters of subcircuits with fixed maximal circuit depth, relevant for scaling up to large system sizes.Comment: 11 pages, 9 figure