The quantum approximate optimization algorithm (QAOA) has been introduced as a heuristic digital quantum computing scheme to find approximate solutions of combinatorial optimization problems. We present a scheme to parallelize this approach for arbitrary all-to-all connected problem graphs in a layout of quantum bits (qubits) with nearest-neighbor interactions. The protocol consists of single qubit operations that encode the optimization problem, whereas interactions are problem-independent pairwise CNOT gates among nearest neighbors. This allows for a parallelizable implementation in quantum devices with a planar lattice geometry. The basis of this proposal is a lattice gauge model, which also introduces additional parameters and protocols for QAOA to improve the efficiency.

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