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Quantum computing provides powerful algorithmic tools that have been shown tooutperform established classical solvers in specific optimization tasks. A corestep in solving optimization problems with known quantum algorithms such as theQuantum Approximate Optimization Algorithm (QAOA) is the problem formulation.While quantum optimization has historically centered around QuadraticUnconstrained Optimization (QUBO) problems, recent studies show, that manycombinatorial problems such as the TSP can be solved more efficiently in theirnative Polynomial Unconstrained Optimization (PUBO) forms. As many optimizationproblems in practice also contain continuous variables, our contributioninvestigates the performance of the QAOA in solving continuous optimizationproblems when using PUBO and QUBO formulations. Our extensive evaluation onsuitable benchmark functions, shows that PUBO formulations generally yieldbetter results, while requiring less qubits. As the multi-qubit interactionsneeded for the PUBO variant have to be decomposed using the hardware gatesavailable, i.e., currently single- and two-qubit gates, the circuit depth ofthe PUBO approach outscales its QUBO alternative roughly linearly in the orderof the objective function. However, incorporating the planned addition ofnative multi-qubit gates such as the global Molmer-Sorenson gate, ourexperiments indicate that PUBO outperforms QUBO for higher order continuousoptimization problems in general.

Evidence that PUBO outperforms QUBO when solving continuous optimization problems with the QAOA