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The Quantum Approximate Optimization Algorithm (QAOA) is a standard methodfor combinatorial optimization with a gate-based quantum computer. The QAOAconsists of a particular ansatz for the quantum circuit architecture, togetherwith a prescription for choosing the variational parameters of the circuit. Wepropose modifications to both. First, we define the Gibbs objective functionand show that it is superior to the energy expectation value for use as anobjective function in tuning the variational parameters. Second, we describe anAnsatz Architecture Search (AAS) algorithm for searching the discrete space ofquantum circuit architectures near the QAOA to find a better ansatz. Applyingthese modifications for a complete graph Ising model results in a $244.7\%$median relative improvement in the probability of finding a low-energy statewhile using $33.3\%$ fewer two-qubit gates. For Ising models on a 2d grid wesimilarly find $44.4\%$ median improvement in the probability with a $20.8\%$reduction in the number of two-qubit gates. This opens a new research field ofquantum circuit architecture design for quantum optimization algorithms.

Quantum Optimization with a Novel Gibbs Objective Function and Ansatz Architecture Search