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

Abstract: The Quantum Approximate Optimization Algorithm (QAOA) is a standard method for combinatorial optimization with a gate-based quantum computer. The QAOA consists of a particular ansatz for the quantum circuit architecture, together with a prescription for choosing the variational parameters of the circuit. We propose modifications to both. First, we define the Gibbs objective function and show that it is superior to the energy expectation value for use as an objective function in tuning the variational parameters. Second, we describe an Ansatz Architecture Search (AAS) algorithm for searching the discrete space of quantum circuit architectures near the QAOA to find a better ansatz. Applying these modifications for a complete graph Ising model results in a $244.7\%$ median relative improvement in the probability of finding a low-energy state while using $33.3\%$ fewer two-qubit gates. For Ising models on a 2d grid we similarly 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 of quantum circuit architecture design for quantum optimization algorithms.