Optimized SWAP networks with equivalent circuit averaging for QAOA

The SWAP network is a qubit routing sequence that can be used to efficiently execute the Quantum Approximate Optimization Algorithm (QAOA). Even with a minimally connected topology on an $n$-qubit processor, this routing sequence enables $\mathcal{O}({n}^{2})$ operations to execute in $\mathcal{O}(n)$ steps. In this work, we optimize the execution of SWAP networks for QAOA through two techniques. First, we take advantage of an overcomplete set of native hardware operations [including 150-ns controlled-$\frac{\ensuremath{\pi}}{2}$ phase gates with up to 99.67(1)% fidelity] to decompose the relevant quantum gates and SWAP networks in a manner which minimizes circuit depth and maximizes gate cancellation. Second, we introduce equivalent circuit averaging, which randomizes over degrees of freedom in the quantum circuit compilation to reduce the impact of systematic coherent errors. Our techniques are experimentally validated at the Advanced Quantum Testbed through the execution of QAOA circuits for finding the ground state of two- and four-node Sherrington-Kirkpatrick spin-glass models with various randomly sampled parameters. We observe a $\ensuremath{\sim}60%$ average reduction in error (total variation distance) for QAOA of depth $p=1$ on four transmon qubits on a superconducting quantum processor.