  The fermionic 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 O(n^2) operations to execute in O(n) steps. In this work, we
optimize the execution of fermionic SWAP networks for QAOA through two
techniques. First, we take advantage of an overcomplete set of native hardware
operations [including 150 ns controlled-pi/2 phase gates with up to 99.67(1)%
fidelity] in order 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 on 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 ~60% average reduction in
error (total variation distance) for QAOA of depth p = 1 on four transmon
qubits on a superconducting quantum processor.
