  Quantum annealing (QA) and Quantum Alternating Operator Ansatz (QAOA) are
both heuristic quantum algorithms intended for sampling optimal solutions of
combinatorial optimization problems. In this article we implement a rigorous
direct comparison between QA on D-Wave hardware and QAOA on IBMQ hardware.
These two quantum algorithms are also compared against classical simulated
annealing. The studied problems are instances of a class of Ising models, with
variable assignments of $+1$ or $-1$, that contain cubic $ZZZ$ interactions
(higher order terms) and match both the native connectivity of the Pegasus
topology D-Wave chips and the heavy hexagonal lattice of the IBMQ chips. The
novel QAOA implementation on the heavy hexagonal lattice has a CNOT depth of
$6$ per round and allows for usage of an entire heavy hexagonal lattice.
Experimentally, QAOA is executed on an ensemble of randomly generated Ising
instances with a grid search over $1$ and $2$ round angles using all 127
programmable superconducting transmon qubits of ibm_washington. The error
suppression technique digital dynamical decoupling is also tested on all QAOA
circuits. QA is executed on the same Ising instances with the programmable
superconducting flux qubit devices D-Wave Advantage_system4.1 and
Advantage_system6.1 using modified annealing schedules with pauses. We find
that QA outperforms QAOA on all problem instances. We also find that dynamical
decoupling enables 2-round QAOA to marginally outperform 1-round QAOA, which is
not the case without dynamical decoupling.
