Quantum Annealing vs. QAOA: 127 Qubit Higher-Order Ising Problems on NISQ Computers
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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. The studied problems are instances of a class of Ising problems, 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 (DDD) 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 DDD enables 2-round QAOA to outperform 1-round QAOA, which is not the case without DDD.
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