Short-depth QAOA circuits and quantum annealing on higher-order ising models

Abstract

We present a direct comparison between QAOA (Quantum Alternating Operator Ansatz), and QA (Quantum Annealing) on 127 qubit problem instances. QAOA with p = 1, 2 rounds is executed on the 127 qubit heavy-hex graph gate-model quantum computer ibm_washington, using on-device grid-searches for angle finding, and QA is executed on two Pegasus-chip D-Wave quantum annealers. The problems are random Ising models whose connectivity matches heavy-hex graphs and the Pegasus graph connectivity, and optionally include hardware-compatible cubic terms (ZZZ terms). The QAOA circuits are heavily optimized and of extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of the heavy-hex lattice. QAOA and QA are both compared against simulated annealing and the optimal solutions are computed exactly using CPLEX. The noiseless mean QAOA expectation values for p = 1, 2 are computed using classical light-cone based simulations. We find QA outperforms QAOA on the evaluated devices.