Scaling Whole-Chip QAOA for Higher-Order Ising Spin Glass Models on Heavy-Hex Graphs

We show through numerical simulation that the Quantum Approximate Optimization Algorithm (QAOA) for higher-order, random-coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p=1 up to p=5, which allows for straight-forward transfer learning of QAOA angles on instance sizes where exhaustive grid-search is prohibitive even for p>1. We use Matrix Product State (MPS) simulation at different bond dimensions to obtain confidence in these results, and we obtain the optimal solutions to these combinatorial optimization problems using CPLEX. In order to assess the ability of current noisy quantum hardware to exploit such parameter concentration, we execute short-depth QAOA circuits with a CNOT depth of 6 per $p$, resulting in circuits which contain $1420$ two qubit gates for $127$ qubit $p=5$ QAOA on 100 higher-order (cubic term) Ising models on IBM quantum superconducting processors with 16, 27, 127 qubits using QAOA angles learned from a single 16-qubit instance. We show that (i) the best quantum processors generally find lower energy solutions up to p=3 for 27 qubit systems and up to p=2 for 127 qubit systems and are overcome by noise at higher values of p, (ii) the best quantum processors find mean energies that are about a factor of two off from the noise-free numerical simulation results. Additional insights from our experiments are that large performance differences exist among different quantum processors even of the same generation and that dynamical decoupling significantly improve performance for some, but decrease performance for other quantum processors. Lastly we show p=1 QAOA angle mean energy landscapes computed using up to a 414 qubit quantum computer, showing that the mean QAOA energy landscapes remain very similar as the problem size changes.