We show 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 computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

我们表明，用于高阶、随机系数、重六边形兼容的自旋玻璃 Ising 模型的量子近似优化算法 （QAOA） 在 p = 1 到 p = 5 的问题大小（从 16 到 127 个量子比特）中具有很强的参数集中性，这允许 QAOA 角度的计算效率参数传递。矩阵乘积状态 （MPS） 仿真用于计算无噪声 QAOA 性能。硬件兼容的短深度 QAOA 电路在具有 16、27 和 127 个量子比特的嘈杂 IBM 量子超导处理器上的 100 个高阶 Ising 模型的集合上执行，使用使用 JuliQAOA 工具从单个 16 量子比特实例中学习的 QAOA 角度。我们表明，最好的量子处理器可以找到高达 p = 2 或 p = 3 的较低能量解决方案，并找到与无噪声分布相差约 2 倍的平均能量。我们表明，p = 1 QAOA 能源景观仍然非常相似，因为使用具有高达 414 量子比特处理器的 NISQ 硬件网格搜索，问题大小增加。