Scaling Quantum Approximate Optimization on Near-term Hardware*

The quantum approximate optimization algorithm (QAOA) is as an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems.  However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations.  Here, we quantify the expected resource requirements by designing optimized circuits for hardware architectures with varying levels of connectivity.  Assuming noisy gate operations, we estimate the number of measurements needed to sample the output of the idealized QAOA circuit with high probability.  We show the number of measurements, and hence total time to solution, grows exponentially in problem size and problem graph degree as well as depth of the QAOA ansatz, gate infidelities, and inverse hardware graph degree.