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The Quantum Approximate Optimization Algorithm (QAOA) is a promising approachfor programming a near-term gate-based hybrid quantum computer to find goodapproximate solutions of hard combinatorial problems. However, little iscurrently know about the capabilities of QAOA, or of the difficulty of therequisite parameters optimization. Here, we study the performance of QAOA onthe MaxCut combinatorial optimization problem, optimizing the quantum circuitson a classical computer using automatic differentiation and stochastic gradientdescent, using QuantumFlow, a quantum circuit simulator implemented withTensorFlow. We find that we can amortize the training cost by optimizing onbatches of problems instances; that QAOA can exceed the performance of theclassical polynomial time Goemans-Williamson algorithm with modest circuitdepth, and that performance with fixed circuit depth is insensitive to problemsize. Moreover, MaxCut QAOA can be efficiently implemented on a gate-basedquantum computer with limited qubit connectivity, using a qubit swap network.These observations support the prospects that QAOA will be an effective methodfor solving interesting problems on near-term quantum computers.

Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem