The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently know about the capabilities of QAOA, or of the difficulty of the requisite parameters optimization. Here, we study the performance of QAOA on the MaxCut combinatorial optimization problem, optimizing the quantum circuits on a classical computer using automatic differentiation and stochastic gradient descent, using QuantumFlow, a quantum circuit simulator implemented with TensorFlow. We find that we can amortize the training cost by optimizing on batches of problems instances; that QAOA can exceed the performance of the classical polynomial time Goemans-Williamson algorithm with modest circuit depth, and that performance with fixed circuit depth is insensitive to problem size. Moreover, MaxCut QAOA can be efficiently implemented on a gate-based quantum computer with limited qubit connectivity, using a qubit swap network. These observations support the prospects that QAOA will be an effective method for solving interesting problems on near-term quantum computers. PACS numbers: 03.67.Ac, 03.67.Lx Introduction -The development of quantum computers continues apace, with the prospect of that intermediate scale machines that exhibit a clear advantage over classical computers will arrive presently [1]. However, our understanding of how to develop noise resilient algorithms that can run on near-term quantum resources remains limited. For a few computational problems, we know that a gate-based quantum computer can outperform any conceivable classical algorithm [2]. But for most problems we do not know how to implement effective algorithms on noisy, near term architectures with a modest number of qubits. One promising approach to solving combinatorial optimization problems on near-term machines is the Quantum Approximate Optimization Algorithm (QAOA) [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] . This is a heuristic method, which can be thought of as a time-discretization of adiabatic quantum computing [23] . Like a number of near-term approaches to quantum computing [24] [25] [26] [27] , QAOA is a hybrid classicalquantum algorithm that combines quantum circuits, and classical optimization of those circuits. The objective is a functional of the quantum state, which in turn is a function parameterized by one and two-qubit gates whose character can be continuously varied. We perform classical optimization on these continuous gate parameters to generate distributions with significant support on the optimal solution. The use of a quantum resource allows us to prepare a distribution over an exponentially large sample space in a short sequence of gates, and the use of classical optimization expands the range of problems that we can explore, and may lead to circuits that are relatively robust to imperfections in the implementation of
In REF the performance of QAOA is studied on different problems.
Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem
arXiv: Quantum Physics
Mathematics Physics