The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes the solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which two unitary operators are alternately applied to the qubits. In this paper, this procedure is modified by updating the operators themselves to include local fields, using information from the measured wavefunction at the end of one iteration step to improve the operators at later steps. It is shown by numerical simulation on MAXCUT problems that this decreases the runtime of QAOA very substantially. This improvement appears to increase with the problem size. Our method requires essentially the same number of quantum gates per optimization step as the standard QAOA. Application of this modified algorithm should bring closer the time to quantum advantage for optimization problems.
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