A loop Quantum Approximate Optimization Algorithm with Hamiltonian updating

Abstract

Designing noisy-resilience quantum algorithms is indispensable for practical applications on Noisy Intermediate-Scale Quantum~(NISQ) devices. Here we propose a quantum approximate optimization algorithm~(QAOA) with a very shallow circuit, called loop-QAOA, to avoid issues of noises at intermediate depths, while still can be able to exploit the power of quantum computing. The key point is to use outputs of shallow-circuit QAOA as a bias to update the problem Hamiltonian that encodes the solution as the ground state. By iterating a loop between updating the problem Hamiltonian and optimizing the parameterized quantum circuit, the loop-QAOA can gradually transform the problem Hamiltonian to one easy for solving. We demonstrate the loop-QAOA on Max-Cut problems both with and without noises. Compared with the conventional QAOA whose performance will decrease due to noises, the performance of the loop-QAOA can still get better with an increase in the number of loops. The insight of exploiting outputs from shallow circuits as bias may be applied for other quantum algorithms.

arXiv comment7 pages, 7 figures

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