Investigations of the quantum alternating operator ansatz or optimization problems with constraints

Presenting Author: Zhihui Wang, NASA - Ames Research Center
Contributing Author(s): Eleanor Rieffel, Stuart Hadfield, Bryan O'Gorman, Nicholas C Rubin, Zhang Jiang, Davide Venturelli

The emerging prototype universal quantum processors enables implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which have the potential to significantly expand the breadth of quantum computing applications. Here, we investigate the Quantum Alternating Operator Ansatz [1], an extension of the framework defined by Farhi et al. [2], that supports optimization problems with constraints and more efficient implementations. We present both theoretical and empirical results that demonstrate that choosing mixing unitaries that maintain the quantum evolution in the feasible subspace achieves better performance than adding penalties to a cost function to enforce the constraints. We discuss design criteria for mixing operators [1], mappings of a variety of specific problems [1], and compilations to near-term hardware [3]. [1] Stuart Hadfield, Zhihui Wang, Bryan O'Gorman, Eleanor G. Rieffel, Davide Venturelli, Rupak Biswas, From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz, arXiv:1709.03489 [2] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem. arXiv:1412.6062 [3] Davide Venturelli, Minh Do, Eleanor G. Rieffel, Jeremy Frank, Compiling Quantum Circuits to Realistic Hardware Architectures using Temporal Planners, arXiv:1705.08927

Read this article online: https://arxiv.org/pdf/1709.03489.pdf

(Session 10 : Saturday from 9:15am-9:45am)


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