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From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz

Algorithms, 2019-02, Vol.12 (2), p.34 [Peer Reviewed Journal]

2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;ISSN: 1999-4893 ;EISSN: 1999-4893 ;DOI: 10.3390/a12020034

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  • Title:
    From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
  • Author: Hadfield, Stuart ; Wang, Zhihui ; O'Gorman, Bryan ; Rieffel, Eleanor ; Venturelli, Davide ; Biswas, Rupak
  • Subjects: Algorithms ; Annealing ; approximate optimization ; Arrays ; constrained optimization ; constraint satisfaction problems ; Cost function ; Design criteria ; Experimentation ; Hamiltonian functions ; Heuristic ; Mixers ; Operators ; Optimization ; Optimization algorithms ; quantum algorithms ; quantum circuit ansatz ; Quantum computers ; Quantum computing ; quantum gate model
  • Is Part Of: Algorithms, 2019-02, Vol.12 (2), p.34
  • Description: The next few years will be exciting as prototype universal quantum processors emerge, enabling the implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation and which have the potential to significantly expand the breadth of applications for which quantum computers have an established advantage. A leading candidate is Farhi et al.’s quantum approximate optimization algorithm, which alternates between applying a cost function based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach, in the spirit of the quantum approximate optimization algorithm, to a wide variety of approximate optimization, exact optimization, and sampling problems. In addition to introducing the quantum alternating operator ansatz, we lay out design criteria for mixing operators, detail mappings for eight problems, and provide a compendium with brief descriptions of mappings for a diverse array of problems.
  • Publisher: Basel: MDPI AG
  • Language: English
  • Identifier: ISSN: 1999-4893
    EISSN: 1999-4893
    DOI: 10.3390/a12020034
  • Source: ROAD: Directory of Open Access Scholarly Resources
    ProQuest Central
    DOAJ Directory of Open Access Journals
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