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

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 si...

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Vydáno v:	Algorithms Ročník 12; číslo 2; s. 34
Hlavní autoři:	Hadfield, Stuart, Wang, Zhihui, O’Gorman, Bryan, Rieffel, Eleanor G., Venturelli, Davide, Biswas, Rupak
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Basel MDPI AG 01.02.2019
Témata:	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
ISSN:	1999-4893, 1999-4893
On-line přístup:	Získat plný text
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Abstract	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.
AbstractList	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.
Author	Wang, Zhihui O’Gorman, Bryan Rieffel, Eleanor G. Hadfield, Stuart Venturelli, Davide Biswas, Rupak
Author_xml	– sequence: 1 givenname: Stuart orcidid: 0000-0002-4607-3921 surname: Hadfield fullname: Hadfield, Stuart – sequence: 2 givenname: Zhihui surname: Wang fullname: Wang, Zhihui – sequence: 3 givenname: Bryan surname: O’Gorman fullname: O’Gorman, Bryan – sequence: 4 givenname: Eleanor G. surname: Rieffel fullname: Rieffel, Eleanor G. – sequence: 5 givenname: Davide orcidid: 0000-0003-0452-7603 surname: Venturelli fullname: Venturelli, Davide – sequence: 6 givenname: Rupak surname: Biswas fullname: Biswas, Rupak
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Snippet	The next few years will be exciting as prototype universal quantum processors emerge, enabling the implementation of a wider variety of algorithms. Of...
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SubjectTerms	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
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Title	From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
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