On the universality of the quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is considered to be one of the most promising approaches towards using near-term quantum computers for practical application. In its original form, the algorithm applies two different Hamiltonians, called the mixer and the cost Hamiltonian, in al...

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Bibliographic Details
Published in:Quantum information processing Vol. 19; no. 9
Main Authors: Morales, M. E. S., Biamonte, J. D., Zimborás, Z.
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2020
Springer Nature B.V
Subjects:
Algorithms
Circuits
Data Structures and Information Theory
Ground state
Mathematical Physics
Optimization
Optimization algorithms
Physics
Physics and Astronomy
Quantum computers
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Quantum computation
Variational quantum algorithms
Quantum control
Universal quantum gate sets
ISSN:1570-0755, 1573-1332
Online Access:Get full text
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Summary:The quantum approximate optimization algorithm (QAOA) is considered to be one of the most promising approaches towards using near-term quantum computers for practical application. In its original form, the algorithm applies two different Hamiltonians, called the mixer and the cost Hamiltonian, in alternation with the goal being to approach the ground state of the cost Hamiltonian. Recently, it has been suggested that one might use such a set-up as a parametric quantum circuit with possibly some other goal than reaching ground states. From this perspective, a recent work (Lloyd, arXiv:1812.11075 ) argued that for one-dimensional local cost Hamiltonians, composed of nearest neighbour ZZ terms, this set-up is quantum computationally universal and provides a universal gate set, i.e. all unitaries can be reached up to arbitrary precision. In the present paper, we complement this work by giving a complete proof and the precise conditions under which such a one-dimensional QAOA might produce a universal gate set. We further generalize this type of gate-set universality for certain cost Hamiltonians with ZZ and ZZZ terms arranged according to the adjacency structure of certain graphs and hypergraphs.
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ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-020-02748-9