On the Universality of the Quantum Approximate Optimization Algorithm
- Publisher:
- Springer
- Publication Type:
- Journal Article
- Citation:
- Quantum Information Processing, 2020, 19, (9), pp. 291
- Issue Date:
- 2020
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| Filename | Description | Size | |||
|---|---|---|---|---|---|
| Morales2020_Article_OnTheUniversalityOfTheQuantumA.pdf | 488.3 kB |
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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 [S. Lloyd,
arXiv:1812.11075] argued that for one-dimensional local cost Hamiltonians,
composed of nearest neighbor ZZ terms, this set-up is quantum computationally
universal, i.e., all unitaries can be reached up to arbitrary precision. In the
present paper, we give the complete proof of this statement and the precise
conditions under which such a one-dimensional QAOA might be considered
universal. We further generalize this type of 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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