Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry

The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the performance of QAOA for preparing ground states of target Hamilton...

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Veröffentlicht in:New journal of physics Jg. 25; H. 1; S. 13015 - 13032
Hauptverfasser: Sun, Zheng-Hang, Wang, Yong-Yi, Cui, Jian, Fan, Heng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Bristol IOP Publishing 01.01.2023
Schlagworte:
Algorithms
Boundary conditions
Circuit design
Critical point
Entangled states
Hamiltonian functions
Optimization
Phase transitions
Physics
Processors
quantum approximate optimization algorithm
quantum computation
Quantum computers
Symmetry
variational quantum simulation
ISSN:1367-2630, 1367-2630
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Zusammenfassung:The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the performance of QAOA for preparing ground states of target Hamiltonians near the critical points of their quantum phase transitions, and generating Greenberger–Horne–Zeilinger (GHZ) states. We reveal that the performance of QAOA is related to the translational invariance of the target Hamiltonian: without the translational symmetry, for instance due to the open boundary condition (OBC) or randomness in the system, the QAOA becomes less efficient. We then propose a generalized QAOA assisted by the parameterized resource Hamiltonian (PRH-QAOA), to achieve a better performance. In addition, based on the PRH-QAOA, we design a low-depth quantum circuit beyond one-dimensional geometry, to generate GHZ states with perfect fidelity. The experimental realization of the proposed scheme for generating GHZ states on Rydberg-dressed atoms is discussed. Our work paves the way for performing QAOA on programmable quantum processors without translational symmetry, especially for recently developed two-dimensional quantum processors with OBC.
Bibliographie:NJP-115425.R1
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ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/acb22c