Kavli Affiliate: Frank Wilczek
| First 5 Authors: Xianjue Zhao, Peiyun Ge, Hongye Yu, Li You, Frank Wilczek
| Summary:
Two quantum Hamiltonian algorithms have been proposed to solve the maximum
independent set problem: the PK algorithm, introduced in [Phys. Rev. A 101
(2020) 012318; Chin. Phys. Lett. 38, (2021) 030304], and the the HV algorithm,
presented in [Science 376 (2022) 1209]. Here we demonstrate that the two
algorithms are mathematically equivalent. Specifically, the Hamiltonian in the
PK algorithm can be viewed as the HV Hamiltonian in the interaction picture. We
remark on potential practical advantages of the PK algorithm.Although they are
mathematically equivalent, their most straightforward physical implementations
are different, and our numerical simulations suggest that the PK algorithm
might can bring significant advantages.
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