Kavli Affiliate: Frank Wilczek
| First 5 Authors: Xianjue Zhao, Peiyun Ge, Hongye Yu, Li You, Frank Wilczek
| Summary:
We compare two quantum Hamiltonian algorithms that address the maximum
independent set problem: one based on emergent non-abelian gauge matrix in
adiabatic evolution of an energetically isolated manifold of states; and one
based on designed application of single-qubit operations. We demonstrate that
they are mathematically equivalent, though at first sight they appear quite
different. Despite their mathematical equivalence, their most straightforward
physical implementations are different. Our numerical simulations show
significant differences in performance, and suggest improved experimental
protocols.Intriguingly, this equivalence unveils a deeper connection. We also
demonstrate that the PXP model, recently prominent in quantum dynamics
research, arises as the non-abelian gauge matrix governing quantum diffusion
over the median graph of all independent sets.
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