Quantum Hamiltonian algorithms for maximum independent sets.

Xianjue Zhao, Peiyun Ge, Hongye Yu, Li You, Frank Wilczek, Biao Wu

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Article in National science review, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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6 authors.

Xianjue ZhaoInternational Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.ORCID https://orcid.org/0009-0001-8720-0421

Peiyun GeState Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China.

Hongye YuDepartment of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USA.

Li YouState Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China.

Frank WilczekCenter for Theoretical Physics, MIT, Cambridge, MA 02139, USA.

Biao WuInternational Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

We compare two quantum Hamiltonian algorithms that address the maximum independent set problem: one based on the emergent non-Abelian gauge matrix in adiabatic evolution of an energetically isolated manifold of states; the other based on designed application of single-qubit operations. We demonstrate that they are mathematically equivalent in the sense that one is the other's interaction picture. Despite their mathematical equivalence, our numerical simulations show significant differences between them in performance, which is explained analytically. Intriguingly, this equivalence unveils that the PXP model, recently prominent in quantum dynamics research, can be viewed as quantum diffusion over the median graph of all independent sets governed by the non-Abelian gauge matrix.

Indexed as

maximum independent setnon-Abelian mixingquantum algorithmRydberg atom array

Identifiers

PMID40933452

DOI10.1093/nsr/nwaf304

PMCPMC12418958

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