TY - JOUR

T1 - Generation of quantum phases of matter and finding a maximum-weight independent set of unit-disk graphs using Rydberg atoms

AU - Farouk, Ahmed M.

AU - Beterov, I. I.

AU - Xu, Peng

AU - Ryabtsev, I. I.

N1 - This work was supported by the Russian Science Foundation (Grant No. 23-42-00031). A.M.F. acknowledges financial support from the joint executive educational program between Egypt and Russia (Grant No. EGY-6544/19). P.X. acknowledges financial support from the National Key Research and Development Program of China (Grant No. 2021YFA1402001) and the National Natural Science Foundation of China (Grants No. 12261131507 and No. U20A2074).

PY - 2024/8/27

Y1 - 2024/8/27

N2 - Recent progress in quantum computing and quantum simulation of many-body systems with arrays of neutral atoms using Rydberg excitation has provided unforeseen opportunities towards computational advantage in solving various optimization problems. The problem of a maximum-weight independent set of unit-disk graphs is an example of an NP-hard optimization problem. It involves finding the largest set of vertices with the maximum sum of their weights for a graph which has edges connecting all pairs of vertices within a unit distance. This problem can be solved using quantum annealing with an array of interacting Rydberg atoms. For a particular graph, a spatial arrangement of atoms represents vertices of the graph, while the detuning from resonance at Rydberg excitation defines the weights of these vertices. The edges of the graph can be drawn according to the unit-disk criterion. Maximum-weight independent sets can be obtained by applying a variational quantum adiabatic algorithm. We consider driving the quantum system of interacting atoms to the many-body ground state using a nonlinear quasiadiabatic profile for sweeping the Rydberg detuning. We also propose using a quantum wire, which is a set of auxiliary atoms of a different chemical element, to mediate strong coupling between the remote vertices of the graph. We investigate this effect for different lengths of the quantum wire. We also investigate the quantum phases of matter realizing commensurate and incommensurate phases in one- and two-dimensional spatial arrangements of the atomic array.

AB - Recent progress in quantum computing and quantum simulation of many-body systems with arrays of neutral atoms using Rydberg excitation has provided unforeseen opportunities towards computational advantage in solving various optimization problems. The problem of a maximum-weight independent set of unit-disk graphs is an example of an NP-hard optimization problem. It involves finding the largest set of vertices with the maximum sum of their weights for a graph which has edges connecting all pairs of vertices within a unit distance. This problem can be solved using quantum annealing with an array of interacting Rydberg atoms. For a particular graph, a spatial arrangement of atoms represents vertices of the graph, while the detuning from resonance at Rydberg excitation defines the weights of these vertices. The edges of the graph can be drawn according to the unit-disk criterion. Maximum-weight independent sets can be obtained by applying a variational quantum adiabatic algorithm. We consider driving the quantum system of interacting atoms to the many-body ground state using a nonlinear quasiadiabatic profile for sweeping the Rydberg detuning. We also propose using a quantum wire, which is a set of auxiliary atoms of a different chemical element, to mediate strong coupling between the remote vertices of the graph. We investigate this effect for different lengths of the quantum wire. We also investigate the quantum phases of matter realizing commensurate and incommensurate phases in one- and two-dimensional spatial arrangements of the atomic array.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85202438179&origin=inward&txGid=532fdd1a0dd9eb4741f0d94bbbe97b09

UR - https://www.mendeley.com/catalogue/28a409f5-f57c-3aeb-afe5-732aa8c505fe/

U2 - 10.1103/PhysRevA.110.022442

DO - 10.1103/PhysRevA.110.022442

M3 - Article

VL - 110

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 022442

ER -