Topologically protected Grover's oracle for the partition problem

Sinitsyn, Nikolai A.; Yan, Bin

doi:10.1103/PhysRevA.108.022412

Topologically protected Grover's oracle for the partition problem

Apr 20, 2023

11 pages

Published in:

Phys.Rev.A 108 (2023) 2, 022412

Published: Aug 14, 2023

e-Print:

2304.10488 [quant-ph]

DOI:

10.1103/PhysRevA.108.022412 (publication)

Report number:

LA-UR-23-24130

View in:

ADS Abstract Service

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Abstract: (APS)

The number partitioning problem (NPP) is one of the NP-complete (nondeterministic polynomial-time complete) computational problems. Its definite exact solution generally requires a check of all

N

solution candidates, which is exponentially large. Here we describe a path to the fast solution of this problem in

\sqrt{N}

quasi-adiabatic quantum annealing steps. We argue that the errors due to the finite duration of the quantum annealing can be suppressed if the annealing time scales with

N

only logarithmically. Moreover, our adiabatic oracle is topologically protected, in the sense that it is robust against small uncertainty and slow time dependence of the physical parameters or the choice of the annealing protocol. We also argue that our approach can solve many other famous NP-complete computational problems in

\sqrt{N}

steps.

Note:

v2: final version; to appear in Physical Review A

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Figures(3)

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