A Quantum Algorithm for Solving the Travelling Salesman Problem by Quantum Phase Estimation and Quantum Search

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Abstract

A quantum algorithm for solving the traveling salesman problem by the quantum phase estimation and quantum search method is considered. An approach is developed that was previously proposed for solving this problem. A quantum register is used to encode the eigenstates of a unitary operator whose phase determines the length of each possible route. The quantum phase estimation algorithm is used to estimate the length of a route. Then, to find the minimum route length, the measured values of length are encoded into the states of the second quantum register, and the search for the optimal route is carried out using a modified Grover algorithm. Numerical simulation of the proposed quantum algorithm is carried out using the Qiskit library for one and two iterations of the modified Grover algorithm.

About the authors

Ch. Tszyun'si

Rzhanov Institute of Semiconductor Physics, Siberian Branch,
Russian Academy of Sciences

Email: beterov@isp.nsc.ru
Novosibirsk, 630090 Russia

I. I. Beterov

Novosibirsk State University;Rzhanov Institute of Semiconductor Physics, Siberian Branch of Russian Academy of Sciences;Institute of Laser Physics, Siberian Branch of Russian Academy of Sciences;Novosibirsk State Technical University

Author for correspondence.
Email: beterov@isp.nsc.ru
Novosibirsk, 630090 Russia;Novosibirsk, 630090 Russia;Novosibirsk, 630090 Russia;Novosibirsk, 630073 Russia

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