TY - EJOU
AU - Ruan, Yue
AU - Marsh, Samuel
AU - Xue, Xilin
AU - Liu, Zhihao
AU - Wang, Jingbo
TI - The Quantum Approximate Algorithm for Solving Traveling Salesman Problem
T2 - Computers, Materials \& Continua
PY - 2020
VL - 63
IS - 3
SN - 1546-2226
AB - The Quantum Approximate Optimization Algorithm (QAOA) is an
algorithmic framework for finding approximate solutions to combinatorial optimization
problems. It consists of interleaved unitary transformations induced by two operators
labelled the mixing and problem Hamiltonians. To fit this framework, one needs to
transform the original problem into a suitable form and embed it into these two
Hamiltonians. In this paper, for the well-known NP-hard Traveling Salesman Problem
(TSP), we encode its constraints into the mixing Hamiltonian rather than the conventional
approach of adding penalty terms to the problem Hamiltonian. Moreover, we map edges
(routes) connecting each pair of cities to qubits, which decreases the search space
significantly in comparison to other approaches. As a result, our method can achieve a
higher probability for the shortest round-trip route with only half the number of qubits
consumed compared to IBM Q’s approach. We argue the formalization approach
presented in this paper would lead to a generalized framework for finding, in the context
of QAOA, high-quality approximate solutions to NP optimization problems.
KW - Quantum approximate optimization algorithm
KW - traveling salesman problem
KW - NP optimization problems
DO - 10.32604/cmc.2020.010001