A genuine quantum operation for traveling salesman problem (TSP)

Abstract

Quantum information processing has a dramatic speedup over its counterpart, classical information processing. Here, quantum algorithms such as Shor`s factorization and Grover`s database search are at the heart of quantum information processing. It is generally acknowledged that such successful algorithms are enabled by genuine quantum operations or their modules, which may be classified to be of novel quantum nature: Parallelism from quantum superposition and non-locality engaged in quantum entanglement. For instance, Shor`s factorization algorithm is equipped with quantum Fourier transformation and Grover`s database search algorithm uses the operation module consisting of quantum oracle and average inversion. In this presentation, we propose another quantum operation module, which plays a crucial role in a new quantum algorithm to solve traveling salesman problem (TSP). The operation module includes a quantum oracle, called as cost oracle. The cost oracle encodes the real physical information onto the phases. The proposed operation module is defined by two query operations as it calls cost oracle twice at each iteration. As an example, we design a quantum algorithm to attack TSP. It has the similar mathematical structure to a generalized Grover algorithm, and it is capable of obtaining quadratic speedup.