Two-particle Quantum Walks over a Line

Abstract

Quantum computing, the quantum analogue of classical computing makes use of qubits - quantum analogue of classical bits, as the elementary quantum registers of storing, manipulating and measuring data (Nakahara and Ohmi, 2008). Mathematically, a qubit is a unit vector of the form so that in a Hilbert space spanned by canonical basis states

When a qubit is queried, obtained is a probabilistic answer, instead of a deterministic one. That will be, the state with probability , and with probability . Also quantum algorithms were designed following this quantization. Various strategies for quantum algorithms emerged, along with the one based upon the idea introduced by Aharanov [4], and it was developed under the term ‘quantum walks’. Currently, two main categories of quantum walks are being considered: discrete and continuous quantum walks; while discrete quantum walks were studied under two subcategories as Markov chain-based and coin-based walks.