Similarity between Grover’s quantum search algorithm and classical two-body collisions

By studying the diffusion operator in Grover’s quantum search algorithm, we find a mathematical analogy between quantum searching and classical, elastic two-body collisions. We exploit this analogy using a thought experiment involving multiple collisions between two-bodies to help illuminate why Grover’s quantum search algorithm works. Related issues are discussed. PACS numbers: 03.67. Quantum computation is based on qubits. A qubit, literally a quantum bit of information, can be represented as a unit vector in a two-dimensional complex vector space. A typical vector can be written as |ψ >= α|0 > +β|1 >, with |α|2 + |β|2 = 1. Measurement of a qubit yields |α|2 and |β|2, the probabilities of the system being in states |0 > and |1 >. Unlike a classical bit, a qubit represents a superposition of the two states. This property leads to quantum parallel computation, which has been widely used in quantum algorithms [1]. Grover proposed a quantum search algorithm which can realize fast searching, such as finding an object in unsorted data consisting of N items [2]. This algorithm can be described as follows. Initially, an n qubit system is set in an equal superposition of all basis states expressed as |Ψ0 >= 1 √ N N−1