Implementation of quantum algorithms with resonant interactions

Construction of quantum computer is an enormously appealing task because of quantum computational potential to perform superfast quantum algorithms. Two classes of quantum logarithms illustrate the great theoretical promise of quantum computers. One is based on Shor’s Fourier transformation including quantum factoring [1], Deutsh-Jozsa logarithm [2] and so on, which are all exponential speedup compared with the classical algorithms. The other is based on Grover’s quantum search [3], which is quadratic speedup compared with the classical ones. The Grover search algorithm is very important because many techniques based on the search algorithm are universally used in our lives. The Grover search algorithm is efficient to look for one item in an unsorted database of size N ≡ 2 [3, 4]. Classically, in order to achieve the task, one needs O(N) queries. However, one needs O( √ N) queries by the Grover search algorithm. Furthermore, the efficiency of the algorithm has been manipulated experimentally in few-qubit cases via Nuclear Magnetic Resonance (NMR) [5, 6] and optics [7, 8]. Here, we first review the general Grover search algorithm. The circuit diagram of the Grover search algorithm with n data qubits and one auxiliary working qubit, which can be used to search one item from 2 items, is shown in Fig. 1. The process can be concluded as the following seven steps: