Nonlocal Implementation Of The Grover Algorithm

A quantum computer allows for more efficient solution of some problems, for instance, the unsorted database search problem and the prime-factorization problem. Despite of its charming computing power, the construction of a realistic quantum computer is a daunting task. At present, the state of the art quantum computer using the nuclear magnetic resonance (NMR) can only implement 7-qubits. Some authors proposed the "distributed quantum computer" scheme, in which a quantum computer with many processors are located in different positions and each processor contains only a small number of qubits. This scheme may be experimentally more feasible than storing a large number of qubits in a single site. This paper examines the nonlocal implementation of the Grover quantum search algorithm. We analyze the Einstein-Podolsky-Rosen (EPR) pair resources required for the nonlocal implementation. As an example, we give the details of the implementation in a two-qubit system. Then we study the nonlocal implementation of a system with arbitrary N-qubit numbers. Our study reveals that in certain circumstances, the required resources in a nonlocal quantum computation is more [π/4N^1/2] × 4m EPR pairs than that in a standard Grover algorithm, even more than that in a classical computation, hence the nonlocal implementation of quantum computation in these cases loses its advantage.