Ion Trap Proposal for Quantum Search
نویسندگان
چکیده
In this letter, we show that the laser Hamiltonian can perform the quantum search. We also show that the process of quantum search is a resonance between the initial state and the target state, which implies that Nature already has a quantum search system to use a transition of energy. In addition, we provide the particular scheme to implement the quantum search algorithm based on a trapped ion. Quantum computation has been in the spotlight, supplying the solution for the problems which are intractable in the context of classical physics. The quantum factorization algorithm and the quantum search algorithm are the good examples.[1] In particular, the quantum search algorithm provides the quadratic speedup in solving a search problem. Here, the search problem is to find the target of the unstructured N itmes. Grover’s fast quantum search algorithm is composed of discrete-time operations(e.g., Walsh-Hadamard). When we use Grover’s algorithm, we need O( √ N) iterations of the Grover operator. There is the analog quantum search algorithm which is based on the Hamiltonian evolution. Farhi and Gutmann proposed the quantum search Hamiltonian.[5] Moreover, Fenner provided another quantum search Hamiltonian.[6] Recently, the generalized quantum search Hamiltonian was proposed.[7] In this letter, we show that a laser Hamiltonian can perform quantum search by resonance between the initial state and the target state. The idea to apply the laser Hamiltonian to quantum search comes from the observation that the generalized quantum search Hamiltonian is apparently similar to the laser one. The difference is that the quantum search Hamiltonian is time-independent but the laser Hamiltonian time-dependent. In order to develop our proposition, we first introduce the generalized quantum search Hamiltonian. Next, we briefly review the laser Hamiltonian and show that the laser Hamiltonian can perform the quantum search. Also we point out that the resonance is the key factor in analog quantum search. Furthermore, we suggest the scheme to implement the quantum search algorithm using a trapped ion. In order to apply quantum mechanics to a search problem, we give a bijection from the N items to the eigenstates of the N -dimensional Hilbert space. The search problem is then to find the target state in the N eigenstates. Grover algorithm is the method that offers Email address: [email protected] Email address: [email protected]
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تاریخ انتشار 2002