Decoherence in Grover search algorithm

Keng Wah Choo

We investigated the use of the quantum Grover algorithm in the mass-spectrometry-based protein identification process. The approach coded the mass spectra on a quantum register and uses the Grover search algorithm for searching multiple solutions to find matches from a database. Measurement of the fidelity between the input and final states was used to quantify the similarity between the experimental and theoretical spectra. The optimal number of iteration is proven to be pi/4sqrt[N/k] , where k refers to the number of marked states. We found that one iteration is sufficient for the search if we let more that 62% of the N states be marked states. By measuring the fidelity after only one iteration of Grover search, we discovered that it resembles that of the correlation-based measurement used in the existing protein identification software. We concluded that the quantum Grover algorithm can be adapted for a correlation-based mass spectra database search, provided that decoherence can be kept to a minimum.

O. V. Zhirov, Dima L. Shepelyansky

Yong Hu, Q Chen, Mang Feng

By virtue of the single-photon input-output process, we present a potentially practical scheme for realization of a multi-qubit Grover search algorithm in decoherence-free subspace (DFS) with low-Q cavities. Our treatment considers the decay of the cavity, which favours the input and output of the single photons, and the DFS encoding suppresses the collective dephasing errors. We show that our scheme for the three-qubit Grover search in DFS would work using near-future available techniques.

Yiyuan Fang, Dagomir Kaszlikowski, Chunming Chin +3 more

Gonzalo Abal, R. Donangelo, Franklin de Lima Marquezino +2 more

Recently several quantum search algorithms based on quantum walks were proposed. Those algorithms differ from Grover's algorithm in many aspects. The goal is to find a marked vertex in a graph faster than classical algorithms. Since the implementation of those new algorithms in quantum computers or in other quantum devices is error-prone, it is important to analyze their robustness under decoherence. In this work we analyze the impact of decoherence on quantum search algorithms implemented on two-dimensional grids and on hypercubes.

Grant Eberle, Gonzalo E. Ordonez