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Implementation of Deutsch-Jozsa algorithm and determination of value of function via Rydberg blockade

Aixi Chen

Published Jan 19, 2011• 18 citations
Publisher

Abstract

We propose an efficient scheme in which the Deutsch-Jozsa algorithm can be realized via Rydberg blockade interaction. Deutsch-Jozsa algorithm can fast determine whether function is constant or balanced, but this algorithm does not give the concrete value of function. Using the Rydberg blockade, value of function may be determined in our scheme. According to the quantitative calculation of Rydberg blockade, we discuss the experimental feasibility of our scheme.

DOI
10.1364/oe.19.002037

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We propose an efficient scheme in which the Deutsch-Jozsa algorithm can be realized via Rydberg blockade interaction. Deutsch-Jozsa algorithm can fast determine whether function is constant or balanced, but this algorithm does not give the concrete value of function. Using the Rydberg blockade, value of function may be determined in our scheme. According to the quantitative calculation of Rydberg blockade, we discuss the experimental feasibility of our scheme.
Deutsch algorithm or Deutsch–Jozsa algorithm only needs one query to determine whether the function f(x) is constant or balanced. That is, the global property of the function f(x) is rapidly known. But these algorithms do not give the concrete value of function f(x). For the f(x), its value is also of interest. Here we propose a scheme in which the value of function f(x) can be determined. We use an entangled state as the input state and send it into quantum black box. Through performing measurement on the output state, we can exactly determine the value of f(x). Its value plus its global property enables us to thoroughly understand elementary information of f(x). Based on these informations, we can determine unitary transformations on the input state walking through quantum black box. The quantum black box becomes quantum white box to a certain extent.
Multiqubit CCZ gates form one of the building blocks of quantum algorithms and have been involved in achieving many theoretical and experimental triumphs. Designing a simple and efficient multiqubit gate for quantum algorithms is still by no means trivial as the number of qubits increases. Here, by virtue of the Rydberg blockade effect, we propose a scheme to rapidly implement a three-Rydberg-atom CCZ gate via a single Rydberg pulse, and successfully apply the gate to realize the three-qubit refined Deutsch-Jozsa algorithm and three-qubit Grover search. The logical states of the three-qubit gate are encoded to the same ground states to avoid an adverse effect of the atomic spontaneous emission. Furthermore, there is no requirement for individual addressing of atoms in our protocol.