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arXiv:cond-mat/0105169 · Physical Review Letters

Quantum Algorithms for Josephson Networks

Jens Siewert, Rosario Fazio

Published Dec 3, 2001• 41 citations
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Abstract

We analyze possible implementations of quantum algorithms in a system of (macroscopic) Josephson charge qubits. System layout and parameters to realize the Deutsch algorithm with up to three qubits are provided. Special attention is paid to the necessity of entangled states in the various implementations. Further, we demonstrate explicitly that the gates to implement the Bernstein-Vazirani algorithm can be realized by using a system of uncoupled qubits.

DOI
10.1103/physrevlett.87.257905

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We analyze possible implementations of quantum algorithms in a system of (macroscopic) Josephson charge qubits. System layout and parameters to realize the Deutsch algorithm with up to three qubits are provided. Special attention is paid to the necessity of entangled states in the various implementations. Further, we demonstrate explicitly that the gates to implement the Bernstein-Vazirani algorithm can be realized by using a system of uncoupled qubits.
We show that the Deutsch-Jozsa algorithm for up to four qubits can be realized with a setup of Josephson charge qubits. While existing proposals for the implementation of the algorithm (for up to three qubits) are based on certain classifications of the oracles, this approach becomes increasingly cumbersome for higher qubit numbers. Here we present a method to implement all balanced functions for the four-qubit algorithm by a fixed sequence of operations. The free parameters which define the implemented function are the rotation angles of 15 one-qubit operations.
An improved architecture, which performs a universal set of gates by current biasing of coupling Josephson junction, has been proposed. This improvement is necessary to the realization of a functional and scalable quantum computer. The proposed architecture is in line with current technology. Secondly, we investigate a scheme for implementing the Deutsch–Jozsa algorithm via the improved architecture. It is a simple, scalable and feasible scheme for the implementation of the Deutsch–Jozsa algorithm based on the current-controlled superconducting charge qubit network.
The implementation of a quantum computer requires the realization of a large number of N-qubit unitary operations which represent the possible oracles or which are part of the quantum algorithm. Until now there have been no standard ways to uniformly generate whole classes of N-qubit gates. We develop a method to generate arbitrary controlled phase-shift operations with a single network of one-qubit and two-qubit operations. This kind of network can be adapted to various physical implementations of quantum computing and is suitable to realize the Deutsch-Jozsa algorithm as well as Grover's search algorithm.