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physica status solidi (b)

Implementation of the Four-Bit Deutsch-Jozsa Algorithm with Josephson Charge Qubits

Norbert Schuch, Jens Siewert

Published Oct 1, 2002• 10 citations
Publisher

Abstract

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.

DOI
10.1002/1521-3951(200210)233:3<482::aid-pssb482>3.0.co;2-f

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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.
It is shown that Deutsch’s algorithm and the Deutsch-Jozsa algorithm for two and three qubits can be efficiently implemented on a classical computer. This is done by analysing the structure of the oracles contained in these algorithms, followed by an implementation in the toy theory proposed by Robert W. Spekkens which uses 2 classical bits to simulate a qubit. Further discussion is given about how to analyse, and possible implementations, of the Deutsch-Jozsa for higher number of qubits in the toy theory.
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 first optical proposal for the realization of the two-bit version of the Deutsch-Jozsa algorithm [D. Deutsch and R. Jozsa, Proc. R. Soc. London A {\bf 493}, 553 (1992)] is presented. The proposal uses Stark shifts in an ensemble of atoms and degenerate sources of photons. The photons interact dispersively with an atomic ensemble, leading to an effective Hamiltonian in atom-field basis, which is useful for performing the required two-qubit operations. Combining these with a set of one-qubit operations, the algorithm can be implemented. A discussion of the experimental feasibility of the proposal is given.