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Performing the Deutsch-Josza and Bernstein-Vazirani algorithms using cluster states

Mark Tame, M. S. Kim

Published Mar 25, 2010• 0 citations
OpenAlex

Abstract

We show that fundamental versions of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms can be performed using a small entangled cluster state resource of only six qubits. We then investigate the minimal resource states needed to demonstrate arbitrary n-qubit versions and a scalable method to produce them. For this purpose we propose a versatile on-chip photonic waveguide setup.

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2-photon multiqubit cluster states

Giuseppe Vallone, R. Ceccarelli, Paolo Mataloni

Cluster states of two photons and four qubits, built on the double entanglement of two photons in the degrees of freedom of polarization and linear momentum, have been used in the realization of a complete set of basic operations of one-way quantum computation. Basic computation algorithms, namely, the Grover's search and the Deutsch's algorithm, have been realized by using these states. Hyperentangled states of increasing size are of paramount importance for the realization of even more complex algorithms and can be extended to a lager number of degrees of freedom of the photons. Some recent results obtained with entangled states of two photons and six qubits are presented.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 2, 2008•0 citations
We show that fundamental versions of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms can be performed using a small entangled cluster state resource of only six qubits. We then investigate the minimal resource states needed to demonstrate arbitrary n-qubit versions and a scalable method to produce them. For this purpose we propose a versatile on-chip photonic waveguide setup.
We show that fundamental versions of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms can be performed using a small entangled cluster state resource of only six qubits. We then investigate the minimal resource states needed to demonstrate general nnn-qubit versions and a scalable method to produce them. For this purpose, we propose a versatile photonic on-chip setup.
We describe an experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a two-bit Boolean function in the framework of one-way quantum computation. For this purpose, a two-photon six-qubit cluster state was engineered. Its peculiar topological structure is the basis of the original measurement pattern allowing the algorithm realization. The good agreement of the experimental results with the theoretical predictions, obtained at  1~1 1 kHz success rate, demonstrates the correct implementation of the algorithm.
The paper introduces an efficient implementation of the Deutsch-Jozsa and Bernstein-Vazirani algorithm using the single-particle discrete-time quantum walk. We also provide a detailed optical framework with specific optical components to achieve these implementations in the photonic quantum walk scheme by simultaneously exploiting both polarization and path degrees of freedom. These implementations demonstrate improved resource efficiency while maintaining the exponential speedup characteristic of both algorithms. This work contributes to the growing field of universal quantum computing using singleparticle discrete-time quantum walk.
Cluster states of two photons and four qubits, built on the double entanglement of two photons in the degrees of freedom of polarization and linear momentum, have been used in the realization of a complete set of basic operations of one-way quantum computation. Basic computation algorithms, namely, the Grover's search and the Deutsch's algorithm, have been realized by using these states. Hyperentangled states of increasing size are of paramount importance for the realization of even more complex algorithms and can be extended to a lager number of degrees of freedom of the photons. Some recent results obtained with entangled states of two photons and six qubits are presented.