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arXiv:1003.4607 · Physical Review A

Experimental realization of the Deutsch-Jozsa algorithm with a six-qubit cluster state

Giuseppe Vallone, Gaia Donati, Natalia Bruno, Andrea Chiuri, Paolo Mataloni

Published May 13, 2010• 26 citations
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Abstract

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 $~1$ kHz success rate, demonstrates the correct implementation of the algorithm.

DOI
10.1103/physreva.81.050302

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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.
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.
Measurement-based quantum computing (MBQC), an alternate paradigm for formulating quantum algorithms, can lead to potentially more flexible and efficient implementations as well as to theoretical insights on the role of entanglement in a quantum algorithm. Using the graph-theoretical ZX-calculus, we describe and apply a general scheme for reformulating quantum circuits as MBQC implementations. After illustrating the method using the two-qubit Deutsch–Jozsa algorithm, we derive a ZX graph-diagram that encodes a general MBQC implementation for the three-qubit Deutsch–Jozsa algorithm. This graph describes an 11-qubit cluster state on which single-qubit measurements are used to execute the algorithm. Particular sets of choices of the axes for the measurements can be used to implement any realization of the oracle. In addition, we derive an equivalent lattice cluster state for the algorithm.
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.