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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Realization and characterization of a 2-photon 4-qubit linear cluster state

Giuseppe Vallone, Enrico Pomarico, Paolo Mataloni, F. De Martini, V. Berardi

Published Jun 1, 2007• 2 citations
Publisher

Abstract

Cluster states, recently introduced as a fundamental resource for one-way quantum computation, represent genuine multiqubits entangled states. The one-way model is based on the initial preparation of entangled qubits in the cluster state, followed by single qubits measurements and feed-forwards. All the difficulties present in the standard computation model, for instance the implementation of two qubits gates, are transferred in the one-way model to the state preparation.

DOI
10.1109/cleoe-iqec.2007.4386764

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Cluster states, recently introduced as a fundamental resource for one-way quantum computation, represent genuine multiqubits entangled states. The one-way model is based on the initial preparation of entangled qubits in the cluster state, followed by single qubits measurements and feed-forwards. All the difficulties present in the standard computation model, for instance the implementation of two qubits gates, are transferred in the one-way model to the state preparation.
We describe the application of four-qubit cluster states, built on the simultaneous entanglement of two photons in the degrees of freedom of polarization and linear momentum, for the realization of a complete set of basic operations of one-way quantum computation. These consist of arbitrary single-qubit rotations, either probabilistic or deterministic, and simple two-qubit gates, such as a controlled-NOT (CNOT) gate for equatorial qubits and a universal controlled-phase gate (controlled-ZZZ or CZ) gate acting on arbitrary target qubits. Other basic computation operations, such as the Grover's search and the Deutsch's algorithms, have been realized by using these states. In all the cases we obtained a high value of the operation fidelities. These results demonstrate that cluster states of two photons entangled in many degrees of freedom are good candidates for the realization of more complex quantum computation operations based on a larger number of qubits.
Quantum computers promise to be more efficient and powerful than their classical counterparts. In the one-way quantum computer model [1], a sequence of measurements processes qubits, which are initially prepared in a highly entangled cluster state. We present here an optical implementation of a 4-qubit cluster state and we show how different algorithms can be experimentally realized by performing the corresponding sequence of measurements. The key advantage of this scheme over the standard network approach of quantum computing is that inherent, randomly induced measurement errors can classically be fed-forward and corrected by adapting the basis of subsequent measurement.
By using 2-photon 4-qubit cluster states we demonstrate deterministic one-way quantum computation in a single qubit rotation algorithm. In this operation feed-forward measurements are automatically implemented by properly choosing the measurement basis of the qubits, while Pauli error corrections are realized by using two fast driven Pockels cells. We realized also a C-NOT gate for equatorial qubits and a C-PHASE gate for a generic target qubit. Our results demonstrate that 2-photon cluster states can be used for rapid and efficient deterministic one-way quantum computing.
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.