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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Implementing an optical CNOT using spatial parity qubits

Kumel H. Kagalwala, Giovanni Di Giuseppe, Ayman F. Abouraddy, Bahaa E. A. Saleh

Published May 13, 2011• 0 citations
Publisher

Abstract

We describe an optical implementation of a CNOT gate in which the control qubit is the polarization of a single photon and the target qubit is the spatial parity of the same photon. The gate is implemented with a polarization- sensitive spatial light modulator. We characterize the operation of the gate using quantum process tomography and the spatial parity is analyzed with a modified Mach-Zehnder interferometer. We also demonstrate the CNOT-gate operation with arbitrary rotation of the target qubit and discuss the possibility of implementing multi-qubit CNOT gates using the same approach.

DOI
10.1117/12.883995

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We describe an optical implementation of a CNOT gate in which the control qubit is the polarization of a single photon and the target qubit is the spatial parity of the same photon. The gate is implemented with a polarization- sensitive spatial light modulator. We characterize the operation of the gate using quantum process tomography and the spatial parity is analyzed with a modified Mach-Zehnder interferometer. We also demonstrate the CNOT-gate operation with arbitrary rotation of the target qubit and discuss the possibility of implementing multi-qubit CNOT gates using the same approach.
Increasing the information-carrying capacity of a single photon may be achieved by utilizing multiple degrees of freedom. We describe here an approach that utilizes two degrees of freedom to encode three qubits per photon: one in polarization and two in the spatial-parity symmetry of the transverse field. In this conception, a polarization-sensitive spatial light modulator corresponds to a three-qubit controlled-unitary gate with one control qubit (polarization) and two target (spatial-parity-symmetry) qubits. We describe the construction of controlled-not (cnot), cnotn\sqrt[n]{cnot}ncnot​, controlled-phase, and Fredkin gates, and the preparation of one-photon, three-qubit Greenberger-Horne-Zeilinger (GHZ) and WWW states. This approach enables simple optical implementations of few-qubit tasks in quantum information processing.
The information-carrying capacity of a single photon can be vastly expanded by exploiting its multiple degrees of freedom: spatial, temporal, and polarization. Although multiple qubits can be encoded per photon, to date only two-qubit single-photon quantum operations have been realized. Here, we report an experimental demonstration of three-qubit single-photon, linear, deterministic quantum gates that exploit photon polarization and the two-dimensional spatial-parity-symmetry of the transverse single-photon field. These gates are implemented using a polarization-sensitive spatial light modulator that provides a robust, non-interferometric, versatile platform for implementing controlled unitary gates. Polarization here represents the control qubit for either separable or entangling unitary operations on the two spatial-parity target qubits. Such gates help generate maximally entangled three-qubit Greenberger-Horne-Zeilinger and W states, which is confirmed by tomographical reconstruction of single-photon density matrices. This strategy provides access to a wide range of three-qubit states and operations for use in few-qubit quantum information processing protocols.Photons are essential for quantum information processing, but to date only two-qubit single-photon operations have been realized. Here the authors demonstrate experimentally a three-qubit single-photon linear deterministic quantum gate by exploiting polarization along with spatial-parity symmetry.