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Nature Communications

Single-photon three-qubit quantum logic using spatial light modulators

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

Published Sep 25, 2017• 70 citations
Publisher

Abstract

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.

DOI
10.1038/s41467-017-00580-x

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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.
For quantum computation using photons, performing deterministic quantum gate operations is a challenge due to the probabilistic nature of the photon-photon interaction. Encoding qubits in multiple degrees-of-freedom of photons and controlling operations between them is one of the promising ways to navigate the probabilistic behavior. Using single-photon discrete-time quantum walk in combination with polarization and path degrees-of-freedom, we experimentally demonstrate the realization of a universal set of quantum gates with high fidelity at room temperature. The deterministic realization of quantum gates through photonic quantum walk are characterized via quantum state tomography. For a three-qubit system using a single photon, the first qubit is encoded using polarization information, and the other two qubits are encoded using path information, closely resembling a Galton-board setup. To generate a six-qubit Greenberger-Horne-Zeilinger state, entangled photon pairs are used to entangle the two three-qubit modules on which gate operations are performed. We also provide insights into the mapping of photonic quantum walk operations to quantum circuits and propose methods to resourcefully scale. This demonstration marks a significant progress towards using quantum walks for quantum computing and provides a framework for using fewer photons in combination with different degrees-of-freedom of photon to scale the number of qubits.
Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing, allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g., wave plates for polarization. However, for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations at high quality by using only a few phase modulation planes. More importantly, we experimentally implement several high-dimensional quantum gates for up to five-dimensional states encoded in the full-field mode structure of photons. In particular, we realize cyclic and quantum Fourier transformations, known as Pauli X ^ -gates and Hadamard H ^ -gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect “unitarity” by means of quantum process tomography, unveiling a process purity of 99%. Last, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e., azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation, and sensing schemes.