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arXiv:2411.16410 · Light Science & Applications

Ultrahigh-fidelity spatial mode quantum gates in high-dimensional space by diffractive deep neural networks

Qianke Wang, Jun Liu, Dawei Lyu, Jian Wang

Published Jan 5, 2024• 38 citations
arXivHTMLPDF

Abstract

Abstract While the spatial mode of photons is widely used in quantum cryptography, its potential for quantum computation remains largely unexplored. Here, we showcase the use of the multi-dimensional spatial mode of photons to construct a series of high-dimensional quantum gates, achieved through the use of diffractive deep neural networks (D2NNs). Notably, our gates demonstrate high fidelity of up to 99.6(2)%, as characterized by quantum process tomography. Our experimental implementation of these gates involves a programmable array of phase layers in a compact and scalable device, capable of performing complex operations or even quantum circuits. We also demonstrate the efficacy of the D2NN gates by successfully implementing the Deutsch algorithm and propose an intelligent deployment protocol that involves self-configuration and self-optimization. Moreover, we conduct a comparative analysis of the D2NN gate’s performance to the wave-front matching approach. Overall, our work opens a door for designing specific quantum gates using deep learning, with the potential for reliable execution of quantum computation.

DOI
10.1038/s41377-023-01336-7

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Abstract While the spatial mode of photons is widely used in quantum cryptography, its potential for quantum computation remains largely unexplored. Here, we showcase the use of the multi-dimensional spatial mode of photons to construct a series of high-dimensional quantum gates, achieved through the use of diffractive deep neural networks (D2NNs). Notably, our gates demonstrate high fidelity of up to 99.6(2)%, as characterized by quantum process tomography. Our experimental implementation of these gates involves a programmable array of phase layers in a compact and scalable device, capable of performing complex operations or even quantum circuits. We also demonstrate the efficacy of the D2NN gates by successfully implementing the Deutsch algorithm and propose an intelligent deployment protocol that involves self-configuration and self-optimization. Moreover, we conduct a comparative analysis of the D2NN gate’s performance to the wave-front matching approach. Overall, our work opens a door for designing specific quantum gates using deep learning, with the potential for reliable execution of quantum computation.
Spatial modes of photons offer a rich encoding resource for high-dimensional quantum information processing. Multiplane light conversion (MPLC) enables spatial mode transformation and is applicable in both classical and quantum optics. Here, we demonstrate a polymer-based MPLC device, fabricated via femtosecond laser three-dimensional printing, that realizes high-dimensional quantum logic gates in an ultracompact format. Specifically, we design a three-dimensional Hadamard gate by training a diffractive neural network to generate the required phase distribution. The device is evaluated through quantum process tomography at the single-photon level within spatial modes, achieving a fidelity of 90%. Compared to traditional spatial light modulator-based implementations, our approach integrates spatial mode manipulation into a miniaturized photonic platform. These results highlight the feasibility of polymer-based MPLC for compact quantum logic and open possibilities for scalable, high-dimensional quantum information processing on integrated photonic chips.
Controlled quantum gates play a crucial role in enabling quantum universal operations by facilitating interactions between qubits. Direct implementation of three-qubit gates simplifies the design of quantum circuits, thereby being conducive to performing complex quantum algorithms. Here, we propose and present an experimental demonstration of a quantum Toffoli gate fully exploiting the polarization and orbital angular momentum of a single photon. The Toffoli gate is implemented using the polarized diffractive neural networks scheme, achieving a mean truth table visibility of 97.27±0.20%. We characterize the gate's performance through quantum state tomography on 216 different input states and quantum process tomography, which yields a process fidelity of 94.05±0.02%. Our method offers a novel approach for realizing the Toffoli gate without requiring exponential optical elements while maintaining extensibility to the implementation of other three-qubit gates.
Abstract In this paper, a novel optical logic operator based on the multifunctional metasurface driven by all‐optical diffractive neural network is reported, which can perform four principal quantum logic operations (Pauli‐X, Pauli‐Y, Pauli‐Z, and Hadamard gates). The two ground states and are characterized by two orthogonal linear polarization states. The proposed spatial‐ and polarization‐multiplexed all‐optical diffractive neural network only contains a hidden layer physically mapped as a metasurface with simple and compact unit cells, which dramatically reduces the volume and computing resources required for the system. The designed optical quantum operator is proven to achieve high fidelities for all four quantum logical gates, up to 99.96% numerically and 99.88% experimentally. The solution will facilitate the construction of large‐scale optical quantum computing systems and scalable optical quantum devices.
Structure photons invoke interesting fundamental properties and enable novel applications, e.g. their use as high-dimensional quantum states, which are known to be beneficial in various quantum information tasks. However, to use their full potential the ability to perform any unitary operations is indispensable. Here, we present a scheme to perform arbitrary unitary operation for all transverse spatial modes, i.e. a so-called multiport for high-dimensional quantum states. We realize it by using multiple consecutive phase modulations, which are designed by wave front matching techniques. At first, we perform near-perfect measurements of full-field modes, i.e. modes with an azimuthal and radial structure [1]. Our method only requires three consecutive phase modulations followed by a single mode fiber and is, in principle, error-free and lossless. We achieve an average error of 4.2% for a set of 9 different full-field Laguerre-Gauss and Hermite-Gauss modes with an efficiency of up to 70%. We further demon-strate its potential in a quantum cryptography protocol and in high-dimensional quantum state tomography. We then use the multiport to implement high-dimensional quantum gates [2], such as cyclic and quantum Fourier transformations, known as Pauli X-gates and Hadamard H-gates, respectively. We achieve an aver-age visibility of more than 90% for dimensions up to 5 and obtain a process purity of 99% by means of a full quantum process tomography. We also 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. Using more efficient phase modulations will pave the way to novel multi-particle high-dimensional quantum information experiments. [1] M. Hiekkamäki, S. Prabhakar, R. Fickler, Near-perfect measuring of full-field transverse-spatial modes of light, arXiv:1909.01685 [2] F. Brandt, M. Hiekkamäki, F. Bouchard, M. Huber, R. Fickler, High-dimensional quantum gates using full-field spatial modes of photons, arXiv:1907.13002
The growing computational demands of classical neural networks have intensified the search for energy-efficient and powerful computational alternatives. Quantum neural networks (QNNs) implemented on integrated photonic platforms offer a compelling avenue, offering exceptional computational power enhancements, with inherent programmability and scalability of integrated architectures. A critical challenge, however, is implementing the fundamental non-unitary and nonlinear activation function of QNNs within a linear quantum photonic system. Existing strategies, such as the adding ancillary qubits and measurement-based feedback or forward are constrained by high qubit resource costs, overhead devices, and poor cascadability. Here, we propose a novel deep photonic QNN with an expanded computational Hilbert space via input replication and mode expansion, which enables the realization of effective non-unitary and nonlinear activation on a linear programmable quantum photonic chip. This approach eliminates the need for physical ancillary qubits, measurement-induced qubit consumption and the measurement device burden, thereby significantly reduce resource costs. The fabricated chip integrates four high-quality entanglement sources and a programmable high-dimensional interferometric network, enabling a two-hidden-layer QNN that exhibits dimension-enhanced expressivity over the existing QNN architectures. We demonstrate its capabilities across diverse tasks, including nonlinear classification, image generation, and quantum Gibbs state preparation. This work establishes a scalable and efficient architecture toward practical quantum deep learning systems capable of tackling problems beyond the reach of classical computation.