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Quantum 2.0 Conference and Exhibition

Quantum state preparation and measurement using liquid crystals and deep learning

Martin Bielak, Dominik Vašinka, Robert Stárek, Michal Mičuda, Miroslav Ježek

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We report fast estimation of single and multi-mode polarization states at an unprecedented fidelity level of 0.9996(4) and deep learning preparation of arbitrary polarization-encoded qubits with 0.998(6) fidelity using twisted nematic liquid-crystals.
DOI
10.1364/quantum.2022.qth3b.3

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Generation of particular polarization states of light, encoding information in polarization degree of freedom, and efficient measurement of unknown polarization are the key tasks in optical metrology, optical communications, polarization-sensitive imaging, and photonic information processing. Liquid crystal devices have proved to be indispensable for these tasks, though their limited precision and the requirement of a custom design impose a limit of practical applicability. Here we report fast preparation and detection of polarization states with unprecedented accuracy using liquid-crystal cells extracted from common twisted nematic liquid-crystal displays. To verify the performance of the device we use it to prepare dozens of polarization states with average fidelity 0.999(1) and average angle deviation 0.5(3) deg. Using four-projection minimum tomography as well as six-projection Pauli measurement, we measure polarization states employing the reported device with the average fidelity of 0.999(1). Polarization measurement data are processed by the maximum likelihood method to reach a valid estimate of the polarization state. In addition to the application in classical polarimetry, we also employ the reported liquid-crystal device for full tomographic characterization of a three-mode Greenberger-Horne-Zeilinger entangled state produced by a photonic quantum processor.
The polarization of light is critical in various applications, including quantum communication, where the photon polarization encoding a qubit can undergo uncontrolled changes when transmitted through optical fibers. Bends in the fiber, internal and external stresses, and environmental factors cause these polarization changes, which lead to errors and therein limit the range of quantum communication. To prevent this, we present a fast and automated method for polarization compensation using liquid crystals. This approach combines polarimetry based on a rotating quarter-waveplate with high-speed control of the liquid-crystal cell, offering high-fidelity compensation suitable for diverse applications. Our method directly solves for the compensation parameters, avoiding reliance on stochastic approaches or cryptographic metrics. Experimental results demonstrate that our method achieves over 99% fidelity within an average of fewer than six iterations, with further fine-tuning to reach above 99.5% fidelity, providing a robust solution for maintaining precise polarization states in optical systems.
Accurate control of light polarization represents a core building block in polarization metrology, imaging, and optical and quantum communications. Voltage-controlled liquid crystals offer an efficient way of polarization transformation. However, common twisted nematic liquid crystals are notorious for lacking an accurate theoretical model linking control voltages and output polarization. An inverse model, which would predict control voltages required to prepare a target polarization, is even more challenging. Here we report both the direct and inverse models based on deep neural networks, radial basis functions, and linear interpolation. We present an inverse--direct compound model solving the problem of control voltages ambiguity. We demonstrate an order of magnitude improvement in accuracy using deep learning compared to the radial basis function method and 2 orders of magnitude improvement compared to the linear interpolation. Errors of the deep neural network model also decrease faster than the other methods with an increasing number of training data. The best direct and inverse models reach average infidelities of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, respectively, which are accuracy levels not reported yet. Furthermore, we demonstrate local and remote preparation of an arbitrary single-photon polarization state using deep learning models. The results will impact the application of twisted-nematic liquid crystals, increasing their control accuracy across the board. The presented bidirectional learning can be used for optimal classical control of complex photonic devices and quantum circuits beyond interpolation.