We demonstrate a new method for optimal bidirectional control of complex physical systems. Employing a set of collaborative neural networks, our approach exhibits unprecedented accuracy, even at the single-photon level.
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.
Obtaining accurate solutions to many-electron quantum systems is of critical importance, in principle, such solutions allow computing most of possible chemical and physical properties from first principles. Exact solutions require utilizing exponentially scaling algorithms, which are not practical for large systems. Neural networks provide a new approach to approximating the solution while keeping a high level of accuracy. In this work, we explore a novel method of optimizing neural network wavefunctions by employing Evolution Strategies (ES) within a Variational Monte Carlo (VMC) framework. This allows us to more robustly find solutions while keeping a small number of parameters, making it an efficient alternative to traditional methods.
This paper explores the potential of quantum-inspired neural networks (QINNs) for solving optimal control problems within stochastic systems. Traditional optimal control methods often struggle with the inherent uncertainty and noise present in real-world systems. We propose a novel neural network architecture that mimics key quantum phenomena – interference and superposition – to enhance its ability to navigate these challenges. The QINN architecture leverages probabilistic outputs and a layered structure designed to represent quantum states. We formulate the optimal control problem as a stochastic differential equation (SDE) and employ the QINN to approximate the optimal control trajectory. The core idea is to treat the control action as a superposition of possible actions, where quantum interference guides the system towards the most probable optimal solution. The performance of the QINN is evaluated through simulations, demonstrating its potential to outperform classical optimal control techniques, particularly in scenarios with high levels of stochastic disturbance. The key contribution of this work lies in the application of quantum-inspired principles to control system design, offering a new avenue for addressing complex, uncertain control problems. The ultimate goal is to develop a more robust and efficient control strategy by harnessing the principles of quantum mechanics.