Continuous-variable quantum neural networks

We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation. Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized model such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the Strawberry Fields software library. These experiments, including a classifier for fraud detection, a network which generates Tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks

A Scalable Training Strategy for Blind Multi-Distribution Noise Removal

Despite recent advances, developing general-purpose universal denoising and artifact-removal networks remains largely an open problem: Given fixed network weights, one inherently trades-off specialization at one task (e.g.,~removing Poisson noise) for performance at another (e.g.,~removing speckle noise). In addition, training such a network is challenging due to the curse of dimensionality: As one increases the dimensions of the specification-space (i.e.,~the number of parameters needed to describe the noise distribution) the number of unique specifications one needs to train for grows exponentially. Uniformly sampling this space will result in a network that does well at very challenging problem specifications but poorly at easy problem specifications, where even large errors will have a small effect on the overall mean squared error. In this work we propose training denoising networks using an adaptive-sampling/active-learning strategy. Our work improves upon a recently proposed universal denoiser training strategy by extending these results to higher dimensions and by incorporating a polynomial approximation of the true specification-loss landscape. This approximation allows us to reduce training times by almost two orders of magnitude. We test our method on simulated joint Poisson-Gaussian-Speckle noise and demonstrate that with our proposed training strategy, a single blind, generalist denoiser network can achieve peak signal-to-noise ratios within a uniform bound of specialized denoiser networks across a large range of operating conditions. We also capture a small dataset of images with varying amounts of joint Poisson-Gaussian-Speckle noise and demonstrate that a universal denoiser trained using our adaptive-sampling strategy outperforms uniformly trained baselines

Morphological Network: How Far Can We Go with Morphological Neurons?

In recent years, the idea of using morphological operations as networks has received much attention. Mathematical morphology provides very efficient and useful image processing and image analysis tools based on basic operators like dilation and erosion, defined in terms of kernels. Many other morphological operations are built up using the dilation and erosion operations. Although the learning of structuring elements such as dilation or erosion using the backpropagation algorithm is not new, the order and the way these morphological operations are used is not standard. In this paper, we have theoretically analyzed the use of morphological operations for processing 1D feature vectors and shown that this gets extended to the 2D case in a simple manner. Our theoretical results show that a morphological block represents a sum of hinge functions. Hinge functions are used in many places for classification and regression tasks (Breiman (1993)). We have also proved a universal approximation theorem -- a stack of two morphological blocks can approximate any continuous function over arbitrary compact sets. To experimentally validate the efficacy of this network in real-life applications, we have evaluated its performance on satellite image classification datasets since morphological operations are very sensitive to geometrical shapes and structures. We have also shown results on a few tasks like segmentation of blood vessels from fundus images, segmentation of lungs from chest x-ray and image dehazing. The results are encouraging and further establishes the potential of morphological networks.Comment: 35 pages, 19 figures, 7 table