Abstract
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.
Highlights
After many years of scientific development, quantum computers are beginning to move out of the laboratory and into the mainstream
II, we review the key concepts from deep learning and from quantum computing which set up the remainder of the paper
We have presented a quantum neural network architecture which leverages the continuous-variable formalism of quantum computing, and explored it in detail through both theoretical exposition and numerical experiments
Summary
After many years of scientific development, quantum computers are beginning to move out of the laboratory and into the mainstream. On the classical computing side, there has recently been a renaissance in machine learning techniques based on neural networks, forming the new field of deep learning [14,15,16] This breakthrough is being fueled by a number of technical factors, including new software libraries [17,18,19,20,21] and powerful special-purpose computational hardware [22,23]. To make this work more accessible to practitioners from diverse backgrounds, we will defer the more technical points to later sections Both deep learning and CV quantum computation are rich fields; further details can be found in various review papers and textbooks [14,16,40,47,48,49]. For an input vector x ∈ Rn, a single layer L : Rn → Rm performs the transformation
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