Continuous-variable quantum neural networks Killoran, Nathan; Bromley, Thomas R.; Arrazola, Juan Miguel ...
Physical review research,
10/2019, Letnik:
1, Številka:
3
Journal Article
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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 models 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.
We introduce an exact classical algorithm for simulating Gaussian boson sampling (GBS). The complexity of the algorithm is exponential in the number of photons detected, which is itself a random ...variable. For a fixed number of modes, the complexity is in fact equivalent to that of calculating output probabilities, up to constant prefactors. The simulation algorithm can be extended to other models such as GBS with threshold detectors, GBS with displacements, and sampling linear combinations of Gaussian states. In the specific case of encoding non-negative matrices into a GBS device, our method leads to an approximate sampling algorithm with polynomial runtime. We implement the algorithm, making the code publicly available as part of Xanadu's The Walrus library and benchmark its performance on GBS with random Haar interferometers and with encoded Erdős-Renyi graphs.
We gather and examine in detail gate decomposition techniques for continuous-variable quantum computers and also introduce some new techniques which expand on these methods. Both exact and ...approximate decomposition methods are studied and gate counts are compared for some common operations. While each having distinct advantages, we find that exact decompositions have lower gate counts whereas approximate techniques can cover decompositions for all continuous-variable operations but require significant circuit depth for a modest precision.
We study the effects of time ordering in photon generation processes such as spontaneous parametric down-conversion (SPDC) and four wave mixing (SFWM). The results presented here are used to ...construct an intuitive picture that allows us to predict when time-ordering effects significantly modify the joint spectral amplitude (JSA) of the photons generated in SPDC and SFWM. These effects become important only when the photons being generated lie with the pump beam that travels through the nonlinear material for a significant amount of time. Thus sources of spectrally separable photons are ideal candidates for the observation of modifications of the JSA due to time ordering.
Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite ...this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We provide evidence for the hardness of GBS, comparable to the strongest theoretical proposals for QCA. We also propose a QCA architecture we call high-dimensional GBS, which is programmable and can be implemented with low loss using few optical components. We show that particular algorithms for simulating GBS are outperformed by high-dimensional GBS experiments at modest system sizes. This work thus opens the path to demonstrating QCA with programmable photonic processors.
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