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Register a new userQuantum autoencoders to denoise quantum data
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Entangled states are an important resource for quantum computation, communication, metrology, and the simulation of many-body systems. However, noise limits the experimental preparation of such states. Classical data can be efficiently denoised by autoencoders---neural networks trained in unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger states subject to spin-flip errors and random unitary noise. Various emergent quantum technologies could benefit from the proposed unsupervised quantum neural networks.
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We implement a Quantum Autoencoder (QAE) as a quantum circuit capable of correcting Greenberger-Horne-Zeilinger (GHZ) states subject to various noisy quantum channels : the bit-flip channel and the more general quantum depolarizing channel. The QAE shows particularly interesting results, as it enables to perform an almost perfect reconstruction of noisy states, but can also, more surprisingly, act as a generative model to create noise-free GHZ states. Finally, we detail a useful application of QAEs : Quantum Secret Sharing (QSS). We analyze how noise corrupts QSS, causing it to fail, and show how the QAE allows the QSS protocol to succeed even in the presence of noise.
Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a new representation of states based on variational autoencoders. Variational autoencoders are a type of generative model in the form of a neural network. We probe the power of this representation by encoding probability distributions associated with states from different classes. Our simulations show that deep networks give a better representation for states that are hard to sample from, while providing no benefit for random states. This suggests that the probability distributions associated to hard quantum states might have a compositional structure that can be exploited by layered neural networks. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterising states of the size expected in first generation quantum hardware.
Quantum machine learning (QML) has emerged as a promising field that leans on the developments in quantum computing to explore large complex machine learning problems. Recently, some purely quantum machine learning models were proposed such as the quantum convolutional neural networks (QCNN) to perform classification on quantum data. However, all of the existing QML models rely on centralized solutions that cannot scale well for large-scale and distributed quantum networks. Hence, it is apropos to consider more practical quantum federated learning (QFL) solutions tailored towards emerging quantum network architectures. Indeed, developing QFL frameworks for quantum networks is critical given the fragile nature of computing qubits and the difficulty of transferring them. On top of its practical momentousness, QFL allows for distributed quantum learning by leveraging existing wireless communication infrastructure. This paper proposes the first fully quantum federated learning framework that can operate over quantum data and, thus, share the learning of quantum circuit parameters in a decentralized manner. First, given the lack of existing quantum federated datasets in the literature, the proposed framework begins by generating the first quantum federated dataset, with a hierarchical data format, for distributed quantum networks. Then, clients sharing QCNN models are fed with the quantum data to perform a classification task. Subsequently, the server aggregates the learnable quantum circuit parameters from clients and performs federated averaging. Extensive experiments are conducted to evaluate and validate the effectiveness of the proposed QFL solution. This work is the first to combine Googles TensorFlow Federated and TensorFlow Quantum in a practical implementation.
We develop a new framework that extends the quantum walk framework of Magniez, Nayak, Roland, and Santha, by utilizing the idea of quantum data structures to construct an efficient method of nesting quantum walks. Surprisingly, only classical data structures were considered before for searching via quantum walks. The recently proposed learning graph framework of Belovs has yielded improved upper bounds for several problems, including triangle finding and more general subgraph detection. We exhibit the power of our framework by giving a simple explicit constructions that reproduce both the $O(n^{35/27})$ and $O(n^{9/7})$ learning graph upper bounds (up to logarithmic factors) for triangle finding, and discuss how other known upper bounds in the original learning graph framework can be converted to algorithms in our framework. We hope that the ease of use of this framework will lead to the discovery of new upper bounds.
Distantly-labeled data can be used to scale up training of statistical models, but it is typically noisy and that noise can vary with the distant labeling technique. In this work, we propose a two-stage procedure for handling this type of data: denoise it with a learned model, then train our final model on clean and denoised distant data with standard supervised training. Our denoising approach consists of two parts. First, a filtering function discards examples from the distantly labeled data that are wholly unusable. Second, a relabeling function repairs noisy labels for the retained examples. Each of these components is a model trained on synthetically-noised examples generated from a small manually-labeled set. We investigate this approach on the ultra-fine entity typing task of Choi et al. (2018). Our baseline model is an extension of their model with pre-trained ELMo representations, which already achieves state-of-the-art performance. Adding distant data that has been denoised with our learned models gives further performance gains over this base model, outperforming models trained on raw distant data or heuristically-denoised distant data.
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