Classification Of Quantum States Research Articles

Generalization in quantum machine learning from few training data

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as sqrt{T/N}. When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to sqrt{K/N}. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

VSQL: Variational Shadow Quantum Learning for Classification

Classification of quantum data is essential for quantum machine learning and near-term quantum technologies. In this paper, we propose a new hybrid quantum-classical framework for supervised quantum learning, which we call Variational Shadow Quantum Learning (VSQL). Our method in particular utilizes the classical shadows of quantum data, which fundamentally represent the side information of quantum data with respect to certain physical observables. Specifically, we first use variational shadow quantum circuits to extract classical features in a convolution way and then utilize a fully-connected neural network to complete the classification task. We show that this method could sharply reduce the number of parameters and thus better facilitate quantum circuit training. Simultaneously, less noise will be introduced since fewer quantum gates are employed in such shadow circuits. Moreover, we show that the Barren Plateau issue, a significant gradient vanishing problem in quantum machine learning, could be avoided in VSQL. Finally, we demonstrate the efficiency of VSQL in quantum classification via numerical experiments on the classification of quantum states and the recognition of multi-labeled handwritten digits. In particular, our VSQL approach outperforms existing variational quantum classifiers in the test accuracy in the binary case of handwritten digit recognition and notably requires much fewer parameters.

Experimental Machine Learning of Quantum States.

Quantum information technologies provide promising applications in communication and computation, while machine learning has become a powerful technique for extracting meaningful structures in "big data." A crossover between quantum information and machine learning represents a new interdisciplinary area stimulating progress in both fields. Traditionally, a quantum state is characterized by quantum-state tomography, which is a resource-consuming process when scaled up. Here we experimentally demonstrate a machine-learning approach to construct a quantum-state classifier for identifying the separability of quantum states. We show that it is possible to experimentally train an artificial neural network to efficiently learn and classify quantum states, without the need of obtaining the full information of the states. We also show how adding a hidden layer of neurons to the neural network can significantly boost the performance of the state classifier. These results shed new light on how classification of quantum states can be achieved with limited resources, and represent a step towards machine-learning-based applications in quantum information processing.

Preface to the special topic on topological insulators

The most important aspect of condensed matter physics in the last century has been the classification of quantum states in terms of spontaneous symmetry breaking. In 1980, the quantum Hall state—which is independent of material details and topologically different from the previously known states of matter— was discovered in the two-dimensional electron gas under an external magnetic field. Two years later, the fractional quantum Hall state was discovered in a similar two-dimensional system. The quantum Hall states belong to a topological class that has no spontaneously broken symmetry. The physical behaviors of the system depend only on its topology and not on its particular geometry. Very recently, a completely new class of states, called topological insulators, has emerged. Topological insulators have a bulk energy gap and gapless edge/surface states that are protected by the time-reversal symmetry and immune to impurities and geometric perturbations. To form such new states, the coupling between the spin and the orbital motion must be strong. Therefore, topological insulator states usually occur in a compound material that is composed of heavy elements. Because of the many exotic phenomena—including the quantum spin Hall effect, the quantum anomalous Hall effect, a magnetic monopole and Majorana fermions—that can exist in topological insulators, this new class of topological states has attracted increasing attention over the last seven years and has largely revolutionized modern condensed matter physics. We selected this particularly interesting area of topological insulators for our first issue ofNational Science Review.The issue contains a general review on topological phases in condensed matter physics by Shunqing Shen, and a review on the newly discovered quantized anomalous Hall effect by Ke He. The interesting story behind this discovery is presented in an interview to Xucun Ma. In a perspective article by Canhua Liu and Jinfeng Jia, they discuss methods to createMajorana fermions with topological insulators. Peizhe Tang and Wenhui Duan report their recent work on the quantum anomalous Hall effect in materials with in-plane magnetization, while Feng Liu and JianWu discuss new organic topological materials in two research highlight articles, respectively. In a perspective article, Kai Chang discusses topological insulating phases in commonly used semiconductors. As the guest editor of this special topic in the inaugural issue, I would like to take this opportunity to thank these authors for their generous contributions. The research of topological insulators is just at its very beginning. I believe further progress will be made in the near future and hope that the special topic can provide some useful information and promote research in this rapidly developing field. Last but not least, I would like to thank the editorial staff ofNational Natural Science for their sustained support during the preparation of this special issue.

A Note on Classification of Quantum States Under SLOCC

A Note on Classification of Quantum States Under SLOCC

QUANTUM MECHANICAL OBSERVERS AND TIME REPARAMETRIZATION SYMMETRY

We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their nonunitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.

Symmetry of the pentacene molecule and classification of electron states studied in the frame of group action on a set

Abstract Pentacene have recently become the subject of intense studies due to their physical properties which follow from the states of their outer-shell electrons that are able to take part in molecule bonding. The symmetry of these molecules provides the classification of quantum states according to the group theory method. In this paper, we apply a molecular state-space factorization scheme for the classification of pentacene molecules based on the structure of their electron states.

Symmetry and classification of electron states in polyacenes

Organic materials have been recently the object of the intense studies due to their opto-electronic properties which follow from the states of the outer-shell electrons, taking part in molecule bonding. The symmetry of molecules provides the classification of quantum states according to the group theory method. We apply molecular state space factorizaton scheme for the states structure classification of selected polyacenes.

A simple algorithm for the group theoretical classification of quantum states

Here we present a simple and easily handled algorithm for the group theoretical classification of quantum states that although, it is implicit in a general group theory formulation, it is not presented the way it is discussed here, and which facilitates its application by non-specialists. It consists in finding the minimal set of symmetry operations needed to identify unequivocally the symmetry for each state and a direct calculation of the character of the representation expanded by the vector state. The algorithm allows simple and fast calculations of the symmetry properties, even for large symmetry groups and systems with many degrees of freedom. In particular the occurrence of accidental degeneracy is distinguished clearly using this method. In order to illustrate the application of the method, we discuss the classification of the vibrational states for two different molecular systems.

Schrödinger Uncertainty Relations and Physical Features of Correlated-Coherent States

We show that the difference between the Schrodinger uncertainty relations (UR) and the Heisenberg UR is fundamental. We propose a modified version of stochastic mechanics that allows clearly demonstrating that the contributions from the anticommutator and the commutator to the Schrodinger UR are equally important. A classification of quantum states minimizing the Schrodinger UR at an arbitrary instant is proposed. We show that the correlation of the coordinate and momentum fluctuations in such correlated-coherent states (CCS) is largely determined by the contributions from not only the commutator but also the anticommutator of the corresponding operators. We demonstrate that the character of this correlation changes qualitatively in time from the antiphase correlation typical for the Heisenberg UR to the inphase correlation for which the contribution from the anticommutator is decisive. We comparatively analyze properties of a free microparticle and a quantum oscillator in CCS and show that the CCS correspond to traveling-standing de Broglie waves in both models.

Toward the Classification of Quantum States in the Hawking-Unruh Effect

Toward the Classification of Quantum States in the Hawking-Unruh Effect

Toward the Classification of Quantum States in the Hawking-Unruh Effect

Toward the Classification of Quantum States in the Hawking-Unruh Effect