We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space occurs through applying a low-depth quantum circuit with a tree tensor network (TTN) topology, which acts as an unsupervised feature extractor to identify the most relevant quantum states in a data-driven fashion. This unsupervised feature extractor then feeds a supervised linear classifier and encodes the output in a small-dimensional quantum register. In contrast to previous work on \emph{quantum-inspired} TTN classifiers, in which the embedding map and class decision weights did not map the data to well-defined quantum states, we present an approach that can be implemented on gate-based quantum computing devices. In particular, we identify an embedding map with accuracy similar to exponential machines (Novikov \emph{et al.}, arXiv:1605.03795), but which produces valid quantum states from classical data vectors, and utilize manifold-based gradient optimization schemes to produce isometric operations mapping quantum states to a register of qubits defining a class decision. We detail methods for efficiently obtaining one- and two-point correlation functions of the decision boundary vectors of the quantum model, which can be used for model interpretability, as well as methods for obtaining classifications from partial data vectors. Further, we show that the use of isometric tensors can significantly aid in the human interpretability of the correlation functions extracted from the decision weights, and may produce models that are less susceptible to adversarial perturbations. We demonstrate our methodologies in applications utilizing the MNIST handwritten digit dataset and a multivariate timeseries dataset of human activity recognition.
We propose a new training algorithm for supervised quantum classifiers. Here, we have harnessed the property of quantum entanglement to build a model that can simultaneously manipulate multiple training samples along with their labels. Subsequently a Bell-inequality based cost function is constructed, that can encode errors from multiple samples, simultaneously, in a way that is not possible by any classical means. We show that upon minimizing this cost function one can achieve successful classification in benchmark datasets. The results presented in this paper are for binary classification pr…
We present quantum-inspired algorithms for classification tasks inspired by the problem of quantum state discrimination. By construction, these algorithms can perform multiclass classification, prevent overfitting, and generate probability outputs. While they could be implemented on a quantum computer, we focus here on classical implementations of such algorithms. The training of these classifiers involves Semi-Definite Programming. We also present a relaxation of these classifiers that utilizes Linear Programming (but that can no longer be interpreted as a quantum measurement). Additionally, …
We face the problem of pattern classification by proposing a quantum-inspired version of the widely used minimum distance classifier (i.e. the Nearest Mean Classifier (NMC)) already introduced in [31,33,28,27] and by applying this quantum-inspired classifier in a biomedical context. In particular, we show and compare the NMC and our quantum model performance to solve a problem related to classify the probability of survival for patients affected by idiopathic pulmonary fibrosis (IPF).
Institute of Financial Analysis（金融分析研究所）；Université de Neuchâtel（纳沙泰尔大学）；Università degli Studi di Milano（米兰大学）
This paper presents Sparse Tensor Classifier (STC), a supervised classification algorithm for categorical data inspired by the notion of superposition of states in quantum physics. By regarding an observation as a superposition of features, we introduce the concept of wave-particle duality in machine learning and propose a generalized framework that unifies the classical and the quantum probability. We show that STC possesses a wide range of desirable properties not available in most other machine learning methods but it is at the same time exceptionally easy to comprehend and use. Empirical e…
Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this "quantum fact of life," we propose a novel method for shortcuts to adiabaticity which enables the system to evolve through the adiabatic manifold at all times, solely by controlling the environment. As main results, we construct the unique form of the driving on the environment that enables such dynamics, for a family of composite states of arbitrary dimension. We compare the cost of this environment-assisted technique with that of counterdiabatic driving, and we illustrate our results for a two-qubit model.
The high energy transfer efficiency of photosynthetic complexes has been a topic of research across many disciplines. Several attempts have been made in order to explain this energy transfer enhancement in terms of quantum mechanical resources such as energetic and vibration coherence and constructive effects of environmental noise. The developments in this line of research have inspired various biomimetic works aiming to use the underlying mechanisms in biological light harvesting complexes for improvement of synthetic systems. In this article we explore the effect of an auxiliary hierarchica…
A single qubit provides sufficient computational capabilities to construct a universal quantum classifier when assisted with a classical subroutine. This fact may be surprising since a single qubit only offers a simple superposition of two states and single-qubit gates only make a rotation in the Bloch sphere. The key ingredient to circumvent these limitations is to allow for multiple data re-uploading. A quantum circuit can then be organized as a series of data re-uploading and single-qubit processing units. Furthermore, both data re-uploading and measurements can accommodate multiple dimensi…
We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, result…
AutoQML: Automatic Generation and Training of Robust Quantum-Inspired Classifiers by Using Genetic Algorithms on Grayscale Images
Consejo Superior de Investigaciones Científicas（西班牙国家研究委员会）；Centre for Automation and Robotics（自动化与机器人中心）；Universidad Politécnica de Madrid（马德里理工大学）；Instituto de Física Fundamental（基础物理研究所）
Pretty Good Measurement for Radiomics: A Quantum-Inspired Multi-Class Classifier for Lung Cancer Subtyping and Prostate Cancer Risk Stratification
Università degli Studi di Cagliari（卡利亚里大学）；Institute of Bioimaging and Complex Biological Systems - National Research Council (IBSBC - CNR)（生物成像与复杂生物系统研究所 - 国家研究委员会）；National Laboratory of South, National Institute for Nuclear Physics(LNS-INFN)（南部国家实验室，核物理研究所）
One of the most promising areas of research to obtain practical advantage is Quantum Machine Learning which was born as a result of cross-fertilisation of ideas between Quantum Computing and Classical Machine Learning. In this paper, we apply Quantum Machine Learning (QML) frameworks to improve binary classification models for noisy datasets which are prevalent in financial datasets. The metric we use for assessing the performance of our quantum classifiers is the area under the receiver operating characteristic curve (ROC/AUC). By combining such approaches as hybrid-neural networks, parametri…
Institute for Computer Science and Control (SZTAKI), Eötvös Loránd Research Network (ELKH)（厄特沃什·洛兰德研究网络（ELKH）计算机科学与控制研究所（SZTAKI））；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
Building on the quantum ensemble based classifier algorithm of Schuld and Petruccione [arXiv:1704.02146v1], we devise equivalent classical algorithms which show that this quantum ensemble method does not have advantage over classical algorithms. Essentially, we simplify their algorithm until it is intuitive to come up with an equivalent classical version. One of the classical algorithms is extremely simple and runs in constant time for each input to be classified. We further develop the idea and, as the main contribution of the paper, we propose methods inspired by combining the quantum ensemb…
Ultra-low latency quantum-inspired machine learning predictors implemented on FPGA
Istituto Nazionale di Fisica Nucleare (INFN)（国家核物理研究所）；Dipartimendo di Fisica e Astronomia (DFA)（物理与天文学系）；University of Padua（帕多瓦大学）；Dipartimendo di Ingegneria dell’Informazione (DEI)（信息工程系）；Dipartimendo di Ingegneria Industriale (DII)（工业工程系）；Padua Quantum Technology Research Center（帕多瓦量子技术研究中心）；Tensor AI Solutions GmbH（张量人工智能解决方案有限公司）
