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arXiv:1905.00293 · Quantum Information and Computation

A thermal quantum classifier

Ufuk Korkmaz, Deniz Türkpençe, Tahir Çetin Akıncı, Cetin Akinci, Serhat Seker

Published Sep 1, 2020• 2 citations
arXivHTMLPDF

Abstract

We find that the additivity of quantum information channels enables one to introduce a quantum classifier or a quantum decision maker. Proper measurement and sensing of temperature are of central importance to the realization of nanoscale quantum devices. Minimal classifiers may constitute the basic units for the physical quantum neural networks. We introduce a binary temperature classifier quantum model that operates in a thermal environment. In the present study, first the mathematical model was introduced through a two-level quantum system weakly coupled to the thermal reservoirs and it was demonstrated that the model faithfully classifies the temperature information of the reservoirs in the thermal steady state limit. A physical model by superconducting circuits composed of transmon qubits was also suggested.

DOI
10.26421/qic20.11-12-4

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We find that the additivity of quantum information channels enables one to introduce a quantum classifier or a quantum decision maker. Proper measurement and sensing of temperature are of central importance to the realization of nanoscale quantum devices. Minimal classifiers may constitute the basic units for the physical quantum neural networks. We introduce a binary temperature classifier quantum model that operates in a thermal environment. In the present study, first the mathematical model was introduced through a two-level quantum system weakly coupled to the thermal reservoirs and it was demonstrated that the model faithfully classifies the temperature information of the reservoirs in the thermal steady state limit. A physical model by superconducting circuits composed of transmon qubits was also suggested.
In this work, we investigate the use of a quantum circuit as a binary classification model in the context of quantum machine learning. We call this model, binary quantum classifier. First, we describe fundamental concepts of quantum computing and introduce the computational tool used: Qibo, an open-source framework for efficient quantum simulations and quantum hardware control. Then, we describe how to design a binary quantum classifier for the classification of images and small arrays of variables by showing how to input data in the circuit, defining a quantum circuit model Ansatz with trainable parameters and a loss function, and implementing multiple minimizers. We test our quantum classifier with two data sets. The first one is the MNIST data set which is composed of handwritten digits (reduced to only handwritten zeros and handwritten ones for binary classification). We study the behavior of different minimizers by increasing the number of layers of the Ansatz. The second data set represents two different high energy collisions that can occur at colliders such as LHC (CERN). Due to in-time proton-proton interactions known as pile-up, we distinguish two different data sets: "without pile-up" and "with pile-up". These collisions can be represented by images of size 32x32 or by six high-level variables that we call features. By increasing the size of the training data set and the number of layers of the Ansatz, we search for the best minimizer. Splitting the data set in training set and test set, we compute: ROC curve, AUC score, confusion matrices and test set accuracy. For "with pile-up" images, we compare the results obtained with the quantum classifier with a small convolutional neural network. We conclude that is possible to build a binary quantum classifier with a quantum circuit and we highlight its performances and limitations in comparison with classical technologies.
We develop a physics-based model for classical computation based on autonomous quantum thermal machines. These machines consist of few interacting quantum bits (qubits) connected to several environments at different temperatures. Heat flows through the machine are here exploited for computing. The process starts by setting the temperatures of the environments according to the logical input. The machine evolves, eventually reaching a nonequilibrium steady state, from which the output of the computation can be determined via the temperature of an auxilliary finite-size reservoir. Such a machine, which we term a "thermodynamic neuron," can implement any linearly separable function, and we discuss explicitly the cases of NOT, 3-MAJORITY, and NOR gates. In turn, we show that a network of thermodynamic neurons can perform any desired function. We discuss the close connection between our model and artificial neurons (perceptrons) and argue that our model provides an alternative physics-based analog implementation of neural networks, and more generally a platform for thermodynamic computing.
We develop a physics-based model for classical computation based on autonomous quantum thermal machines. These machines consist of few interacting quantum bits (qubits) connected to several environments at different temperatures. Heat flows through the machine are here exploited for computing. The process starts by setting the temperatures of the environments according to the logical input. The machine evolves, eventually reaching a non-equilibrium steady state, from which the output of the computation can be determined via the temperature of an auxilliary finite-size reservoir. Such a machine, which we term a "thermodynamic neuron", can implement any linearly-separable function, and we discuss explicitly the cases of NOT, 3-majority and NOR gates. In turn, we show that a network of thermodynamic neurons can perform any desired function. We discuss the close connection between our model and artificial neurons (perceptrons), and argue that our model provides an alternative physics-based analogue implementation of neural networks, and more generally a platform for thermodynamic computing.
In this study, we show that as a result of weak interaction of different information environments structured with a single probe qubit, these environments can perform binary classification of the information they contain. In this way, we refer to these environments as quantum information baths because they consist of sequences of identical qubits in certain pure quantum states. A micro-maser like master equation has been developed to clearly describe the system dynamics analytically and the quantum states of different information reservoirs. The model can also be treated as a quantum neuron, due to the single-qubit probe that makes a binary decision depending on the reservoir parameters in its steady state. The numerical results of the repeated interaction process based on the divisibility and additivity of the quantum dynamic maps are compared with the analytical results. Besides being a single quantum classifier, the model we present can also serve as a basic unit of a quantum neural network within the framework of the dissipative model of quantum computing.
We report the realization of a versatile classifier based on the quantum mechanics of a single atom. The problem of classification has been extensively studied by the classical machine learning community, with plenty of proposed algorithms that have been refined over time. Quantum computation must necessarily develop quantum classifiers and benchmark them against their classical counterparts. It is not obvious how to make use of our increasing ability to precisely control and evolve a quantum state to solve this kind of problems, while there is only a limited number of strong theorems backing the quantum algorithms for classification. Here we show that both of these limitations can be successfully addressed by the implementation of a recently proposed data re-uploading algorithm in an ion trap based quantum processing unit. The quantum classifier is trained in two steps: first, the quantum circuit is fed with an optimal set of variational parameters found by classical simulation; then, the variational circuit is optimized by inspecting the parameter landscape with only the quantum processing unit. This second step provides a partial cancellation of the systematic errors inherent to the quantum device. The accuracy of our quantum supervised classifier is benchmarked on a variety of datasets, that imply, finding the separation of classes associated to regions in a plane in both binary and multi-class problems, as well as in higher-dimensional feature spaces. Our experiments show that a single-ion quantum classifier circuit made out of kkk gates is as powerful as a neural network with one intermediate hidden layer of kkk neurons.