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arXiv:1703.10793 · Europhysics Letters (EPL)

Implementing a distance-based classifier with a quantum interference circuit

M. Schuld, Mark Fingerhuth, Francesco Petruccione

Published Sep 1, 2017• 285 citations
arXivHTMLPDF

Abstract

Lately, much attention has been given to quantum algorithms that solve pattern recognition tasks in machine learning. Many of these quantum machine learning algorithms try to implement classical models on large-scale universal quantum computers that have access to non-trivial subroutines such as Hamiltonian simulation, amplitude amplification and phase estimation. We approach the problem from the opposite direction and analyse a distance-based classifier that is realised by a simple quantum interference circuit. After state preparation, the circuit only consists of a Hadamard gate as well as two single-qubit measurements, and computes the distance between data points in quantum parallel. We demonstrate the proof of principle using the IBM Quantum Experience and analyse the performance of the classifier with numerical simulations.

DOI
10.1209/0295-5075/119/60002

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Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which - similar to Bayesian learning - the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which -- similar to Bayesian learning -- the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.
The advancement of technology in Quantum Computing has brought possibilities for the execution of algorithms in real quantum devices. However, the existing errors in the current quantum hardware and the low number of available qubits make it necessary to use solutions that use fewer qubits and fewer operations, mitigating such obstacles. Hadamard Classifier (HC) is a distance-based quantum machine learning model for pattern recognition. We present a new classifier based on HC named Quantum One-class Classifier (QOCC) that consists of a minimal quantum machine learning model with fewer operations and qubits, thus being able to mitigate errors from NISQ (Noisy Intermediate-Scale Quantum) computers. Experimental results were obtained by running the proposed classifier on a quantum device and show that QOCC has advantages over HC.
Today computers are used to store data in memory and then process them. In our big data era, we are facing the challenge of storing and processing the data simply due to their fast ever growing size. Quantum computation offers solutions to these two prominent issues quantum mechanically and beautifully. Through careful design to employ superposition, entanglement, and interference of quantum states, a quantum algorithm can allow a quantum computer to store datasets of exponentially large size as linear size and then process them in parallel. Quantum computing has found its way in the world of machine learning where new ideas and approaches are in great need as the classical computers have reached their capacity and the demand for processing big data grows much faster than the computing power the classical computers can provide today. Nearest neighbor algorithms are simple, robust, and versatile supervised machine learning algorithms, which store all training data points as their learned “model” and make the prediction of a new test data point by computing the distances between the query point and all the training data points. Quantum counterparts of these classical algorithms provide efficient and elegant ways to deal with the two major issues of storing data in memory and computing the distances. The purpose of our study is to select two similar quantum nearest neighbor algorithms and use a simple dataset to give insight into how they work, highlight their quantum nature, and compare their performances on IBM’s quantum simulator.
Abstract Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by engineering the quantum interference effect to carry out the kernel evaluation in parallel. For practical applications of these quantum machine learning methods, an important issue is to minimize the size of quantum circuits. We present the simplest quantum circuit for constructing a kernel-based binary classifier. This is achieved by generalizing the interference circuit to encode data labels in the relative phases of the quantum state and by introducing compact amplitude encoding, which encodes two training data vectors into one quantum register. When compared to the simplest known quantum binary classifier, the number of qubits is reduced by two and the number of steps is reduced linearly with respect to the number of training data. The two-qubit measurement with post-selection required in the previous method is simplified to single-qubit measurement. Furthermore, the final quantum state has a smaller amount of entanglement than that of the previous method, which advocates the cost-effectiveness of our method. Our design also provides a straightforward way to handle an imbalanced data set, which is often encountered in many machine learning problems.