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arXiv:1907.08267

Implementation of a Hamming-Distance-Like Genomic Quantum Classifier Using Inner Products on IBMQX4 and IBMQX16

Kunal Kathuria, Aakrosh Ratan, Michael J. McConnell, Stefan Bekiranov

Published Jul 18, 2019• 0 citations
arXivHTMLPDF

Abstract

Motivated by the problem of classifying individuals with a disease versus controls using functional genomic attributes as input, we encode the input as a string of 1s (presence) or 0s (absence) of the genomic attribute across the genome. Blocks of physical regions in the subdivided genome serve as the feature dimensions, which takes full advantage of remaining in the computational basis of a quantum computer. Given that a natural distance between two binary strings is the Hamming distance and that this distance shares properties with an inner product between qubits, we developed two Hamming-distance-like classifiers which apply two different kinds of inner products ("active" and "symmetric") to directly and efficiently classify a test input into either of two training classes. To account for multiple disease and control samples, each train class can be composed of an arbitrary number of bit strings (i.e., number of samples) that can be compressed into one input string per class. Thus, our circuits require the same number of qubits regardless of the number of training samples. These algorithms, which implement a training bisection decision plane, were simulated and implemented on IBMQX4 and IBMQX16. The latter allowed for encoding of $64$ training features across the genome for $2$ (disease and control) training classes.

DOI
10.48550/arxiv.1907.08267

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Motivated by the problem of classifying individuals with a disease versus controls using functional genomic attributes as input, we encode the input as a string of 1s (presence) or 0s (absence) of the genomic attribute across the genome. Blocks of physical regions in the subdivided genome serve as the feature dimensions, which takes full advantage of remaining in the computational basis of a quantum computer. Given that a natural distance between two binary strings is the Hamming distance and that this distance shares properties with an inner product between qubits, we developed two Hamming-distance-like classifiers which apply two different kinds of inner products ("active" and "symmetric") to directly and efficiently classify a test input into either of two training classes. To account for multiple disease and control samples, each train class can be composed of an arbitrary number of bit strings (i.e., number of samples) that can be compressed into one input string per class. Thus, our circuits require the same number of qubits regardless of the number of training samples. These algorithms, which implement a training bisection decision plane, were simulated and implemented on IBMQX4 and IBMQX16. The latter allowed for encoding of 646464 training features across the genome for 222 (disease and control) training classes.
Abstract Motivated by the problem of classifying individuals with a disease versus controls using a functional genomic attribute as input, we present relatively efficient general purpose inner product–based kernel classifiers to classify the test as a normal or disease sample. We encode each training sample as a string of 1 s (presence) and 0 s (absence) representing the attribute’s existence across ordered physical blocks of the subdivided genome. Having binary-valued features allows for highly efficient data encoding in the computational basis for classifiers relying on binary operations. Given that a natural distance between binary strings is Hamming distance, which shares properties with bit-string inner products, our two classifiers apply different inner product measures for classification. The active inner product (AIP) is a direct dot product–based classifier whereas the symmetric inner product (SIP) classifies upon scoring correspondingly matching genomic attributes. SIP is a strongly Hamming distance–based classifier generally applicable to binary attribute-matching problems whereas AIP has general applications as a simple dot product–based classifier. The classifiers implement an inner product betweenN= 2ndimension test and train vectors usingnFredkin gates while the training sets are respectively entangled with the class-label qubit, without use of an ancilla. Moreover, each training class can be composed of an arbitrary numbermof samples that can be classically summed into one input string to effectively execute all test–train inner products simultaneously. Thus, our circuits require the same number of qubits for any number of training samples and are O(log⁡N)O(\log {N})O(logN) O(logN) in gate complexity after the states are prepared. Our classifiers were implemented on ibmqx2 (IBM-Q-team 2019b) and ibmq_16_melbourne (IBM-Q-team 2019a). The latter allowed encoding of 64 training features across the genome.
Machine learning is a powerful tool which, when given the availability of comprehensive datasets, required training iterations and the necessary resources to support them, can achieve impressive results in a variety of classification tasks. In this paper, we put forward a quantum alternative for users that do not posses the ability to gather and store large amounts of data to be used subsequently in lengthy training iterations. A light-weight probabilistic quantum binary classifier can be built by encoding the two chosen class representatives (images) into quantum vectors, such that a Principal Component decomposition can express the differences between them only along one dimension (basis vector). A standard measurement in the computational basis will then project any transformed input sample along one of the two classes. The classifier accepts quantum representations of images as input, which require exponentially fewer number of quantum bits compared with the number of classical bits used to store an image. The technique is illustrated on a "proof of concept" example, in which a quantum character recognizer is built to label any input sample image as either letter {\bf A} or {\bf P}. The quantum classifier can be tuned to "favor" any of the two classes and the measurement probabilities follow closely how far an input sample is from the two class representatives. Despite its relative simplicity, the quantum classifier can distinguish between the standard letter {\bf A} and the standard letter {\bf P} with 98%98\%98% accuracy. In principle, the procedure can be applied to any image classification task, including gray-scale and color images, as well as classification problems in which an input sample is characterized by a collection of properties given by their values.
Quantum classifiers provide sophisticated embeddings of input data in Hilbert space promising quantum advantage. The advantage stems from quantum feature maps encoding the inputs into quantum states with variational quantum circuits. A recent work shows how to map discrete features with fewer quantum bits using Quantum Random Access Coding (QRAC) to encode binary strings into quantum states. We propose a new method to embed discrete features with trainable quantum circuits by combining QRAC and a recently proposed strategy for training quantum feature map called quantum metric learning. The proposed trainable embedding requires not only as few qubits as QRAC but also overcomes the limitations of QRAC to classify inputs whose classes are based on hard Boolean functions. We numerically demonstrate its use in variational quantum classifiers to achieve better performances to classify real-world datasets, and thus its possibility to use near-term quantum computers for machine learning.
Machine learning (ML) classification tasks can be carried out on a quantum computer (QC) using probabilistic quantum memory (PQM) and its extension, parametric PQM (P-PQM), by calculating the Hamming distance between an input pattern and a database ofrrrpatterns containingzzzfeatures withaaadistinct attributes. For PQM and P-PQM to correctly compute the Hamming distance, the feature must be encoded using one-hot encoding, which is memory intensive for multiattribute datasets witha>2a>2a>2. We can represent multiattribute data more compactly by replacing one-hot encoding with label encoding; both encodings yield the same Hamming distance. Implementing this replacement on a classical computer is trivial. However, replacing these encoding schemes on a QC is not straightforward because PQM and P-PQM operate at the bit level, rather than at the feature level (a feature is represented by a binary string of 0’s and 1’s). We present an enhanced P-PQM, called efficient P-PQM (EP-PQM), that allows label encoding of data stored in a PQM data structure and reduces the circuit depth of the data storage and retrieval procedures. We show implementations for an ideal QC and a noisy intermediate-scale quantum (NISQ) device. Our complexity analysis shows that the EP-PQM approach requiresO(zlog⁡2(a))O(z \log _{2}(a))O(zlog2​(a))qubits as opposed toO(za)O(za)O(za)qubits for P-PQM. EP-PQM also requires fewer gates, reducing gate count fromO(rza)O(rza)O(rza)toO(rzlog⁡2(a))O(rz\log _{2}(a))O(rzlog2​(a)). For five datasets, we demonstrate that training an ML classification model using EP-PQM requires 48% to 77% fewer qubits than P-PQM for datasets witha>2a>2a>2. EP-PQM reduces circuit depth in the range of 60% to 96%, depending on the dataset. The depth decreases further with a decomposed circuit, ranging between 94% and 99%. EP-PQM requires less space; thus, it can train on and classify larger datasets than previous PQM implementations on NISQ devices. Furthermore, reducing the number of gates speeds up the classification and reduces the noise associated with deep quantum circuits. Thus, EP-PQM brings us closer to scalable ML on an NISQ device.
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.
Quantum classifiers provide sophisticated embeddings of input data in Hilbert space promising quantum advantage. The advantage stems from quantum feature maps encoding the inputs into quantum states with variational quantum circuits. A recent work shows how to map discrete features with fewer quantum bits using Quantum Random Access Coding (QRAC), an important primitive to encode binary strings into quantum states. We propose a new method to embed discrete features with trainable quantum circuits by combining QRAC and a recently proposed strategy for training quantum feature map called quantum metric learning. We show that the proposed trainable embedding requires not only as few qubits as QRAC but also overcomes the limitations of QRAC to classify inputs whose classes are based on hard Boolean functions. We numerically demonstrate its use in variational quantum classifiers to achieve better performances in classifying real-world datasets, and thus its possibility to leverage near-term quantum computers for quantum machine learning.