Natural language processing (NLP) is the field that attempts to make human language accessible to computers, and it relies on applying a mathematical model to express the meaning of symbolic language. One such model, DisCoCat, defines how to express both the meaning of individual words as well as their compositional nature. This model can be naturally implemented on quantum computers, leading to the field quantum NLP (QNLP). Recent experimental work used quantum machine learning techniques to map from text to class label using the expectation value of the quantum encoded sentence. Theoretical work has been done on computing the similarity of sentences but relies on an unrealized quantum memory store. The main goal of this thesis is to leverage the DisCoCat model to design a quantum-based kernel function that can be used by a support vector machine (SVM) for NLP tasks. Two similarity measures were studied: (i) the transition amplitude approach and (ii) the SWAP test. A simple NLP meaning classification task from previous work was used to train the word embeddings and evaluate the performance of both models. The Python module lambeq and its related software stack was used for implementation. The explicit model from previous work was used to train word embeddings and achieved a testing accuracy of $93.09 \pm 0.01$%. It was shown that both the SVM variants achieved a higher testing accuracy of $95.72 \pm 0.01$% for approach (i) and $97.14 \pm 0.01$% for (ii). The SWAP test was then simulated under a noise model defined by the real quantum device, ibmq_guadalupe. The explicit model achieved an accuracy of $91.94 \pm 0.01$% while the SWAP test SVM achieved 96.7% on the testing dataset, suggesting that the kernelized classifiers are resilient to noise. These are encouraging results and motivate further investigations of our proposed kernelized QNLP paradigm.
Variational quantum algorithms are the leading candidate for advantage on near-term quantum hardware. When training a parametrized quantum circuit in this setting to solve a specific problem, the choice of ansatz is one of the most important factors that determines the trainability and performance of the algorithm. In quantum machine learning (QML), however, the literature on ansatzes that are motivated by the training data structure is scarce. In this work, we introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations. We evaluate the performance of this ansatz on a complex learning task, namely neural combinatorial optimization, where a machine learning model is used to learn a heuristic for a combinatorial optimization problem. We analytically and numerically study the performance of our model, and our results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML.
Variational quantum machine learning is an extensively studied application of near-term quantum computers. The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes an inductive bias relevant to the learning task. However, precious little is known about guiding principles for the construction of suitable parametrizations. In this work, we holistically explore when and how symmetries of the learning problem can be exploited to construct quantum learning models with outcomes invariant under the symmetry of the learning task. Building on tools from representation theory, we show how a standard gateset can be transformed into an equivariant gateset that respects the symmetries of the problem at hand through a process of gate symmetrization. We benchmark the proposed methods on two toy problems that feature a non-trivial symmetry and observe a substantial increase in generalization performance. As our tools can also be applied in a straightforward way to other variational problems with symmetric structure, we show how equivariant gatesets can be used in variational quantum eigensolvers.
The data representation in a machine-learning model strongly influences its performance. This becomes even more important for quantum machine learning models implemented on noisy intermediate scale quantum (NISQ) devices. Encoding high dimensional data into a quantum circuit for a NISQ device without any loss of information is not trivial and brings a lot of challenges. While simple encoding schemes (like single qubit rotational gates to encode high dimensional data) often lead to information loss within the circuit, complex encoding schemes with entanglement and data re-uploading lead to an increase in the encoding gate count. This is not well-suited for NISQ devices. This work proposes 'incremental data-uploading', a novel encoding pattern for high dimensional data that tackles these challenges. We spread the encoding gates for the feature vector of a given data point throughout the quantum circuit with parameterized gates in between them. This encoding pattern results in a better representation of data in the quantum circuit with a minimal pre-processing requirement. We show the efficiency of our encoding pattern on a classification task using the MNIST and Fashion-MNIST datasets, and compare different encoding methods via classification accuracy and the effective dimension of the model.
Quantum Machine Learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes. As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand. In this work we present a simple, yet powerful, framework where the underlying invariances in the data are used to build QML models that, by construction, respect those symmetries. These so-called group-invariant models produce outputs that remain invariant under the action of any element of the symmetry group $\mathfrak{G}$ associated to the dataset. We present theoretical results underpinning the design of $\mathfrak{G}$-invariant models, and exemplify their application through several paradigmatic QML classification tasks including cases when $\mathfrak{G}$ is a continuous Lie group and also when it is a discrete symmetry group. Notably, our framework allows us to recover, in an elegant way, several well known algorithms for the literature, as well as to discover new ones. Taken together, we expect that our results will help pave the way towards a more geometric and group-theoretic approach to QML model design.
We propose a quantum algorithm for `extremal learning', which is the process of finding the input to a hidden function that extremizes the function output, without having direct access to the hidden function, given only partial input-output (training) data. The algorithm, called quantum extremal learning (QEL), consists of a parametric quantum circuit that is variationally trained to model data input-output relationships and where a trainable quantum feature map, that encodes the input data, is analytically differentiated in order to find the coordinate that extremizes the model. This enables the combination of established quantum machine learning modelling with established quantum optimization, on a single circuit/quantum computer. We have tested our algorithm on a range of classical datasets based on either discrete or continuous input variables, both of which are compatible with the algorithm. In case of discrete variables, we test our algorithm on synthetic problems formulated based on Max-Cut problem generators and also considering higher order correlations in the input-output relationships. In case of the continuous variables, we test our algorithm on synthetic datasets in 1D and simple ordinary differential functions. We find that the algorithm is able to successfully find the extremal value of such problems, even when the training dataset is sparse or a small fraction of the input configuration space. We additionally show how the algorithm can be used for much more general cases of higher dimensionality, complex differential equations, and with full flexibility in the choice of both modeling and optimization ansatz. We envision that due to its general framework and simple construction, the QEL algorithm will be able to solve a wide variety of applications in different fields, opening up areas of further research.
Because of the rotational components on quantum circuits, some quantum neural networks based on variational circuits can be considered equivalent to the classical Fourier networks. In addition, they can be used to predict the Fourier coefficients of continuous functions. Time series data indicates a state of a variable in time. Since some time series data can be also considered as continuous functions, we can expect quantum machine learning models to do many data analysis tasks successfully on time series data. Therefore, it is important to investigate new quantum logics for temporal data processing and analyze intrinsic relationships of data on quantum computers. In this paper, we go through the quantum analogues of classical data preprocessing and forecasting with ARIMA models by using simple quantum operators requiring a few number of quantum gates. Then we discuss future directions and some of the tools/algorithms that can be used for temporal data analysis on quantum computers.
Barren plateaus are a notorious problem in the optimization of variational quantum algorithms and pose a critical obstacle in the quest for more efficient quantum machine learning algorithms. Many potential reasons for barren plateaus have been identified but few solutions have been proposed to avoid them in practice. Existing solutions are mainly focused on the initialization of unitary gate parameters without taking into account the changes induced by input data. In this paper, we propose an alternative strategy which initializes the parameters of a unitary gate by drawing from a beta distribution. The hyperparameters of the beta distribution are estimated from the data. To further prevent barren plateau during training we add a novel perturbation at every gradient descent step. Taking these ideas together, we empirically show that our proposed framework significantly reduces the possibility of a complex quantum neural network getting stuck in a barren plateau.
Quantum machine learning is receiving significant attention currently, but its usefulness in comparison to classical machine learning techniques for practical applications remains unclear. However, there are indications that certain quantum machine learning algorithms might result in improved training capabilities with respect to their classical counterparts -- which might be particularly beneficial in situations with little training data available. Such situations naturally arise in medical classification tasks. Within this paper, different hybrid quantum-classical convolutional neural networks (QCCNN) with varying quantum circuit designs and encoding techniques are proposed. They are applied to two- and three-dimensional medical imaging data, e.g. featuring different, potentially malign, lesions in computed tomography scans. The performance of these QCCNNs is already similar to the one of their classical counterparts -- therefore encouraging further studies towards the direction of applying these algorithms within medical imaging tasks.
Given is a set of images, where all images show views of the same area at different points in time and from different viewpoints. The task is the alignment of all images such that relevant information, e.g., poses, changes, and terrain, can be extracted from the fused image. In this work, we focus on quantum methods for keypoint extraction and feature matching, due to the demanding computational complexity of these sub-tasks. To this end, k-medoids clustering, kernel density clustering, nearest neighbor search, and kernel methods are investigated and it is explained how these methods can be re-formulated for quantum annealers and gate-based quantum computers. Experimental results obtained on digital quantum emulation hardware, quantum annealers, and quantum gate computers show that classical systems still deliver superior results. However, the proposed methods are ready for the current and upcoming generations of quantum computing devices which have the potential to outperform classical systems in the near future.
Quantum computing leverages quantum effects to build algorithms that are faster then their classical variants. In machine learning, for a given model architecture, the speed of training the model is typically determined by the size of the training dataset. Thus, quantum machine learning methods have the potential to facilitate learning using extremely large datasets. While the availability of data for training machine learning models is steadily increasing, oftentimes it is much easier to collect feature vectors that to obtain the corresponding labels. One of the approaches for addressing this issue is to use semi-supervised learning, which leverages not only the labeled samples, but also unlabeled feature vectors. Here, we present a quantum machine learning algorithm for training Semi-Supervised Kernel Support Vector Machines. The algorithm uses recent advances in quantum sample-based Hamiltonian simulation to extend the existing Quantum LS-SVM algorithm to handle the semi-supervised term in the loss. Through a theoretical study of the algorithm's computational complexity, we show that it maintains the same speedup as the fully-supervised Quantum LS-SVM.
Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly investigated. Here we develop a framework for using QML methods to simulate quantum dynamics on near-term quantum hardware. We use generalization bounds, which bound the error a machine learning model makes on unseen data, to rigorously analyze the training data requirements of an algorithm within this framework. This provides a guarantee that our algorithm is resource-efficient, both in terms of qubit and data requirements. Our numerics exhibit efficient scaling with problem size, and we simulate 20 times longer than Trotterization on IBMQ-Bogota.
Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.
Synthetic data generation has proven to be a promising solution for addressing data availability issues in various domains. Even more challenging is the generation of synthetic time series data, where one has to preserve temporal dynamics, i.e., the generated time series must respect the original relationships between variables across time. Recently proposed techniques such as generative adversarial networks (GANs) and quantum-GANs lack the ability to attend to the time series specific temporal correlations adequately. We propose using the inherent nature of quantum computers to simulate quantum dynamics as a technique to encode such features. We start by assuming that a given time series can be generated by a quantum process, after which we proceed to learn that quantum process using quantum machine learning. We then use the learned model to generate out-of-sample time series and show that it captures unique and complex features of the learned time series. We also study the class of time series that can be modeled using this technique. Finally, we experimentally demonstrate the proposed algorithm on an 11-qubit trapped-ion quantum machine.
In this chapter a quantum music generation application called QuiKo will be discussed. It combines existing quantum algorithms with data encoding methods from quantum machine learning to build drum and audio sample patterns from a database of audio tracks. QuiKo leverages the physical properties and characteristics of quantum computers to generate what can be referred to as Soft Rules proposed by Alexis Kirke. These rules take advantage of the noise produced by quantum devices to develop flexible rules and grammars for quantum music generation. These properties include qubit decoherence and phase kickback due controlled quantum gates within the quantum circuit. QuiKo builds upon the concept of soft rules in quantum music generation and takes it a step further. It attempts to mimic and react to an external musical inputs, similar to the way that human musicians play and compose with one another. Audio signals are used as inputs into the system. Feature extraction is then performed on the signal to identify the harmonic and percussive elements. This information is then encoded onto the quantum circuit. Measurements of the quantum circuit are then taken providing results in the form of probability distributions for external music applications to use to build the new drum patterns.
Machine Learning (ML) for Ligand Based Virtual Screening (LB-VS) is an important in-silico tool for discovering new drugs in a faster and cost-effective manner, especially for emerging diseases such as COVID-19. In this paper, we propose a general-purpose framework combining a classical Support Vector Classifier (SVC) algorithm with quantum kernel estimation for LB-VS on real-world databases, and we argue in favor of its prospective quantum advantage. Indeed, we heuristically prove that our quantum integrated workflow can, at least in some relevant instances, provide a tangible advantage compared to state-of-art classical algorithms operating on the same datasets, showing strong dependence on target and features selection method. Finally, we test our algorithm on IBM Quantum processors using ADRB2 and COVID-19 datasets, showing that hardware simulations provide results in line with the predicted performances and can surpass classical equivalents.
In the last few years, quantum computing has experienced a growth spurt. One exciting avenue of quantum computing is quantum machine learning (QML) which can exploit the high dimensional Hilbert space to learn richer representations from limited data and thus can efficiently solve complex learning tasks. Despite the increased interest in QML, there have not been many studies that discuss the security aspects of QML. In this work, we explored the possible future applications of QML in the hardware security domain. We also expose the security vulnerabilities of QML and emerging attack models, and corresponding countermeasures.
Quantum computing promises to enhance machine learning and artificial intelligence. Different quantum algorithms have been proposed to improve a wide spectrum of machine learning tasks. Yet, recent theoretical works show that, similar to traditional classifiers based on deep classical neural networks, quantum classifiers would suffer from the vulnerability problem: adding tiny carefully-crafted perturbations to the legitimate original data samples would facilitate incorrect predictions at a notably high confidence level. This will pose serious problems for future quantum machine learning applications in safety and security-critical scenarios. Here, we report the first experimental demonstration of quantum adversarial learning with programmable superconducting qubits. We train quantum classifiers, which are built upon variational quantum circuits consisting of ten transmon qubits featuring average lifetimes of 150 $\mu$s, and average fidelities of simultaneous single- and two-qubit gates above 99.94% and 99.4% respectively, with both real-life images (e.g., medical magnetic resonance imaging scans) and quantum data. We demonstrate that these well-trained classifiers (with testing accuracy up to 99%) can be practically deceived by small adversarial perturbations, whereas an adversarial training process would significantly enhance their robustness to such perturbations. Our results reveal experimentally a crucial vulnerability aspect of quantum learning systems under adversarial scenarios and demonstrate an effective defense strategy against adversarial attacks, which provide a valuable guide for quantum artificial intelligence applications with both near-term and future quantum devices.
Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parameterized quantum circuits in the limit of a large number of qubits and variational parameters. We then find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. We finally validate our analytic results with numerical experiments.
Multiclass classification is of great interest for various applications, for example, it is a common task in computer vision, where one needs to categorize an image into three or more classes. Here we propose a quantum machine learning approach based on quantum convolutional neural networks for solving the multiclass classification problem. The corresponding learning procedure is implemented via TensorFlowQuantum as a hybrid quantum-classical (variational) model, where quantum output results are fed to the softmax activation function with the subsequent minimization of the cross entropy loss via optimizing the parameters of the quantum circuit. Our conceptional improvements here include a new model for a quantum perceptron and an optimized structure of the quantum circuit. We use the proposed approach to solve a 4-class classification problem for the case of the MNIST dataset using eight qubits for data encoding and four ancilla qubits; previous results have been obtained for 3-class classification problems. Our results show that accuracies of our solution are similar to classical convolutional neural networks with comparable numbers of trainable parameters. We expect that our finding provide a new step towards the use of quantum neural networks for solving relevant problems in the NISQ era and beyond.