Showing papers in "Quantum Machine Intelligence in 2022"

Quantum convolutional neural network for classical data classification

Abstract: With the rapid advance of quantum machine learning, several proposals for the quantum-analogue of convolutional neural network (CNN) have emerged. In this work, we benchmark fully parameterized quantum convolutional neural networks (QCNNs) for classical data classification. In particular, we propose a quantum neural network model inspired by CNN that only uses two-qubit interactions throughout the entire algorithm. We investigate the performance of various QCNN models differentiated by structures of parameterized quantum circuits, quantum data encoding methods, classical data pre-processing methods, cost functions and optimizers on MNIST and Fashion MNIST datasets. In most instances, QCNN achieved excellent classification accuracy despite having a small number of free parameters. The QCNN models performed noticeably better than CNN models under the similar training conditions. Since the QCNN algorithm presented in this work utilizes fully parameterized and shallow-depth quantum circuits, it is suitable for Noisy Intermediate-Scale Quantum (NISQ) devices.

Quantum transfer learning for breast cancer detection

Abstract: One of the areas with the potential to be explored in quantum computing (QC) is machine learning (ML), giving rise to quantum machine learning (QML). In an era when there is so much data, ML may benefit from either speed, complexity or smaller amounts of storage. In this work, we explore a quantum approach to a machine learning problem. Based on the work of Mari et al., we train a set of hybrid classical-quantum neural networks using transfer learning (TL). Our task was to solve the problem of classifying full-image mammograms into malignant and benign, provided by BCDR. Throughout the course of our work, heatmaps were used to highlight the parts of the mammograms that were being targeted by the networks while evaluating different performance metrics. Our work shows that this method may hold benefits regarding the generalization of complex data; however, further tests are needed. We also show that, depending on the task, some architectures perform better than others. Nonetheless, our results were superior to those reported in the state-of-the-art (accuracy of 84% against 76.9%, respectively). In addition, experiments were conducted in a real quantum device, and results were compared with the classical and simulator.

Quantum transfer learning for breast cancer detection

Abstract: One of the areas with the potential to be explored in quantum computing (QC) is machine learning (ML), giving rise to quantum machine learning (QML). In an era when there is so much data, ML may benefit from either speed, complexity or smaller amounts of storage. In this work, we explore a quantum approach to a machine learning problem. Based on the work of Mari et al., we train a set of hybrid classical-quantum neural networks using transfer learning (TL). Our task was to solve the problem of classifying full-image mammograms into malignant and benign, provided by BCDR. Throughout the course of our work, heatmaps were used to highlight the parts of the mammograms that were being targeted by the networks while evaluating different performance metrics. Our work shows that this method may hold benefits regarding the generalization of complex data; however, further tests are needed. We also show that, depending on the task, some architectures perform better than others. Nonetheless, our results were superior to those reported in the state-of-the-art (accuracy of 84% against 76.9%, respectively). In addition, experiments were conducted in a real quantum device, and results were compared with the classical and simulator.

Quantum neural network autoencoder and classifier applied to an industrial case study

Abstract: Abstract Quantum computing technologies are in the process of moving from academic research to real industrial applications, with the first hints of quantum advantage demonstrated in recent months. In these early practical uses of quantum computers, it is relevant to develop algorithms that are useful for actual industrial processes. In this work, we propose a quantum pipeline, comprising a quantum autoencoder followed by a quantum classifier, which are used to first compress and then label classical data coming from a separator, i.e., a machine used in one of Eni’s Oil Treatment Plants. This work represents one of the first attempts to integrate quantum computing procedures in a real-case scenario of an industrial pipeline, in particular using actual data coming from physical machines, rather than pedagogical data from benchmark datasets.

Overfitting in quantum machine learning and entangling dropout

Abstract: The ultimate goal in machine learning is to construct a model function that has a generalization capability for unseen dataset, based on given training dataset. If the model function has too much expressibility power, then it may overfit to the training data and as a result lose the generalization capability. To avoid such overfitting issue, several techniques have been developed in the classical machine learning regime, and the dropout is one such effective method. This paper proposes a straightforward analogue of this technique in the quantum machine learning regime, the entangling dropout, meaning that some entangling gates in a given parametrized quantum circuit are randomly removed during the training process to reduce the expressibility of the circuit. Some simple case studies are given to show that this technique actually suppresses the overfitting.

Hybrid classical-quantum autoencoder for anomaly detection

Abstract: We propose a hybrid classical-quantum autoencoder (HAE) model, which is a synergy of a classical autoencoder (AE) and a parametrized quantum circuit (PQC) that is inserted into its bottleneck. The PQC augments the classical latent space by lifting it to a quantum latent space whereby further data manipulations occur before performing a measurement and collapsing the state to its original classical latent space representation. From this resulting data, a standard outlier detection method is applied to search for anomalous data points within a classical dataset. Using this model and applying it to both standard benchmarking datasets, and a specific use-case dataset, which relates to predictive maintenance of gas power plants, we show that the addition of the PQC to the autoencoder bottleneck leads to a performance enhancement in terms of precision, recall, and F1 score. Furthermore, we probe different PQC Ansätze and analyze which PQC features make them effective for this task.

Feature selection on quantum computers

Abstract: In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a quadratic unconstrained binary optimization (QUBO) problem, which allows to select a specified number of features based on their importance and redundancy. In contrast to iterative or greedy methods, our direct approach yields higherquality solutions. QUBO problems are particularly interesting because they can be solved on quantum hardware. To evaluate our proposed algorithm, we conduct a series of numerical experiments using a classical computer, a quantum gate computer and a quantum annealer. Our evaluation compares our method to a range of standard methods on various benchmark datasets. We observe competitive performance.

Optimisation-free density estimation and classification with quantum circuits

Abstract: We demonstrate the implementation of a novel machine learning framework for probability density estimation and classification using quantum circuits. The framework maps a training data set or a single data sample to the quantum state of a physical system through quantum feature maps. The quantum state of the arbitrarily large training data set summarises its probability distribution in a finite-dimensional quantum wave function. By projecting the quantum state of a new data sample onto the quantum state of the training data set, one can derive statistics to classify or estimate the density of the new data sample. Remarkably, the implementation of our framework on a real quantum device does not require any optimisation of quantum circuit parameters. Nonetheless, we discuss a variational quantum circuit approach that could leverage quantum advantage for our framework.

Deep tensor networks with matrix product operators

Abstract: We introduce deep tensor networks, which are exponentially wide neural networks based on the tensor network representation of the weight matrices. We evaluate the proposed method on the image classification (MNIST, FashionMNIST) and sequence prediction (cellular automata) tasks. In the image classification case, deep tensor networks improve our matrix product state baselines and achieve 0.49% error rate on MNIST and 8.3% error rate on FashionMNIST. In the sequence prediction case, we demonstrate an exponential improvement in the number of parameters compared to the one-layer tensor network methods. In both cases, we discuss the non-uniform and the uniform tensor network models and show that the latter generalises well to different input sizes.

Exploring quantum perceptron and quantum neural network structures with a teacher-student scheme

Abstract: Near-term quantum devices can be used to build quantum machine learning models, such as quantum kernel methods and quantum neural networks (QNN), to perform classification tasks. There have been many proposals on how to use variational quantum circuits as quantum perceptrons or as QNNs. The aim of this work is to introduce a teacher-student scheme that could systematically compare any QNN architectures and evaluate their relative expressive power. Specifically, the teacher model generates the datasets mapping random inputs to outputs which then have to be learned by the student models. This way, we avoid training on arbitrary data sets and allow to compare the learning capacity of different models directly via the loss, the prediction map, the accuracy and the relative entropy between the prediction maps. Here, we focus particularly on a quantum perceptron model inspired by the recent work of Tacchino et al. (2019) and compare it to the data re-uploading scheme that was originally introduced by Pérez-Salinas et al. (2020). We discuss alterations of the perceptron model and the formation of deep QNN to better understand the role of hidden units and the non-linearities in these architectures.

A hybrid quantum image edge detector for the NISQ era

Abstract: Abstract Edges are image locations where the gray value intensity changes suddenly. They are among the most important features to understand and segment an image. Edge detection is a standard task in digital image processing, solved, for example, using filtering techniques. However, the amount of data to be processed grows rapidly and pushes even supercomputers to their limits. Quantum computing promises exponentially lower memory usage in terms of the number of qubits compared to the number of classical bits. In this paper, we propose a hybrid method for quantum edge detection based on the idea of a quantum artificial neuron. Our method can be practically implemented on quantum computers, especially on those of the current noisy intermediate-scale quantum era. We compare six variants of the method to reduce the number of circuits and thus the time required for the quantum edge detection. Taking advantage of the scalability of our method, we can practically detect edges in images considerably larger than reached before.

Decohering tensor network quantum machine learning models

Abstract: Abstract Tensor network quantum machine learning (QML) models are promising applications on near-term quantum hardware. While decoherence of qubits is expected to decrease the performance of QML models, it is unclear to what extent the diminished performance can be compensated for by adding ancillas to the models and accordingly increasing the virtual bond dimension of the models. We investigate here the competition between decoherence and adding ancillas on the classification performance of two models, with an analysis of the decoherence effect from the perspective of regression. We present numerical evidence that the fully decohered unitary tree tensor network (TTN) with two ancillas performs at least as well as the non-decohered unitary TTN, suggesting that it is beneficial to add at least two ancillas to the unitary TTN regardless of the amount of decoherence may be consequently introduced.

Non-IID quantum federated learning with one-shot communication complexity

Abstract: Federated learning refers to the task of machine learning based on decentralized data from multiple clients with secured data privacy. Recent studies show that quantum algorithms can be exploited to boost its performance. However, when the clients’ data are not independent and identically distributed (IID), the performance of conventional federated algorithms is known to deteriorate. In this work, we explore the non-IID issue in quantum federated learning with both theoretical and numerical analysis. We further prove that a global quantum channel can be exactly decomposed into local channels trained by each client with the help of local density estimators. This observation leads to a general framework for quantum federated learning on non-IID data with one-shot communication complexity. Numerical simulations show that the proposed algorithm outperforms the conventional ones significantly under non-IID settings.

Using Shor’s algorithm on near term Quantum computers: a reduced version

Abstract: Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor’s algorithm, this peculiar problem can be solved in polynomial time. However, both the number of qubits and applied gates detrimentally affect the ability to run a particular quantum circuit on the near term Quantum hardware. In this work, we help addressing both these problems by introducing a reduced version of Shor’s algorithm that proposes a step forward in increasing the range of numbers that can be factorized on noisy Quantum devices. More specifically, the structure of the Shor’s circuit has been modified to reduce the number of gates in the modular arithmetic and the Quantum Fourier Transform. The implementation presented in this work is general and does not use any assumptions on the number to factor. In particular, we have found noteworthy results in most cases, often being able to factor the given number with only one iteration of the proposed algorithm. Finally, comparing the original quantum algorithm with our version on simulator, the outcomes are identical for some of the numbers considered.

Mixer-phaser Ansätze for quantum optimization with hard constraints

Abstract: Abstract We introduce multiple parametrized circuit ansätze and present the results of a numerical study comparing their performance with a standard Quantum Alternating Operator Ansatz approach. The ansätze are inspired by mixing and phase separation in the QAOA, and also motivated by compilation considerations with the aim of running on near-term superconducting quantum processors. The methods are tested on random instances of a quadratic binary constrained optimization problem that is fully connected for which the space of feasible solutions has constant Hamming weight. For the parameter setting strategies and evaluation metric used, the average performance achieved by the QAOA is effectively matched by the one obtained by a ”mixer-phaser” ansatz that can be compiled in less than half-depth of standard QAOA on most superconducting qubit processors.

Learning with density matrices and random features

Abstract: A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement, system combination and expectations as linear algebra operations. This paper explores how density matrices can be used as a building block to build machine learning models exploiting their ability to straightforwardly combine linear algebra and probability. One of the main results of the paper is to show that density matrices coupled with random Fourier features could approximate arbitrary probability distributions over $\mathbb{R}^n$. Based on this finding the paper builds different models for density estimation, classification and regression. These models are differentiable, so it is possible to integrate them with other differentiable components, such as deep learning architectures and to learn their parameters using gradient-based optimization. In addition, the paper presents optimization-less training strategies based on estimation and model averaging. The models are evaluated in benchmark tasks and the results are reported and discussed.

Deep tensor networks with matrix product operators

Abstract: We introduce deep tensor networks, which are exponentially wide neural networks based on the tensor network representation of the weight matrices. We evaluate the proposed method on the image classification (MNIST, FashionMNIST) and sequence prediction (cellular automata) tasks. In the image classification case, deep tensor networks improve our matrix product state baselines and achieve 0.49% error rate on MNIST and 8.3% error rate on FashionMNIST. In the sequence prediction case, we demonstrate an exponential improvement in the number of parameters compared to the one-layer tensor network methods. In both cases, we discuss the non-uniform and the uniform tensor network models and show that the latter generalises well to different input sizes.

Deep tensor networks with matrix product operators

Abstract: We introduce deep tensor networks, which are exponentially wide neural networks based on the tensor network representation of the weight matrices. We evaluate the proposed method on the image classification (MNIST, FashionMNIST) and sequence prediction (cellular automata) tasks. In the image classification case, deep tensor networks improve our matrix product state baselines and achieve 0.49% error rate on MNIST and 8.3% error rate on FashionMNIST. In the sequence prediction case, we demonstrate an exponential improvement in the number of parameters compared to the one-layer tensor network methods. In both cases, we discuss the non-uniform and the uniform tensor network models and show that the latter generalises well to different input sizes.

Dimension-adaptive machine learning-based quantum state reconstruction

Abstract: We introduce an approach for performing quantum state reconstruction on systems of n qubits using a machine learning-based reconstruction system trained exclusively on m qubits, where m ≥ n. This approach removes the necessity of exactly matching the dimensionality of a system under consideration with the dimension of a model used for training. We demonstrate our technique by performing quantum state reconstruction on randomly sampled systems of one, two, and three qubits using machine learning-based methods trained exclusively on systems containing at least one additional qubit. The reconstruction time required for machine learning-based methods scales significantly more favorably than the training time; hence this technique can offer an overall saving of resources by leveraging a single neural network for dimension-variable state reconstruction, obviating the need to train dedicated machine learning systems for each Hilbert space.

Policy gradients using variational quantum circuits

Abstract: Abstract Variational quantum circuits are being used as versatile quantum machine learning models. Some empirical results exhibit an advantage in supervised and generative learning tasks. However, when applied to reinforcement learning, less is known. In this work, we considered a variational quantum circuit composed of a low-depth hardware-efficient ansatz as the parameterized policy of a reinforcement learning agent. We show that an 𝜖 -approximation of the policy gradient can be obtained using a logarithmic number of samples concerning the total number of parameters. We empirically verify that such quantum models behave similarly to typical classical neural networks used in standard benchmarking environments and quantum control, using only a fraction of the parameters. Moreover, we study the barren plateau phenomenon in quantum policy gradients using the Fisher information matrix spectrum.

Quantum algorithms for SVD-based data representation and analysis

Abstract: Abstract This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in machine learning. The power and practical use of these subroutines is shown through new quantum algorithms, sublinear in the input matrix’s size, for principal component analysis, correspondence analysis, and latent semantic analysis. We provide a theoretical analysis of the run-time and prove tight bounds on the randomized algorithms’ error. We run experiments on multiple datasets, simulating PCA’s dimensionality reduction for image classification with the novel routines. The results show that the run-time parameters that do not depend on the input’s size are reasonable and that the error on the computed model is small, allowing for competitive classification performances.