Recent days have witnessed significant interests in applying quantum-enhanced techniques for solving a variety of machine learning tasks. Variational methods that use quantum resources of imperfect quantum devices with the help of classical computing techniques are popular for supervised learning. Variational quantum classification (VQC) is one of such methods with possible quantum advantage in using quantum-enhanced features that are hard to compute by classical methods. Its performance depends on the mapping of classical features into a quantum-enhanced feature space. Although there have been many quantum-mapping functions proposed so far, there is little discussion on efficient mapping of discrete features, such as age group, zip code, and others, which are often significant for classifying datasets of interest. We first introduce the use of quantum random-access coding (QRAC) to map such discrete features efficiently into limited number of qubits for VQC. In numerical simulations, we present a range of encoding strategies and demonstrate their limitations and capabilities. We experimentally show that QRAC can help speeding up the training of VQC by reducing its parameters via saving on the number of qubits for the mapping. We confirm the effectiveness of the QRAC in VQC by experimenting on classification of real-world datasets with both simulators and real quantum devices.
A hybrid variational quantum circuit approach for stabilizer states classifiers
Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS, University of Technology of Belfort-Montbéliard（贝尔福-蒙贝利亚尔技术大学）；Mathematics and Statistics Department, Auburn University（奥本大学）
We focus on using an architecture similar to the $β$-Variational Autoencoder ($β$-VAE) to discriminate if a quantum state is entangled or separable based on measurements. We split the data into two sets, the set of local and correlated measurements. Using the latent space, which is a low dimensional representation of the data, we show that restricting ourselves to the set of local data it is not possible to distinguish between entangled and separable states. Meanwhile, when considering both correlated and local measurements, an accuracy of over 80% is attained in the structure of the latent sp…
Ensemble-learning error mitigation for variational quantum shallow-circuit classifiers
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院）；The Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology（香港科技大学电子与计算机工程学系）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges by introducing a new variational quantum algorithm that benefits from two innovations: multi-basis graph encodings and nonlinear activation functions. Our technique results in increased optimization performance, a factor of two increase in effective quantum resources, and a quadratic reduction in measurement complexity. Wh…
Matrix encoding method in variational algorithm of calculating eigenvalues and generalized eigenvalues
Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry RAS（俄罗斯科学院化学物理与医药化学问题联邦研究中心）；School of Mathematical Sciences, Zhejiang University（浙江大学数学科学学院）
Dementia is the fifth cause of death worldwide with 10 million new cases every year. Healthcare applications using machine learning techniques have almost reached the physical limits while more data is becoming available resulting from the increasing rate of diagnosis. Recent research in Quantum Machine Learning (QML) techniques have found different approaches that may be useful to accelerate the training process of existing machine learning models and provide an alternative to learn more complex patterns. This work aims to report a real-world application of a Quantum Machine Learning Algorith…
Department of Computational Mathematics, Science, and Engineering, Michigan State University（密歇根州立大学计算数学、科学与工程系）；School of Informatics, University of Edinburgh（爱丁堡大学信息学院）
Data representation is crucial for the success of machine learning models. In the context of quantum machine learning with near-term quantum computers, equally important considerations of how to efficiently input (encode) data and effectively deal with noise arise. In this work, we study data encodings for binary quantum classification and investigate their properties both with and without noise. For the common classifier we consider, we show that encodings determine the classes of learnable decision boundaries as well as the set of points which retain the same classification in the presence o…
We propose a novel algorithm for fast training of variational classifiers by processing multiple samples parallelly. The algorithm can be adapted for any ansatz used in the variational circuit. The presented algorithm utilizes qRAM and other quantum circuits in the forward pass. Further, instead of the usual practice of computing the loss classically, we calculate the loss using a Swap-test circuit. The algorithm thus brings down the training cost of a variational classifier to O(logN)from the usual O(N)when training on a dataset of N samples. Although we discuss only binary classification in …
Physics-Informed Variational Quantum Classifier for Phase Detection in Strongly Correlated Matter
Instituto de Física Corpuscular, Universitat de València – Consejo Superior de Investigaciones Científicas（瓦伦西亚大学-西班牙国家研究委员会粒子物理研究所）；Escuela de Ciencias, Ingeniería y Diseño, Universidad Europea de Valencia（瓦伦西亚欧洲大学科学与工程设计学院）；Facultat de Física, Universitat de València（瓦伦西亚大学物理学院）
National Institute of Technology, Agartala（阿加尔塔拉国家理工学院）；Chitkara University Institute of Engineering & Technology, Chitkara University（奇特卡拉大学工程与技术学院）；Mansoura University（曼苏拉大学）
In quantum computing, the variational quantum algorithms (VQAs) are well suited for finding optimal combinations of things in specific applications ranging from chemistry all the way to finance. The training of VQAs with gradient descent optimization algorithm has shown a good convergence. At an early stage, the simulation of variational quantum circuits on noisy intermediate-scale quantum (NISQ) devices suffers from noisy outputs. Just like classical deep learning, it also suffers from vanishing gradient problems. It is a realistic goal to study the topology of loss landscape, to visualize th…
The University of Tokyo（东京大学）；Keio University（庆应义塾大学）；IBM Japan（IBM日本）
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…
Qubit-Efficient Variational Quantum Optimization via Pauli Correlation Encoding: Application to Large-Scale Power Demand Portfolio Optimization
Strategic Technology Center, TISI Inc.（TISI公司战略技术中心）；Graduate School of Engineering Science, Osaka University（大阪大学工程科学研究科）；Center for Quantum Information and Quantum Biology, Osaka University（大阪大学量子信息与量子生物学中心）；Center for Quantum Computing, RIKEN（理化学研究所量子计算中心）
A Resource-Efficient Variational Quantum Framework for the Traveling Salesman Problem
Shenzhen SpinQ Technology Co., Ltd（深圳启元科技有限公司）；School of Energy Storage Science and Engineering, North China University of Technology（华北电力大学能源存储科学与工程学院）
University of British Columbia（不列颠哥伦比亚大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；Stewart Blusson Quantum Matter Institute（斯图尔特·布吕松量子物质研究所）
Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that variational quantum classifiers and support vector machines with quantum kernels can solve a classification problem based on the $k$-Forrelation problem, which is known to be PromiseBQP-complete. Because the PromiseBQP complexity class includes all Bounded-Error Quantum Polynomial-Time (BQP) decision problems, our results imply that there exists a feature map a…
Quantum machine learning aims to release the prowess of quantum computing to improve machine learning methods. By combining quantum computing methods with classical neural network techniques we aim to foster an increase of performance in solving classification problems. Our algorithm is designed for existing and near-term quantum devices. We propose a novel hybrid variational quantum classifier that combines the quantum gradient descent method with steepest gradient descent to optimise the parameters of the network. By applying this algorithm to a resonance search in di-top final states, we fi…
Hybrid quantum-classical algorithms based on variational circuits are a promising approach to quantum machine learning problems for near-term devices, but the selection of the variational ansatz is an open issue. Recently, tensor network-inspired circuits have been proposed as a natural choice for such ansatz. Their employment on binary classification tasks provided encouraging results. However, their effectiveness on more difficult tasks is still unknown. Here, we present numerical experiments on multi-class classifiers based on tree tensor network and multiscale entanglement renormalization …
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not 'optimal' either in terms of the circuit depth (and therefore the error burden) or the specifics of the target platform, i.e. the native gates and topology of a system. This work introduces a variational compiler for efficiently finding the encoding circuit of general quantum error correcting codes with given quantum hardware. Focusing on the noi…
Efficient methods for encoding and compression are likely to pave way towards the problem of efficient trainability on higher dimensional Hilbert spaces overcoming issues of barren plateaus. Here we propose an alternative approach to variational autoencoders to reduce the dimensionality of states represented in higher dimensional Hilbert spaces. To this end we build a variational based autoencoder circuit that takes as input a dataset and optimizes the parameters of Parameterized Quantum Circuit (PQC) ansatz to produce an output state that can be represented as tensor product of 2 subsystems b…
Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits
Georgia Institute of Technology（佐治亚理工学院）；NVIDIA Research（NVIDIA研究）；IBM Research（IBM研究）；Hon Hai (Foxconn) Quantum Computing Research Center（鸿海（富士康）量子计算研究中心）
In recent years, quantum machine learning has seen a substantial increase in the use of variational quantum circuits (VQCs). VQCs are inspired by artificial neural networks, which achieve extraordinary performance in a wide range of AI tasks as massively parameterized function approximators. VQCs have already demonstrated promising results, for example, in generalization and the requirement for fewer parameters to train, by utilizing the more robust algorithmic toolbox available in quantum computing. A VQCs' trainable parameters or weights are usually used as angles in rotational gates and cur…
Machine learning has achieved dramatic success in a broad spectrum of applications. Its interplay with quantum physics may lead to unprecedented perspectives for both fundamental research and commercial applications, giving rise to an emergent research frontier of quantum machine learning. Along this line, quantum classifiers, which are quantum devices that aim to solve classification problems in machine learning, have attracted tremendous attention recently. In this review, we give a relatively comprehensive overview for the studies of quantum classifiers, with a focus on recent advances. Fir…
The current generation of quantum computing technologies call for quantum algorithms that require a limited number of qubits and quantum gates, and which are robust against errors. A suitable design approach are variational circuits where the parameters of gates are learnt, an approach that is particularly fruitful for applications in machine learning. In this paper, we propose a low-depth variational quantum algorithm for supervised learning. The input feature vectors are encoded into the amplitudes of a quantum system, and a quantum circuit of parametrised single and two-qubit gates together…
One of the major objectives of the experimental programs at the LHC is the discovery of new physics. This requires the identification of rare signals in immense backgrounds. Using machine learning algorithms greatly enhances our ability to achieve this objective. With the progress of quantum technologies, quantum machine learning could become a powerful tool for data analysis in high energy physics. In this study, using IBM gate-model quantum computing systems, we employ the quantum variational classifier method in two recent LHC flagship physics analyses: $t\bar{t}H$ (Higgs boson production i…
Quantum computers can be used for supervised learning by treating parametrised quantum circuits as models that map data inputs to predictions. While a lot of work has been done to investigate practical implications of this approach, many important theoretical properties of these models remain unknown. Here we investigate how the strategy with which data is encoded into the model influences the expressive power of parametrised quantum circuits as function approximators. We show that one can naturally write a quantum model as a partial Fourier series in the data, where the accessible frequencies…
IT4Innovations, VSB - Technical University of Ostrava（IT4Innovations奥斯特拉瓦技术大学）；Faculty of Electrical Engineering and Computer Science, VSB - Technical University of Ostrava（电气工程与计算机科学学院，奥斯特拉瓦技术大学）
Many applications of quantum computing in the near term rely on variational quantum circuits (VQCs). They have been showcased as a promising model for reaching a quantum advantage in machine learning with current noisy intermediate scale quantum computers (NISQ). It is often believed that the power of VQCs relies on their exponentially large feature space, and extensive works have explored the expressiveness and trainability of VQCs in that regard. In our work, we propose a classical sampling method that may closely approximate a VQC with Hamiltonian encoding, given only the description of its…
Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components of a given real-valued data vector into the amplitude of quantum state, while the previous proposal can only load the absolute values of those components. The key of our algorithm is to variationally train a shallow parameterized quantum circuit, using the results of two types of measurement; the standard computational-basis measurement plus the measurement…
The aim of this paper is to provide a quantum counterpart of the well known minimum-distance classifier named Nearest Mean Classifier (NMC). In particular, we refer to the following previous works: i) in Sergioli et al. 2016, we have introduced a detailed quantum version of the NMC, named Quantum Nearest Mean Classifier (QNMC), for two-dimensional problems and we have proposed a generalization to abitrary dimensions; ii) in Sergioli et al. 2017, the n-dimensional problem was analyzed in detail and a particular encoding for arbitrary n-feature vectors into density operators has been presented. …
Quantum machine learning has emerged as a potential practical application of near-term quantum devices. In this work, we study a two-layer hybrid classical-quantum classifier in which a first layer of quantum stochastic neurons implementing generalized linear models (QGLMs) is followed by a second classical combining layer. The input to the first, hidden, layer is obtained via amplitude encoding in order to leverage the exponential size of the fan-in of the quantum neurons in the number of qubits per neuron. To facilitate implementation of the QGLMs, all weights and activations are binary. Whi…
Banasthali Vidyapith（巴纳斯塔利大学）；Umm Al Quwain University（乌姆盖万大学）
In this paper, we have studied the performance and role of local optimizers in quantum variational circuits. We studied the performance of the two most popular optimizers and compared their results with some popular classical machine learning algorithms. The classical algorithms we used in our study are support vector machine (SVM), gradient boosting (GB), and random forest (RF). These were compared with a variational quantum classifier (VQC) using two sets of local optimizers viz AQGD and COBYLA. For experimenting with VQC, IBM Quantum Experience and IBM Qiskit was used while for classical ma…
Solving the traveling salesman problem on $\lceil \log_2 (N-1)! \rceil$ qubits with a variational quantum Kolmogorov--Arnold network: exact-gradient CVaR training and generalization over time-dependent graphs
Brookhaven National Laboratory（布鲁克海文国家实验室）；National Taiwan University（台湾大学）
One key step in performing quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices is the dimension reduction of the input data prior to their encoding. Traditional principle component analysis (PCA) and neural networks have been used to perform this task; however, the classical and quantum layers are usually trained separately. A framework that allows for a better integration of the two key components is thus highly desirable. Here we introduce a hybrid model combining the quantum-inspired tensor networks (TN) and the variational quantum circuits (VQC) to perform sup…
