Hybrid quantum-classical classifier based on tensor network and variational quantum circuit
Brookhaven National Laboratory（布鲁克海文国家实验室）；National Taiwan University（台湾大学）
Samuel Yen-Chi Chen, Chih-Min Huang, Chia-Wei Hsing, Ying-Jer Kao
备注：
8 pages, 7 figures, and 1 table. Proceeding for the First Workshop on Quantum Tensor Networks in Machine Learning, 34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada
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 supervised learning tasks, which allows for an end-to-end training. We show that a matrix product state based TN with low bond dimensions performs better than PCA as a feature extractor to compress data for the input of VQCs in the binary classification of MNIST dataset. The architecture is highly adaptable and can easily incorporate extra quantum resource when available.
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…
Impact of Circuit Depth versus Qubit Count on Variational Quantum Classifiers for Higgs Boson Signal Detection
School of Computing, Universiti Utara Malaysia（乌拉尔大学计算机学院）；Faculty of Science and Technology, UIN Sunan Gunung Djati Bandung（Sunan Gunung Djati Bandung大学科学与技术学院）
Sub-universal variational circuits for combinatorial optimization problems
Department of Physics, University of Colorado Boulder, Boulder, CO 80309, USA（科罗拉多大学博尔德分校物理系）；University of Technology Sydney, Centre for Quantum Software（悉尼技术大学量子软件中心）；Department of Electrical, Computer and Energy Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA（科罗拉多大学博尔德分校电气、计算机与能源工程系）
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…
We propose a method for finding approximate compilations of quantum unitary transformations, based on techniques from policy gradient reinforcement learning. The choice of a stochastic policy allows us to rephrase the optimization problem in terms of probability distributions, rather than variational gates. In this framework, the optimal configuration is found by optimizing over distribution parameters, rather than over free angles. We show numerically that this approach can be more competitive than gradient-free methods, for a comparable amount of resources, both for noiseless and noisy circu…
Quantum Machine Learning (QML) is considered to be one of the most promising applications of near term quantum devices. However, the optimization of quantum machine learning models presents numerous challenges arising from the imperfections of hardware and the fundamental obstacles in navigating an exponentially scaling Hilbert space. In this work, we evaluate the potential of contemporary methods in deep reinforcement learning to augment gradient based optimization routines in quantum variational circuits. We find that reinforcement learning augmented optimizers consistently outperform gradie…
University of Minho（米尼奥大学）；INESC TEC（葡萄牙系统与计算机工程研究所（INESC TEC））；International Nanotechnology Laboratory (INL)（国际纳米技术实验室（INL））
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 …
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…
National University of Defense Technology（国防科技大学）；National Innovation Institute of Defense Technology（国防科技创新研究院）
Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth, so that only polynomial measurements are required, even for highly-entangled states. After that, a subsequent classical circuit simulator is used to transform the information of the target …
Delhi Technological University（德里理工大学）；CHRIST (Deemed to be University)（克里斯大学（被视为大学））
There are numerous models of quantum neural networks that have been applied to variegated problems such as image classification, pattern recognition etc.Quantum inspired algorithms have been relevant for quite awhile. More recently, in the NISQ era, hybrid quantum classical models have shown promising results. Multi-feature regression is common problem in classical machine learning. Hence we present a comparative analysis of continuous variable quantum neural networks (Variational circuits) and quantum backpropagating multi layer perceptron (QBMLP). We have chosen the contemporary problem of p…
In this paper, classical and continuous variable (CV) quantum neural network hybrid multiclassifiers are presented using the MNIST dataset. The combination of cutoff dimension and probability measurement method in the CV model allows a quantum circuit to produce output vectors of size equal to n raised to the power of n where n represents cutoff dimension and m, the number of qumodes. They are then translated as one-hot encoded labels, padded with an appropriate number of zeros. The total of eight different classifiers are built using 2,3,...,8 qumodes, based on the binary classifier architect…
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…
Provably Robust Training of Quantum Circuit Classifiers Against Parameter Noise
Computer Science, University of California Los Angeles（计算机科学，加州大学洛杉矶分校）；Electrical and Computer Engineering, University of California Los Angeles（电气与计算机工程，加州大学洛杉矶分校）
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）
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Department of Computer Science（计算机科学系）；Troy NY, USA（美国纽约州特洛伊市（此处仅为地址信息，根据提取规则应忽略，正确仅保留大学））
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new parameters at every optimization step. However, this process can be extremely challenging, due to the nature of navigating the exponentially scaling complex Hilbert space, barren plateaus, and the noise present in all foreseeable quantum hardware. Although a variety of optimization algorithms are employed in practice, there is often a lack of theoretical or empiri…
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 …
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 t…
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate reinforcement learning problems. Quantum computing approaches offer important potential improvements in time and space complexity over traditional algorithms because of its ability to exploit the quantum phenomena of superposition and entanglement. Specifically, we investigate the use of quantum variational circuits, a form of quantum machine learning. We present…
Maximising Quantum-Computing Expressive Power through Randomised Circuits
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）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to design variational circuits is to base the circuit architecture on tensor networks. Here, we comprehensively describe tensor-network quantum circuits and how to implement them in simulations. This includes leveraging circuit cutting, a technique used to evaluate circuits with more qubits than those available on current quantum devices. We then illustrate the …
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…
We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a Symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally trained unitary that maps any vector output by ansatz A(~α) from a defined subspace to a vector in the symmetry space. The parameters are trained varitionally to minimize the energy thus keeping the output within the labelled symmetry value. The method was tested for a spin XXZ hamiltonian using rotation and reflection symmetry and H2 hamiltonian within S_z = 0 …
National Taiwan University（台湾大学）；Georgia Institute of Technology（佐治亚理工学院）；IBM Research（IBM研究院）
The state-of-the-art machine learning approaches are based on classical von Neumann computing architectures and have been widely used in many industrial and academic domains. With the recent development of quantum computing, researchers and tech-giants have attempted new quantum circuits for machine learning tasks. However, the existing quantum computing platforms are hard to simulate classical deep learning models or problems because of the intractability of deep quantum circuits. Thus, it is necessary to design feasible quantum algorithms for quantum machine learning for noisy intermediate s…
We demonstrate the simulation of a noncollinear molecule, e.g. H2O molecule using Variational Quantum Eigensolver (VQE) with high chemical accuracy. The 2D and 3D potential energy surface (PES) were reported. Taking advantage of the potential speedup in Qiskit runtime program, the optimal initial parameters for the variational quantum circuits were obtained after several consecutive iterations, thus resulting in accurate prediction of water's PES matching result obtained from exact diagonalization of the full Hamiltonian.
We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.
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…
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 …
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…
Institute for Advanced Study（高等研究院）；Samsung Research（三星研究院）；Korea Institute for Advanced Study（韩国高等研究院）；Korea Advanced Institute of Science and Technology（韩国科学技术院）
We explore the effectiveness of variational quantum circuits in simulating the ground states of quantum many-body Hamiltonians. We show that generic high-depth circuits, performing a sequence of layer unitaries of the same form, can accurately approximate the desired states. We demonstrate their universal success by using two Hamiltonian systems with very different properties: the transverse field Ising model and the Sachdev-Ye-Kitaev model. The energy landscape of the high-depth circuits has a proper structure for the gradient-based optimization, i.e. the presence of local extrema -- near any…
We propose a hybrid quantum-classical approach to model continuous classical probability distributions using a variational quantum circuit. The architecture of the variational circuit consists of two parts: a quantum circuit employed to encode a classical random variable into a quantum state, called the quantum encoder, and a variational circuit whose parameters are optimized to mimic a target probability distribution. Samples are generated by measuring the expectation values of a set of operators chosen at the beginning of the calculation. Our quantum generator can be complemented with a clas…
Image Classification with Rotation-Invariant Variational Quantum Circuits
Ikerlan Technology Research Centre, Basque Research and Technology Alliance (BRTA)（伊克兰技术研究中心、巴斯克研究与技术联盟）；Donostia International Physics Center（多诺西亚国际物理中心）
This paper proposes a hybrid quantum-classical algorithm that learns a suitable quantum feature map that separates unlabelled data that is originally non linearly separable in the classical space using a Variational quantum feature map and q-means as a subroutine for unsupervised learning. The objective of the Variational circuit is to maximally separate the clusters in the quantum feature Hilbert space. First part of the circuit embeds the classical data into quantum states. Second part performs unsupervised learning on the quantum states in the quantum feature Hilbert space using the q-means…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the capacity of current quantum devices. To reduce the quantum circuit complexity, it has been suggested to incorporate a part of the electronic correlation into an effective Hamiltonian, which is often obtained from a similarity transformation of the electronic Hamiltonian. In this work, we introduce a new transformation in the form of a product of a linear com…
