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Adaptive Online Learning of Quantum States

Xinyi Chen, Elad Hazan, Tongyang Li, Zhou Lu, Xinzhao Wang, Rui Yang

Jun 02 2022 cs.LG quant-ph arXiv:2206.00220v1

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In the fundamental problem of shadow tomography, the goal is to efficiently learn an unknown dd-dimensional quantum state using projective measurements. However, it is rarely the case that the underlying state remains stationary: changes may occur due to measurements, environmental noise, or an underlying Hamiltonian state evolution. In this paper we adopt tools from adaptive online learning to learn a changing state, giving adaptive and dynamic regret bounds for online shadow tomography that are polynomial in the number of qubits and sublinear in the number of measurements. Our analysis utilizes tools from complex matrix analysis to cope with complex numbers, which may be of independent interest in online learning. In addition, we provide numerical experiments that corroborate our theoretical results.

Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz

Antonio Anna Mele, Glen Bigan Mbeng, Giuseppe Ernesto Santoro, Mario Collura, Pietro Torta

Jun 07 2022 quant-ph arXiv:2206.01982v1

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A large ongoing research effort focuses on Variational Quantum Algorithms (VQAs), representing leading candidates to achieve computational speed-ups on current quantum devices. The scalability of VQAs to a large number of qubits, beyond the simulation capabilities of classical computers, is still debated. Two major hurdles are the proliferation of low-quality variational local minima, and the exponential vanishing of gradients in the cost function landscape, a phenomenon referred to as barren plateaus. Here we show that by employing iterative search schemes one can effectively prepare the ground state of paradigmatic quantum many-body models, circumventing also the barren plateau phenomenon. This is accomplished by leveraging the transferability to larger system sizes of iterative solutions, displaying an intrinsic smoothness of the variational parameters, a result that does not extend to other solutions found via random-start local optimization. Our scheme could be directly tested on near-term quantum devices, running a refinement optimization in a favorable local landscape with non-vanishing gradients.

Quantum Neural Network Classifiers: A Tutorial

Weikang Li, Zhide Lu, Dong-Ling Deng

Jun 08 2022 quant-ph cond-mat.dis-nn cs.AI cs.LG arXiv:2206.02806v1

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Machine learning has achieved dramatic success over the past decade, with applications ranging from face recognition to natural language processing. Meanwhile, rapid progress has been made in the field of quantum computation including developing both powerful quantum algorithms and advanced quantum devices. The interplay between machine learning and quantum physics holds the intriguing potential for bringing practical applications to the modern society. Here, we focus on quantum neural networks in the form of parameterized quantum circuits. We will mainly discuss different structures and encoding strategies of quantum neural networks for supervised learning tasks, and benchmark their performance utilizing Yao.jl, a quantum simulation package written in Julia Language. The codes are efficient, aiming to provide convenience for beginners in scientific works such as developing powerful variational quantum learning models and assisting the corresponding experimental demonstrations.

Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm

Danylo Lykov, Jonathan Wurtz, Cody Poole, Mark Saffman, Tom Noel, Yuri Alexeev

Jun 09 2022 quant-ph cs.CC arXiv:2206.03579v1

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In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs. The goal is to identify under which conditions QAOA can achieve “quantum advantage” over classical algorithms, in terms of both solution quality and time to solution. One might be able to achieve quantum advantage on hundreds of qubits and moderate depth pp by sampling the QAOA state at a frequency of order 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linearlinear time complexity. In order to match this quality for largelarge graph sizes NN, a quantum device must support depth p>11p>11. Otherwise, we demonstrate that the number of required samples grows exponentially with NN, hindering the scalability of QAOA with p≤11p≤11. These results put challenging bounds on achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, maximum independent set, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.

Entanglement entropy production in Quantum Neural Networks

Marco Ballarin, Stefano Mangini, Simone Montangero, Chiara Macchiavello, Riccardo Mengoni

Jun 07 2022 quant-ph arXiv:2206.02474v1

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Quantum Neural Networks (QNN) are considered a candidate for achieving quantum advantage in the Noisy Intermediate Scale Quantum computer (NISQ) era. Several QNN architectures have been proposed and successfully tested on benchmark datasets for machine learning. However, quantitative studies of the QNN-generated entanglement have not been investigated in details, and only for up to few qubits. Tensor network methods allow to emulate quantum circuits with a large number of qubits in a wide variety of scenarios. Here, we employ matrix product states to characterize recently studied QNN architectures with up to fifty qubits showing that their entanglement, measured in terms of entanglement entropy between qubits, tends to that of Haar distributed random states as the depth of the QNN is increased. We show a universal behavior for the entanglement entropy production for any given QNN architecture, consequently we introduce a new measure to characterize the entanglement production in QNNs: the entangling speed. Finally, in agreement with known results in the literature, we argue that the most promising regime for quantum advantage with QNNs is defined by a trade-off between high entanglement and expressibility.

Predict better with less training data using a QNN

Barry D. Reese, Marek Kowalik, Christian Metzl, Christian Bauckhage, Eldar Sultanow

Jun 09 2022 quant-ph cs.LG arXiv:2206.03960v1

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Over the past decade, machine learning revolutionized vision-based quality assessment for which convolutional neural networks (CNNs) have now become the standard. In this paper, we consider a potential next step in this development and describe a quanvolutional neural network (QNN) algorithm that efficiently maps classical image data to quantum states and allows for reliable image analysis. We practically demonstrate how to leverage quantum devices in computer vision and how to introduce quantum convolutions into classical CNNs. Dealing with a real world use case in industrial quality control, we implement our hybrid QNN model within the PennyLane framework and empirically observe it to achieve better predictions using much fewer training data than classical CNNs. In other words, we empirically observe a genuine quantum advantage for an industrial application where the advantage is due to superior data encoding.

Recent Advances for Quantum Neural Networks in Generative Learning

Jinkai Tian, Xiaoyu Sun, Yuxuan Du, Shanshan Zhao, Qing Liu, Kaining Zhang, Wei Yi, Wanrong Huang, Chaoyue Wang, Xingyao Wu, Min-Hsiu Hsieh, Tongliang Liu, Wenjing Yang, Dacheng Tao

Jun 08 2022 quant-ph cs.CV cs.LG arXiv:2206.03066v1

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Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relation and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.

QMLP: An Error-Tolerant Nonlinear Quantum MLP Architecture using Parameterized Two-Qubit Gates

Cheng Chu, Nai-Hui Chia, Lei Jiang, Fan Chen

Jun 06 2022 cs.ET quant-ph arXiv:2206.01345v1

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Despite potential quantum supremacy, state-of-the-art quantum neural networks (QNNs) suffer from low inference accuracy. First, the current Noisy Intermediate-Scale Quantum (NISQ) devices with high error rates of 0.001 to 0.01 significantly degrade the accuracy of a QNN. Second, although recently proposed Re-Uploading Units (RUUs) introduce some non-linearity into the QNN circuits, the theory behind it is not fully understood. Furthermore, previous RUUs that repeatedly upload original data can only provide marginal accuracy improvements. Third, current QNN circuit ansatz uses fixed two-qubit gates to enforce maximum entanglement capability, making task-specific entanglement tuning impossible, resulting in poor overall performance. In this paper, we propose a Quantum Multilayer Perceptron (QMLP) architecture featured by error-tolerant input embedding, rich nonlinearity, and enhanced variational circuit ansatz with parameterized two-qubit entangling gates. Compared to prior arts, QMLP increases the inference accuracy on the 10-class MNIST dataset by 10% with 2 times fewer quantum gates and 3 times reduced parameters. Our source code is available and can be found in [1]

Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform

Marco A. S. Trindade, Vinicius N. L. Rocha, S. Floquet

Jun 07 2022 quant-ph math-ph math.MP arXiv:2206.01808v1

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We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras are the natural framework for multidimensional data analysis in a quantum setting. Implementation of activation functions and unitary learning rules are discussed. In this scheme, we also provide an algebraic generalization of the quantum Fourier transform containing additional parameters that allow performing quantum machine learning. Furthermore, some interesting properties of the generalized quantum Fourier transform have been proved.

Near-Term Advances in Quantum Natural Language Processing

Dominic Widdows, Daiwei Zhu, Chase Zimmerman

Jun 07 2022 cs.CL quant-ph arXiv:2206.02171v1

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This paper describes experiments showing that some problems in natural language processing can already be addressed using quantum computers. The examples presented here include topic classification using both a quantum support vector machine and a bag-of-words approach, bigram modeling that can be applied to sequences of words and formal concepts, and ambiguity resolution in verb-noun composition. While the datasets used are still small, the systems described have been run on physical quantum computers. These implementations and their results are described along with the algorithms and mathematical approaches used.

Error mitigation for quantum kernel based machine learning methods on IonQ and IBM quantum computers

Sasan Moradi, Christoph Brandner, Macauley Coggins, Robert Wille, Wolfgang Drexler, Laszlo Papp

Jun 06 2022 quant-ph arXiv:2206.01573v2

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Kernel methods are the basis of most classical machine learning algorithms such as Gaussian Process (GP) and Support Vector Machine (SVM). Computing kernels using noisy intermediate scale quantum (NISQ) devices has attracted considerable attention due to recent progress in the design of NISQ devices. However noise and errors on current NISQ devices can negatively affect the predicted kernels. In this paper we utilize two quantum kernel machine learning (ML) algorithms to predict the labels of a Breast Cancer dataset on two different NISQ devices: quantum kernel Gaussian Process (qkGP) and quantum kernel Support Vector Machine (qkSVM). We estimate the quantum kernels on the 11 qubit IonQ and the 5 qubit IBMQ Belem quantum devices. Our results demonstrate that the predictive performances of the error mitigated quantum kernel machine learning algorithms improve significantly compared to their non-error mitigated counterparts. On both NISQ devices the predictive performances became comparable to those of noiseless quantum simulators and their classical counterparts

Optimize cooling-by-measurement by reinforcement learning

Jia-shun Yan, Jun Jing

Jun 02 2022 quant-ph arXiv:2206.00246v1

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Cooling by the conditional measurement demonstrates a transparent advantage over that by the unconditional counterpart on the average-population-reduction rate. This advantage, however, is blemished by few percentage of the successful probability of finding the detector system in the measured state. In this work, we propose an optimized architecture to cool down a target resonator, which is initialized as a thermal state, using an interpolation of the conditional and unconditional measurement strategies. Analogous to the conditional measurement, an optimal measurement-interval τuoptτoptu for the unconditional (nonselective) measurement is analytically found for the first time, which is inversely proportional to the collective dominant Rabi frequency ΩdΩd as a function of the resonator’s population at the end of the last round. A cooling algorithm under the global optimization by the reinforcement learning results in the maximum value for the cooperative cooling performance, an indicator function to quantify the comprehensive cooling efficiency for arbitrary cooling-by-measurement architecture. In particular, the average population of the target resonator under only 1616 rounds of measurements can be reduced by over four orders in magnitude with a successful probability about 30%30%.

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