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Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm

Charles Moussa, Hao Wang, Thomas Bäck, Vedran Dunjko

Feb 22 2022 quant-ph arXiv:2202.09408v1

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As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of the quantum circuit output. One of these algorithms, the Quantum Approximate Optimization Algorithm stands out as a promising approach to tackle combinatorial problems, due to many interesting properties. However finding the appropriate parameters is a difficult task. Although QAOA exhibits concentration properties, they can depend on instances characteristics which may not be easy to identify, but may nonetheless offer useful information to find good parameters. In this work, we study unsupervised Machine Learning approaches for setting these parameters without optimization. We perform clustering with the angle values but also instances encodings (using instance features or the output of a variational graph autoencoder), and compare different approaches. These angle-fiding strategies can be used to reduce calls to quantum circuits when leveraging QAOA as a subroutine. We showcase them within Recursive-QAOA up to depth 33 where the number of QAOA parameters used per iteration is limited to 3, achieving a median approximation ratio of 0.94 for MaxCut over 200 Erdős-Rényi graphs. We obtain similar performances to the case where we extensively optimize the angles, hence saving numerous circuit calls.

A tensor network discriminator architecture for classification of quantum data on quantum computers

Michael L. Wall, Paraj Titum, Gregory Quiroz, Michael Foss-Feig, Kaden R. A. Hazzard

Feb 23 2022 quant-ph arXiv:2202.10911v1

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We demonstrate the use of matrix product state (MPS) models for discriminating quantum data on quantum computers using holographic algorithms, focusing on classifying a translationally invariant quantum state based on LL qubits of quantum data extracted from it. We detail a process in which data from single-shot experimental measurements are used to optimize an isometric tensor network, the tensors are compiled into unitary quantum operations using greedy compilation heuristics, parameter optimization on the resulting quantum circuit model removes the post-selection requirements of the isometric tensor model, and the resulting quantum model is inferenced on either product state or entangled quantum data. We demonstrate our training and inference architecture on a synthetic dataset of six-site single-shot measurements from the bulk of a one-dimensional transverse field Ising model (TFIM) deep in its antiferromagnetic and paramagnetic phases. We experimentally evaluate models on Quantinuum’s H1-2 trapped ion quantum computer using entangled input data modeled as translationally invariant, bond dimension 4 MPSs across the known quantum phase transition of the TFIM. Using linear regression on the experimental data near the transition point, we find predictions for the critical transverse field of h=0.962h=0.962 and 0.9940.994 for tensor network discriminators of bond dimension χ=2χ=2 and χ=4χ=4, respectively. These predictions compare favorably with the known transition location of h=1h=1 despite training on data far from the transition point. Our techniques identify families of short-depth variational quantum circuits in a data-driven and hardware-aware fashion and robust classical techniques to precondition the model parameters, and can be adapted beyond machine learning to myriad applications of tensor networks on quantum computers, such as quantum simulation and error correction.

From Quantum Graph Computing to Quantum Graph Learning: A Survey

Yehui Tang, Junchi Yan, Hancock Edwin

Feb 22 2022 quant-ph cs.LG arXiv:2202.09506v1

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Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational power. In this paper, we provide a targeted survey of the development of QC for graph-related tasks. We first elaborate the correlations between quantum mechanics and graph theory to show that quantum computers are able to generate useful solutions that can not be produced by classical systems efficiently for some problems related to graphs. For its practicability and wide-applicability, we give a brief review of typical graph learning techniques designed for various tasks. Inspired by these powerful methods, we note that advanced quantum algorithms have been proposed for characterizing the graph structures. We give a snapshot of quantum graph learning where expectations serve as a catalyst for subsequent research. We further discuss the challenges of using quantum algorithms in graph learning, and future directions towards more flexible and versatile quantum graph learning solvers.

Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions

Simone Tibaldi, Giuseppe Magnifico, Davide Vodola, Elisa Ercolessi

Feb 21 2022 cond-mat.supr-con cond-mat.dis-nn quant-ph arXiv:2202.09281v1

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The recent advances in machine learning algorithms have boosted the application of these techniques to the field of condensed matter physics, in order e.g. to classify the phases of matter at equilibrium or to predict the real-time dynamics of a large class of physical models. Typically in these works, a machine learning algorithm is trained and tested on data coming from the same physical model. Here we demonstrate that unsupervised and supervised machine learning techniques are able to predict phases of a non-exactly solvable model when trained on data of a solvable model. In particular, we employ a training set made by single-particle correlation functions of a non-interacting quantum wire and by using principal component analysis, k-means clustering, and convolutional neural networks we reconstruct the phase diagram of an interacting superconductor. We show that both the principal component analysis and the convolutional neural networks trained on the data of the non-interacting model can identify the topological phases of the interacting model with a high degree of accuracy. Our findings indicate that non-trivial phases of matter emerging from the presence of interactions can be identified by means of unsupervised and supervised techniques applied to data of non-interacting systems.

Pulse based Variational Quantum Optimal Control for hybrid quantum computing

Robert de Keijzer, Oliver Tse, Servaas Kokkelmans

Feb 21 2022 quant-ph arXiv:2202.08908v1

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This work studies pulse based variational quantum algorithms (VQAs), which are designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. In contrast to more standard gate based methods, pulse based methods aim to directly optimize the laser pulses interacting with the qubits, instead of using some parametrized gate based circuit. Using the mathematical formalism of optimal control, these laser pulses are optimized. This method has been used in quantum computing to optimize pulses for quantum gate implementations, but has only recently been proposed for full optimization in VQAs. Pulse based methods have several advantages over gate based methods such as faster state preparation, simpler implementation and more freedom in moving through the state space. Based on these ideas, we present the development of a novel adjoint based variational method. This method can be tailored towards and applied in neutral atom quantum computers. This method of pulse based variational quantum optimal control is able to approximate molecular ground states of simple molecules up to chemical accuracy and is able to compete with the gate based variational quantum eigensolver in terms of total number of quantum evaluations. The total evolution time TT and the form of the control Hamiltonian HcHc are important factors in the convergence behavior to the ground state energy, both having influence on the quantum speed limit and the controllability of the system.

Completely Quantum Neural Networks

Steve Abel, Juan C. Criado, Michael Spannowsky

Feb 25 2022 quant-ph cs.LG hep-ph hep-th arXiv:2202.11727v1

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Artificial neural networks are at the heart of modern deep learning algorithms. We describe how to embed and train a general neural network in a quantum annealer without introducing any classical element in training. To implement the network on a state-of-the-art quantum annealer, we develop three crucial ingredients: binary encoding the free parameters of the network, polynomial approximation of the activation function, and reduction of binary higher-order polynomials into quadratic ones. Together, these ideas allow encoding the loss function as an Ising model Hamiltonian. The quantum annealer then trains the network by finding the ground state. We implement this for an elementary network and illustrate the advantages of quantum training: its consistency in finding the global minimum of the loss function and the fact that the network training converges in a single annealing step, which leads to short training times while maintaining a high classification performance. Our approach opens a novel avenue for the quantum training of general machine learning models.

Improved variational quantum eigensolver via quasi-dynamical evolution

Manpreet Singh Jattana, Fengping Jin, Hans De Raedt, Kristel Michielsen

Feb 22 2022 quant-ph arXiv:2202.10130v1

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The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There are problems with VQE that forbid a favourable scaling towards quantum advantage. In order to alleviate the problems, we propose and extensively test a quantum annealing inspired heuristic that supplements VQE. The improved VQE enables an efficient initial state preparation mechanism, in a recursive manner, for a quasi-dynamical unitary evolution. We conduct an in-depth scaling analysis of finding the ground state energies with increasing lattice sizes of the Heisenberg model, employing simulations of up to 4040 qubits that manipulate the complete state vector. For the current devices, we further propose a benchmarking toolkit using a mean-field model and test it on IBM Q devices. The improved VQE avoids barren plateaus, exits local minima, and works with low-depth circuits. Realistic gate execution times estimate a longer computational time to complete the same computation on a fully functional error-free quantum computer than on a quantum computer emulator implemented on a classical computer. However, our proposal can be expected to help accurate estimations of the ground state energies beyond 5050 qubits when the complete state vector can no longer be stored on a classical computer, thus enabling quantum advantage.

Quantum Deep Reinforcement Learning for Robot Navigation Tasks

Dirk Heimann, Hans Hohenfeld, Felix Wiebe, Frank Kirchner

Feb 25 2022 cs.RO cs.LG quant-ph arXiv:2202.12180v1

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In this work, we utilize Quantum Deep Reinforcement Learning as method to learn navigation tasks for a simple, wheeled robot in three simulated environments of increasing complexity. We show similar performance of a parameterized quantum circuit trained with well established deep reinforcement learning techniques in a hybrid quantum-classical setup compared to a classical baseline. To our knowledge this is the first demonstration of quantum machine learning (QML) for robotic behaviors. Thus, we establish robotics as a viable field of study for QML algorithms and henceforth quantum computing and quantum machine learning as potential techniques for future advancements in autonomous robotics. Beyond that, we discuss current limitations of the presented approach as well as future research directions in the field of quantum machine learning for autonomous robots.

Quantum Heterogeneous Distributed Deep Learning Architectures: Models, Discussions, and Applications

Yunseok Kwak, Won Joon Yun, Jae Pyoung Kim, Hyunhee Cho, Minseok Choi, Soyi Jung, Joongheon Kim

Feb 24 2022 quant-ph cs.AI cs.ET cs.LG cs.NE cs.NI arXiv:2202.11200v1

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Deep learning (DL) has already become a state-of-the-art technology for various data processing tasks. However, data security and computational overload problems frequently occur due to their high data and computational power dependence. To solve this problem, quantum deep learning (QDL) and distributed deep learning (DDL) are emerging to complement existing DL methods by reducing computational overhead and strengthening data security. Furthermore, a quantum distributed deep learning (QDDL) technique that combines these advantages and maximizes them is in the spotlight. QDL takes computational gains by replacing deep learning computations on local devices and servers with quantum deep learning. On the other hand, besides the advantages of the existing distributed learning structure, it can increase data security by using a quantum secure communication protocol between the server and the client. Although many attempts have been made to confirm and demonstrate these various possibilities, QDDL research is still in its infancy. This paper discusses the model structure studied so far and its possibilities and limitations to introduce and promote these studies. It also discusses the areas of applied research so far and in the future and the possibilities of new methodologies.

Study of Feature Importance for Quantum Machine Learning Models

Aaron Baughman, Kavitha Yogaraj, Raja Hebbar, Sudeep Ghosh, Rukhsan Ul Haq, Yoshika Chhabra

Feb 24 2022 quant-ph cs.LG arXiv:2202.11204v2

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Predictor importance is a crucial part of data preprocessing pipelines in classical and quantum machine learning (QML). This work presents the first study of its kind in which feature importance for QML models has been explored and contrasted against their classical machine learning (CML) equivalents. We developed a hybrid quantum-classical architecture where QML models are trained and feature importance values are calculated from classical algorithms on a real-world dataset. This architecture has been implemented on ESPN Fantasy Football data using Qiskit statevector simulators and IBM quantum hardware such as the IBMQ Mumbai and IBMQ Montreal systems. Even though we are in the Noisy Intermediate-Scale Quantum (NISQ) era, the physical quantum computing results are promising. To facilitate current quantum scale, we created a data tiering, model aggregation, and novel validation methods. Notably, the feature importance magnitudes from the quantum models had a much higher variation when contrasted to classical models. We can show that equivalent QML and CML models are complementary through diversity measurements. The diversity between QML and CML demonstrates that both approaches can contribute to a solution in different ways. Within this paper we focus on Quantum Support Vector Classifiers (QSVC), Variational Quantum Circuit (VQC), and their classical counterparts. The ESPN and IBM fantasy footballs Trade Assistant combines advanced statistical analysis with the natural language processing of Watson Discovery to serve up personalized trade recommendations that are fair and proposes a trade. Here, player valuation data of each player has been considered and this work can be extended to calculate the feature importance of other QML models such as Quantum Boltzmann machines.

Machine-learning assisted quantum control in random environment

Tang-You Huang, Yue Ban, E. Ya. Sherman, Xi Chen

Feb 22 2022 cond-mat.dis-nn quant-ph arXiv:2202.10291v1

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Disorder in condensed matter and atomic physics is responsible for a great variety of fascinating quantum phenomena, which are still challenging for understanding, not to mention the relevant dynamical control. Here we introduce proof of the concept and analyze neural network-based machine learning algorithm for achieving feasible high-fidelity quantum control of a particle in random environment. To explicitly demonstrate its capabilities, we show that convolutional neural networks are able to solve this problem as they can recognize the disorder and, by supervised learning, further produce the policy for the efficient low-energy cost control of a quantum particle in a time-dependent random potential. We have shown that the accuracy of the proposed algorithm is enhanced by a higher-dimensional mapping of the disorder pattern and using two neural networks, each properly trained for the given task. The designed method, being computationally more efficient than the gradient-descent optimization, can be applicable to identify and control various noisy quantum systems on a heuristic basis.

Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data

Jack Y. Araz, Michael Spannowsky

Feb 23 2022 quant-ph cs.LG hep-ex hep-ph arXiv:2202.10471v1

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Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum circuits in the context of Machine Learning on highly complex, simulated LHC data. We show that classical TNs require exponentially large bond dimensions and higher Hilbert-space mapping to perform comparably to their quantum counterparts. While such an expansion in the dimensionality allows better performance, we observe that, with increased dimensionality, classical TNs lead to a highly flat loss landscape, rendering the usage of gradient-based optimization methods highly challenging. Furthermore, by employing quantitative metrics, such as the Fisher information and effective dimensions, we show that classical TNs require a more extensive training sample to represent the data as efficiently as TN-inspired quantum circuits. We also engage with the idea of hybrid classical-quantum TNs and show possible architectures to employ a larger phase-space from the data. We offer our results using three main TN ansatz: Tree Tensor Networks, Matrix Product States, and Multi-scale Entanglement Renormalisation Ansatz.

Translational Quantum Machine Intelligence for Modeling Tumor Dynamics in Oncology

Nam Nguyen, Kwang-Cheng Chen

Feb 23 2022 q-bio.OT quant-ph arXiv:2202.10919v1

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Quantifying the dynamics of tumor burden reveals useful information about cancer evolution concerning treatment effects and drug resistance, which play a crucial role in advancing model-informed drug developments (MIDD) towards personalized medicine and precision oncology. The emergence of Quantum Machine Intelligence offers unparalleled insights into tumor dynamics via a quantum mechanics perspective. This paper introduces a novel hybrid quantum-classical neural architecture named η−η−Net that enables quantifying quantum dynamics of tumor burden concerning treatment effects. We evaluate our proposed neural solution on two major use cases, including cohort-specific and patient-specific modeling. In silico numerical results show a high capacity and expressivity of η−η−Net to the quantified biological problem. Moreover, the close connection to representation learning – the foundation for successes of modern AI, enables efficient transferability of empirical knowledge from relevant cohorts to targeted patients. Finally, we leverage Bayesian optimization to quantify the epistemic uncertainty of model predictions, paving the way for η−η−Net towards reliable AI in decision-making for clinical usages.

A Classical-Quantum Convolutional Neural Network for Detecting Pneumonia from Chest Radiographs

Viraj Kulkarni, Sanjesh Pawale, Amit Kharat

Feb 23 2022 cs.CV cs.LG quant-ph arXiv:2202.10452v1

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While many quantum computing techniques for machine learning have been proposed, their performance on real-world datasets remains to be studied. In this paper, we explore how a variational quantum circuit could be integrated into a classical neural network for the problem of detecting pneumonia from chest radiographs. We substitute one layer of a classical convolutional neural network with a variational quantum circuit to create a hybrid neural network. We train both networks on an image dataset containing chest radiographs and benchmark their performance. To mitigate the influence of different sources of randomness in network training, we sample the results over multiple rounds. We show that the hybrid network outperforms the classical network on different performance measures, and that these improvements are statistically significant. Our work serves as an experimental demonstration of the potential of quantum computing to significantly improve neural network performance for real-world, non-trivial problems relevant to society and industry.

Improving the performance of fermionic neural networks with the Slater exponential

AnsatzDenis Bokhan, Aleksey S. Boev, Aleksey K. Fedorov, Dmitrii N. Trubnikov

Feb 22 2022 quant-ph physics.chem-ph arXiv:2202.10126v1

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In this work, we propose a technique for the use of fermionic neural networks (FermiNets) with the Slater exponential Ansatz for electron-nuclear and electron-electron distances, which provides faster convergence of target ground-state energies due to a better description of the interparticle interaction in the vicinities of the coalescence points. Analysis of learning curves indicates on the possibility to obtain accurate energies with smaller batch sizes using arguments of the bagging approach. In order to obtain even more accurate results for the ground-state energies, we suggest an extrapolation scheme, which estimates Monte Carlo integrals in the limit of an infinite number of points. Numerical tests for a set of molecules demonstrate a good agreement with the results of original FermiNets (achieved with larger batch sizes than required by our approach) and with results of coupled-cluster singles and doubles with perturbative triples (CCSD(T)) method, calculated in the complete basis set (CBS) limit.

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