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Adiabatic quantum computers can solve difficult optimization problems (e.g., the quadratic unconstrained binary optimization problem), and they seem well suited to train machine learning models. In this paper, we describe an adiabatic quantum approach for training support vector machines. We show that the time complexity of our quantum approach is an order of magnitude better than the classical approach. Next, we compare the test accuracy of our quantum approach against a classical approach that uses the Scikit-learn library in Python across five benchmark datasets (Iris, Wisconsin Breast Cancer (WBC), Wine, Digits, and Lambeq). We show that our quantum approach obtains accuracies on par with the classical approach. Finally, we perform a scalability study in which we compute the total training times of the quantum approach and the classical approach with increasing number of features and number of data points in the training dataset. Our scalability results show that the quantum approach obtains a 3.5--4.5 times speedup over the classical approach on datasets with many (millions of) features.

Quantum Computers offer an intriguing challenge in modern Computer Science. With the inevitable physical limitations to Moore's Law, quantum hardware provides avenues to solve grander problems faster by utilizing Quantum Mechanical properties at subatomic scales. These futuristic devices will likely never replace traditional HPC, but rather work alongside them to perform complex tasks, utilizing the best of decades of HPC and quantum computing research. We leverage the capabilities of scientific workflows to make traditional HPC and Quantum Computers work together. To demonstrate this capability, we implemented three algorithms: Grover's Search Algorithm, Shor's Factoring Algorithm, and a 4-node Traveling Salesman Algorithm. The algorithms' implementation and generated inputs are sent from ORNL HPC to IBMQ, the algorithms run on IBMQ, and the results return. The entire process is automated as a workflow by encoding it into the Parsl parallel scripting and workflow platform., Comment: 15 pages, 8 figures

This work describes the investigation of neuromorphic computing-based spiking neural network (SNN) models used to filter data from sensor electronics in high energy physics experiments conducted at the High Luminosity Large Hadron Collider. We present our approach for developing a compact neuromorphic model that filters out the sensor data based on the particle's transverse momentum with the goal of reducing the amount of data being sent to the downstream electronics. The incoming charge waveforms are converted to streams of binary-valued events, which are then processed by the SNN. We present our insights on the various system design choices - from data encoding to optimal hyperparameters of the training algorithm - for an accurate and compact SNN optimized for hardware deployment. Our results show that an SNN trained with an evolutionary algorithm and an optimized set of hyperparameters obtains a signal efficiency of about 91% with nearly half as many parameters as a deep neural network., Comment: Manuscript accepted at ICONS'23

Quantum computing presents a promising approach for machine learning with its capability for extremely parallel computation in high-dimension through superposition and entanglement. Despite its potential, existing quantum learning algorithms, such as Variational Quantum Circuits(VQCs), face challenges in handling more complex datasets, particularly those that are not linearly separable. What's more, it encounters the deployability issue, making the learning models suffer a drastic accuracy drop after deploying them to the actual quantum devices. To overcome these limitations, this paper proposes a novel spatial-temporal design, namely ST-VQC, to integrate non-linearity in quantum learning and improve the robustness of the learning model to noise. Specifically, ST-VQC can extract spatial features via a novel block-based encoding quantum sub-circuit coupled with a layer-wise computation quantum sub-circuit to enable temporal-wise deep learning. Additionally, a SWAP-Free physical circuit design is devised to improve robustness. These designs bring a number of hyperparameters. After a systematic analysis of the design space for each design component, an automated optimization framework is proposed to generate the ST-VQC quantum circuit. The proposed ST-VQC has been evaluated on two IBM quantum processors, ibm_cairo with 27 qubits and ibmq_lima with 7 qubits to assess its effectiveness. The results of the evaluation on the standard dataset for binary classification show that ST-VQC can achieve over 30% accuracy improvement compared with existing VQCs on actual quantum computers. Moreover, on a non-linear synthetic dataset, the ST-VQC outperforms a linear classifier by 27.9%, while the linear classifier using classical computing outperforms the existing VQC by 15.58%.

In many neuromorphic workflows, simulators play a vital role for important tasks such as training spiking neural networks (SNNs), running neuroscience simulations, and designing, implementing and testing neuromorphic algorithms. Currently available simulators are catered to either neuroscience workflows (such as NEST and Brian2) or deep learning workflows (such as BindsNET). While the neuroscience-based simulators are slow and not very scalable, the deep learning-based simulators do not support certain functionalities such as synaptic delay that are typical of neuromorphic workloads. In this paper, we address this gap in the literature and present SuperNeuro, which is a fast and scalable simulator for neuromorphic computing, capable of both homogeneous and heterogeneous simulations as well as GPU acceleration. We also present preliminary results comparing SuperNeuro to widely used neuromorphic simulators such as NEST, Brian2 and BindsNET in terms of computation times. We demonstrate that SuperNeuro can be approximately 10--300 times faster than some of the other simulators for small sparse networks. On large sparse and large dense networks, SuperNeuro can be approximately 2.2 and 3.4 times faster than the other simulators respectively.

Neuromorphic computers perform computations by emulating the human brain, and use extremely low power. They are expected to be indispensable for energy-efficient computing in the future. While they are primarily used in spiking neural network-based machine learning applications, neuromorphic computers are known to be Turing-complete, and thus, capable of general-purpose computation. However, to fully realize their potential for general-purpose, energy-efficient computing, it is important to devise efficient mechanisms for encoding numbers. Current encoding approaches have limited applicability and may not be suitable for general-purpose computation. In this paper, we present the virtual neuron as an encoding mechanism for integers and rational numbers. We evaluate the performance of the virtual neuron on physical and simulated neuromorphic hardware and show that it can perform an addition operation using 23 nJ of energy on average using a mixed-signal memristor-based neuromorphic processor. We also demonstrate its utility by using it in some of the mu-recursive functions, which are the building blocks of general-purpose computation.

Some of the biggest achievements of the modern era of particle physics, such as the discovery of the Higgs boson, have been made possible by the tremendous effort in building and operating large-scale experiments like the Large Hadron Collider or the Tevatron. In these facilities, the ultimate theory to describe matter at the most fundamental level is constantly probed and verified. These experiments often produce large amounts of data that require storing, processing, and analysis techniques that often push the limits of traditional information processing schemes. Thus, the High-Energy Physics (HEP) field has benefited from advancements in information processing and the development of algorithms and tools for large datasets. More recently, quantum computing applications have been investigated in an effort to understand how the community can benefit from the advantages of quantum information science. In this manuscript, we provide an overview of the state-of-the-art applications of quantum computing to data analysis in HEP, discuss the challenges and opportunities in integrating these novel analysis techniques into a day-to-day analysis workflow, and whether there is potential for a quantum advantage., Comment: 23 pages, initially submitted to Snowmass 2021

Quantum computing offers a new paradigm for advancing high-energy physics research by enabling novel methods for representing and reasoning about fundamental quantum mechanical phenomena. Realizing these ideals will require the development of novel computational tools for modeling and simulation, detection and classification, data analysis, and forecasting of high-energy physics (HEP) experiments. While the emerging hardware, software, and applications of quantum computing are exciting opportunities, significant gaps remain in integrating such techniques into the HEP community research programs. Here we identify both the challenges and opportunities for developing quantum computing systems and software to advance HEP discovery science. We describe opportunities for the focused development of algorithms, applications, software, hardware, and infrastructure to support both practical and theoretical applications of quantum computing to HEP problems within the next 10 years., Comment: A contribution to the 2021 Snowmass Proceedings, Computational Frontier, Topical Group on Quantum Computing

Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns have become increasingly pressing as conventional computers quickly approach physical limitations that will slow performance improvements in years to come. For these reasons, scientists have begun to explore alternative computing platforms, like quantum computers, for training neural networks. In recent years, variational quantum circuits have emerged as one of the most successful approaches to quantum deep learning on noisy intermediate scale quantum devices. We propose a hybrid quantum-classical neural network architecture where each neuron is a variational quantum circuit. We empirically analyze the performance of this hybrid neural network on a series of binary classification data sets using a simulated universal quantum computer and a state of the art universal quantum computer. On simulated hardware, we observe that the hybrid neural network achieves roughly 10% higher classification accuracy and 20% better minimization of cost than an individual variational quantum circuit. On quantum hardware, we observe that each model only performs well when the qubit and gate count is sufficiently small., Comment: Added reference to section I. Fixed error in methods (Section III.C)

Quantum machine learning (QML) algorithms have obtained great relevance in the machine learning (ML) field due to the promise of quantum speedups when performing basic linear algebra subroutines (BLAS), a fundamental element in most ML algorithms. By making use of BLAS operations, we propose, implement and analyze a quantum k-means (qk-means) algorithm with a low time complexity of $\mathcal{O}(NKlog(D)I/C)$ to apply it to the fundamental problem of discriminating quantum states at readout. Discriminating quantum states allows the identification of quantum states $|0\rangle$ and $|1\rangle$ from low-level in-phase and quadrature signal (IQ) data, and can be done using custom ML models. In order to reduce dependency on a classical computer, we use the qk-means to perform state discrimination on the IBMQ Bogota device and managed to find assignment fidelities of up to 98.7% that were only marginally lower than that of the k-means algorithm. Inspection of assignment fidelity scores resulting from applying both algorithms to a combination of quantum states showed concordance to our correlation analysis using Pearson Correlation coefficients, where evidence shows cross-talk in the (1, 2) and (2, 3) neighboring qubit couples for the analyzed device.

Energy efficient routing in wireless sensor networks has attracted attention from researchers in both academia and industry, most recently motivated by the opportunity to use SDN (software defined network)-inspired approaches. These problems are NP-hard, with algorithms needing computation time which scales faster than polynomial in the problem size. Consequently, heuristic algorithms are used in practice, which are unable to guarantee optimally. In this short paper, we show proof-of-principle for the use of a quantum annealing processor instead of a classical processor, to find optimal or near-optimal solutions very quickly. Our preliminary results for small networks show that this approach using quantum computing has great promise and may open the door for other significant improvements in the efficacy of network algorithms.

Neuromorphic computing is a non-von Neumann computing paradigm that performs computation by emulating the human brain. Neuromorphic systems are extremely energy-efficient and known to consume thousands of times less power than CPUs and GPUs. They have the potential to drive critical use cases such as autonomous vehicles, edge computing and internet of things in the future. For this reason, they are sought to be an indispensable part of the future computing landscape. Neuromorphic systems are mainly used for spike-based machine learning applications, although there are some non-machine learning applications in graph theory, differential equations, and spike-based simulations. These applications suggest that neuromorphic computing might be capable of general-purpose computing. However, general-purpose computability of neuromorphic computing has not been established yet. In this work, we prove that neuromorphic computing is Turing-complete and therefore capable of general-purpose computing. Specifically, we present a model of neuromorphic computing, with just two neuron parameters (threshold and leak), and two synaptic parameters (weight and delay). We devise neuromorphic circuits for computing all the {\mu}-recursive functions (i.e., constant, successor and projection functions) and all the {\mu}-recursive operators (i.e., composition, primitive recursion and minimization operators). Given that the {\mu}-recursive functions and operators are precisely the ones that can be computed using a Turing machine, this work establishes the Turing-completeness of neuromorphic computing.

Quantum computers have the unique ability to operate relatively quickly in high-dimensional spaces -- this is sought to give them a competitive advantage over classical computers. In this work, we propose a novel quantum machine learning model called the Quantum Discriminator, which leverages the ability of quantum computers to operate in the high-dimensional spaces. The quantum discriminator is trained using a quantum-classical hybrid algorithm in O(N logN) time, and inferencing is performed on a universal quantum computer in linear time. The quantum discriminator takes as input the binary features extracted from a given datum along with a prediction qubit initialized to the zero state and outputs the predicted label. We analyze its performance on the Iris data set and show that the quantum discriminator can attain 99% accuracy in simulation.

Today's deep learning models are primarily trained on CPUs and GPUs. Although these models tend to have low error, they consume high power and utilize large amount of memory owing to double precision floating point learning parameters. Beyond the Moore's law, a significant portion of deep learning tasks would run on edge computing systems, which will form an indispensable part of the entire computation fabric. Subsequently, training deep learning models for such systems will have to be tailored and adopted to generate models that have the following desirable characteristics: low error, low memory, and low power. We believe that deep neural networks (DNNs), where learning parameters are constrained to have a set of finite discrete values, running on neuromorphic computing systems would be instrumental for intelligent edge computing systems having these desirable characteristics. To this extent, we propose the Combinatorial Neural Network Training Algorithm (CoNNTrA), that leverages a coordinate gradient descent-based approach for training deep learning models with finite discrete learning parameters. Next, we elaborate on the theoretical underpinnings and evaluate the computational complexity of CoNNTrA. As a proof of concept, we use CoNNTrA to train deep learning models with ternary learning parameters on the MNIST, Iris and ImageNet data sets and compare their performance to the same models trained using Backpropagation. We use following performance metrics for the comparison: (i) Training error; (ii) Validation error; (iii) Memory usage; and (iv) Training time. Our results indicate that CoNNTrA models use 32x less memory and have errors at par with the Backpropagation models.

In this work, we attempt to solve the integer-weight knapsack problem using the D-Wave 2000Q adiabatic quantum computer. The knapsack problem is a well-known NP-complete problem in computer science, with applications in economics, business, finance, etc. We attempt to solve a number of small knapsack problems whose optimal solutions are known; we find that adiabatic quantum optimization fails to produce solutions corresponding to optimal filling of the knapsack in all problem instances. We compare results obtained on the quantum hardware to the classical simulated annealing algorithm and two solvers employing a hybrid branch-and-bound algorithm. The simulated annealing algorithm also fails to produce the optimal filling of the knapsack, though solutions obtained by simulated and quantum annealing are no more similar to each other than to the correct solution. We discuss potential causes for this observed failure of adiabatic quantum optimization.

Adiabatic quantum computers are a promising platform for approximately solving challenging optimization problems. We present a quantum approach to solving the balanced $k$-means clustering training problem on the D-Wave 2000Q adiabatic quantum computer. Existing classical approaches scale poorly for large datasets and only guarantee a locally optimal solution. We show that our quantum approach better targets the global solution of the training problem, while achieving better theoretic scalability on large datasets. We test our quantum approach on a number of small problems, and observe clustering performance similar to the best classical algorithms.

Training machine learning models on classical computers is usually a time and compute intensive process. With Moore's law coming to an end and ever increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers like the D-Wave 2000Q can approximately solve NP-hard optimization problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore's law era. In order to solve a problem on adiabatic quantum computers, it must be formulated as a QUBO problem, which is a challenging task in itself. In this paper, we formulate the training problems of three machine learning models---linear regression, support vector machine (SVM) and equal-sized k-means clustering---as QUBO problems so that they can be trained on adiabatic quantum computers efficiently. We also analyze the time and space complexities of our formulations and compare them to the state-of-the-art classical algorithms for training these machine learning models. We show that the time and space complexities of our formulations are better (in the case of SVM and equal-sized k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.

A major challenge in machine learning is the computational expense of training these models. Model training can be viewed as a form of optimization used to fit a machine learning model to a set of data, which can take up significant amount of time on classical computers. Adiabatic quantum computers have been shown to excel at solving optimization problems, and therefore, we believe, present a promising alternative to improve machine learning training times. In this paper, we present an adiabatic quantum computing approach for training a linear regression model. In order to do this, we formulate the regression problem as a quadratic unconstrained binary optimization (QUBO) problem. We analyze our quantum approach theoretically, test it on the D-Wave 2000Q adiabatic quantum computer and compare its performance to a classical approach that uses the Scikit-learn library in Python. Our analysis shows that the quantum approach attains up to 2.8x speedup over the classical approach on larger datasets, and performs at par with the classical approach on the regression error metric.

Training neural networks for neuromorphic deployment is non-trivial. There have been a variety of approaches proposed to adapt back-propagation or back-propagation-like algorithms appropriate for training. Considering that these networks often have very different performance characteristics than traditional neural networks, it is often unclear how to set either the network topology or the hyperparameters to achieve optimal performance. In this work, we introduce a Bayesian approach for optimizing the hyperparameters of an algorithm for training binary communication networks that can be deployed to neuromorphic hardware. We show that by optimizing the hyperparameters on this algorithm for each dataset, we can achieve improvements in accuracy over the previous state-of-the-art for this algorithm on each dataset (by up to 15 percent). This jump in performance continues to emphasize the potential when converting traditional neural networks to binary communication applicable to neuromorphic hardware., Comment: 9 pages, 3 figures, To appear in WCCI 2020