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Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications, information processing, and artificial intelligence. However, quantum computers face a fundamental issue since quantum bits are extremely noisy and prone to decoherence. Keeping qubits error free is one of the most important steps towards reliable quantum computing. Different stabilizer codes for quantum error correction have been proposed in past decades and several methods have been proposed to import classical error correcting codes to the quantum domain. Design of encoding and decoding circuits for the stabilizer codes have also been proposed. Optimization of these circuits in terms of the number of gates is critical for reliability of these circuits. In this paper, we propose a procedure for optimization of encoder circuits for stabilizer codes. Using the proposed method, we optimize the encoder circuit in terms of the number of 2-qubit gates used. The proposed optimized eight-qubit encoder uses 18 CNOT gates and 4 Hadamard gates, as compared to 14 single qubit gates, 33 2-qubit gates, and 6 CCNOT gates in a prior work. The encoder and decoder circuits are verified using IBM Qiskit. We also present encoder circuits for the Steane code and a 13-qubit code, that are optimized with respect to the number of gates used, leading to a reduction in number of CNOT gates by 1 and 8, respectively. 

Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve quantum advantage. However, quantum bits are extremely noisy and prone to decoherence. Thus, keeping the qubits error free is extremely important toward reliable quantum computing. Quantum error correcting codes have been studied for several decades and methods have been proposed to import classical error correcting codes to the quantum domain. Along with the exploration into novel and more efficient quantum error correction codes, it is also essential to design circuits for practical realization of these codes. This paper serves as a tutorial on designing and simulating quantum encoder and decoder circuits for stabilizer codes. We first describe Shor’s 9-qubit code which was the first quantum error correcting code. We discuss the stabilizer formalism along with the design of encoding and decoding circuits for stabilizer codes such as the five-qubit code and Steane code. We also design nearest neighbor compliant circuits for the above codes. The circuits were simulated and verified using IBM Qiskit. 

Graph Neural Networks (GNNs) are a form of deep learning that have found use for a variety of problems, including the modeling of drug interactions, time-series analysis, and traffic prediction. They represent the problem using non-Euclidian graphs, allowing for a high degree of versatility, and are able to learn complex relationships by iteratively aggregating more contextual information from neighbors that are farther away. Inspired by its power in transformers, Graph Attention Networks (GATs) incorporate an attention mechanism on top of graph aggregation. GATs are considered the state of the art due to their superior performance. To learn the best parameters for a given graph problem, GATs use traditional backpropagation to compute weight updates. To the best of our knowledge, these updates are calculated in software, and closed-form equations describing their calculation for GATs aren’t well known. This paper derives closed-form equations for backpropagation in GATs using matrix notation. These equations can form the basis for design of hardware accelerators for training GATs. 

Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine translation. Most state-of-the-art neural networks are over-parameterized and require a high computational cost. One straightforward solution is to replace the layers of the networks with their low-rank tensor approximations using different tensor decomposition methods. This article reviews six tensor decomposition methods and illustrates their ability to compress model parameters of convolutional neural networks (CNNs), recurrent neural networks (RNNs) and Transformers. The accuracy of some compressed models can be higher than the original versions. Evaluations indicate that tensor decompositions can achieve significant reductions in model size, run-time and energy consumption, and are well suited for implementing neural networks on edge devices. 

Graph neural networks (GNNs) have emerged as a powerful tool to process graph-based data in fields like communication networks, molecular interactions, chemistry, social networks, and neuroscience. GNNs are characterized by the ultra-sparse nature of their adjacency matrix that necessitates the development of dedicated hardware beyond general-purpose sparse matrix multipliers. While there has been extensive research on designing dedicated hardware accelerators for GNNs, few have extensively explored the impact of the sparse storage format on the efficiency of the GNN accelerators. This paper proposes SCV-GNN with the novel sparse compressed vectors (SCV) format optimized for the aggregation operation. We use Z-Morton ordering to derive a data-locality-based computation ordering and partitioning scheme. The paper also presents how the proposed SCV-GNN is scalable on a vector processing system. Experimental results over various datasets show that the proposed method achieves a geometric mean speedup of 7.96× and 7.04× over CSC and CSR aggregation operations, respectively. The proposed method also reduces the memory traffic by a factor of 3.29× and 4.37× over compressed sparse column (CSC) and compressed sparse row (CSR), respectively. Thus, the proposed novel aggregation format reduces the latency and memory access for GNN inference. 

This paper describes a group-level classification of 14 patients with prefrontal cortex (pFC) lesions from 20 healthy controls using multi-layer graph convolutional networks (GCN) with features inferred from the scalp EEG recorded from the encoding phase of working memory (WM) trials. We first construct undirected and directed graphs to represent the WM encoding for each trial for each subject using distance correlation- based functional connectivity measures and differential directed information-based effective connectivity measures, respectively. Centrality measures of betweenness centrality, eigenvector centrality, and closeness centrality are inferred for each of the 64 channels from the brain connectivity. Along with the three centrality measures, each graph uses the relative band powers in the five frequency bands - delta, theta, alpha, beta, and gamma- as node features. The summarized graph representation is learned using two layers of GCN followed by mean pooling, and fully connected layers are used for classification. The final class label for a subject is decided using majority voting based on the results from all the subject's trials. The GCN-based model can correctly classify 28 of the 34 subjects (82.35% accuracy) with undirected edges represented by functional connectivity measure of distance correlation and classify all 34 subjects (100% accuracy) with directed edges characterized by effective connectivity measure of differential directed information. 

This paper describes a group-level analysis of 14 subjects with prefrontal cortex (pFC) lesions and 20 healthy controls performing multiple lateralized visuospatial working memory (WM) trials. Using effective brain connectivity measures inferred from directed information (DI) during memory encoding, we first show that DI features can correctly classify 18 control subjects and 11 subjects with pFC lesions, providing an overall accuracy of 85.3%. Second, we show that differential DI, the change in DI during the encoding phase from pretrial, can successfully overcome inter-subject variability and correctly identify the class of all 34 subjects (100% accuracy). These accuracy results are based on two-thirds majority thresholding among all trials. Finally, we use Welch’s t-test to identify the crucial differences in the two classes’ sub-networks responsible for memory encoding. While the inflow of information to the prefrontal region is significant among subjects with pFC lesions, the outflow from the prefrontal to the frontal and central regions is diminished compared to the control subjects. We further identify specific neural pathways that are exclusively activated for each group during the encoding phase. 

Objective: Inferring causal or effective connectivity between measured timeseries is crucial to understanding directed interactions in complex systems. This task is especially challenging in the brain as the underlying dynamics are not well-understood. This paper aims to introduce a novel causality measure called frequency-domain convergent cross-mapping (FDCCM) that utilizes frequency-domain dynamics through nonlinear state-space reconstruction. Method: Using synthesized chaotic timeseries, we investigate general applicability of FDCCM at different causal strengths and noise levels. We also apply our method on two resting-state Parkinson's datasets with 31 and 54 subjects, respectively. To this end, we construct causal networks, extract network features, and perform machine learning analysis to distinguish Parkinson's disease patients (PD) from age and gender-matched healthy controls (HC). Specifically, we use the FDCCM networks to compute the betweenness centrality of the network nodes, which act as features for the classification models. Result: The analysis on simulated data showed that FDCCM is resilient to additive Gaussian noise, making it suitable for real-world applications. Our proposed method also decodes scalp-EEG signals to classify the PD and HC groups with approximately 97% leave-one-subject-out cross-validation accuracy. We compared decoders from six cortical regions to find that features derived from the left temporal lobe lead to a higher classification accuracy of 84.5% compared to other regions. Moreover, when the classifier trained using FDCCM networks from one dataset was tested on an independent out-of-sample dataset, it attained an accuracy of 84%. This accuracy is significantly higher than correlational networks (45.2%) and CCM networks (54.84%). Significance: These findings suggest that our spectral-based causality measure can improve classification performance and reveal useful network biomarkers of Parkinson's disease. 

This paper addresses the design of accelerators using systolic architectures to train convolutional neural networks using a novel gradient interleaving approach. Training the neural network involves computation and backpropagation of gradients of error with respect to the activation functions and weights. It is shown that the gradient with respect to the activation function can be computed using a weight-stationary systolic array, while the gradient with respect to the weights can be computed using an output-stationary systolic array. The novelty of the proposed approach lies in interleaving the computations of these two gradients on the same configurable systolic array. This results in the reuse of the variables from one computation to the other and eliminates unnecessary memory accesses and energy consumption associated with these memory accesses. The proposed approach leads to 1.4−2.2× savings in terms of the number of cycles and 1.9× savings in terms of memory accesses in the fully-connected layer. Furthermore, the proposed method uses up to 25% fewer cycles and memory accesses, and 16% less energy than baseline implementations for state-of-the-art CNNs. Under iso-area comparisons, for Inception-v4, compared to weight-stationary (WS), Intergrad achieves 12% savings in energy, 17% savings in memory, and 4% savings in cycles. Savings for Densenet-264 are 18% , 26% , and 27% with respect to energy, memory, and cycles, respectively. Thus, the proposed novel accelerator architecture reduces the latency and energy consumption for training deep neural networks. 

This paper analyzes the scalp electroencephalogram (EEG) recorded from 14 human subjects with pFC lesions and 20 healthy controls while performing lateral visuospatial working memory tasks to identify the directional brain networks responsible for memory encoding. First, we show that effective connectivity features using directed information (DI) are more accurate and robust than the functional connectivity measure of correlation coefficients in classifying the memory encoding stage from the pretrial phase, with a mean accuracy of 99.36%. Second, we identify the functional segregation of memory encoding to a much smaller sub-network by showing that the top 2.5% of the observed DI features can distinguish memory encoding from the pretrial phase with a mean accuracy of 93.1%. Finally, using graph features, we reveal the increased significance of frontocentral, centroparietal, and temporal regions in memory encoding for subjects with pFC lesions and reduced information flow in the prefrontal, frontal and parietooccipital areas when compared to healthy control.