arXiv subjects

Jishnu Mahmud

Publications and source records attributed to Jishnu Mahmud.

6 recordsLinked to original sources

arXiv2026

Moment-Structured Block Encodings of Periodic Finite-Difference Operators

Block encoding is the standard technique for accessing matrix data in quantum linear-algebra algorithms. Its implementation directly affects its subnormalization, which in turn controls the algorithm's success probability, simulation time, and downstream costs. Explicit construction of block encodings with provably optimal subnormalization exists for only a handful of operators, with bespoke calculations used in its design. In this work, we develop a framework to block encode translation-invariant finite-difference operators on a periodic grid. These operators are the finite-difference discretizations of the constant-coefficient partial differential equations that sit at the core of scientific computing. We show that the moment order of these stencils can be used to simultaneously determine the continuum operator approximated, the vanishing order of the Fourier symbol, and the cost of the block encoding. From there, we derive a closed-form optimality criterion as a function of the stencil coefficients, which certifies whether the construction attains the optimal subnormalization for an entire operator family, uniformly in grid size, and quantifies the gap when it does not. The framework subsumes optimal constructions for the Laplacian operator in the literature and can be used to certify new instances at higher even orders, including the biharmonic operator. Furthermore, we derive success-probability floors parameterized by spectral properties of the operator's symbol and find explicit constants for the block encoding of the advection-diffusion family for which no prior explicit spatial block encoding exists.

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arXiv2026

Explicit Block Encoding of Difference-of-Gaussian Operators on a Periodic Grid

The Difference-of-Gaussian (DoG) is a widely used operator across applications, including image processing (feature and edge detection), quantum machine learning, and finite-difference methods (approximations of the Laplacian-of-Gaussian). In this paper, we construct an explicit quantum block encoding of the DoG operator on a periodic grid, exploiting its natural probabilistic structure. The central observation is that the DoG admits a natural decomposition to two normalized Gaussian distributions, each preparable by explicit and efficient circuits, with the negation encoded using a single Pauli-$Z$ gate on a branch-indicator qubit. This enables the operator's block encoding to be directly mapped to the Linear Combination of Unitaries framework without requiring signed amplitude loading, quantum random-access memory, or any other black-box oracles. The proposed method achieves a constant subnormalization factor $\lambda = 2$ independent of the grid size $N$, the spatial dimension $D$, and the stencil width. Additionally, we show that the DoG operator is diagonalized by the discrete Fourier basis, which allows us to derive an exact closed-form expression for the block-encoding success probability in terms of the input signal's power spectrum, weighted by the operator's transfer function. Finally, we prove that the expression reduces to $O(h^4)$ scaling with respect to grid spacing $h$ as the periodic grid becomes finer. This implementation provides an explicit construction method for a tunable, wide-stencil bandpass filter whose frequency response is controlled by two Gaussian scale parameters.

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arXiv2025

Hybrid Quantum-Classical Learning for Multiclass Image Classification

This study explores the challenge of improving multiclass image classification through quantum machine-learning techniques. It explores how the discarded qubit states of Noisy Intermediate-Scale Quantum (NISQ) quantum convolutional neural networks (QCNNs) can be leveraged alongside a classical classifier to improve classification performance. Current QCNNs discard qubit states after pooling; yet, unlike classical pooling, these qubits often remain entangled with the retained ones, meaning valuable correlated information is lost. We experiment with recycling this information and combining it with the conventional measurements from the retained qubits. Accordingly, we propose a hybrid quantum-classical architecture that couples a modified QCNN with fully connected classical layers. Two shallow fully connected (FC) heads separately process measurements from retained and discarded qubits, whose outputs are ensembled before a final classification layer. Joint optimisation with a classical cross-entropy loss allows both quantum and classical parameters to adapt coherently. The method outperforms comparable lightweight models on MNIST, Fashion-MNIST and OrganAMNIST. These results indicate that reusing discarded qubit information is a promising approach for future hybrid quantum-classical models and may extend to tasks beyond image classification.

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arXiv2025

Selective Feature Re-Encoded Quantum Convolutional Neural Network with Joint Optimization for Image Classification

Quantum Machine Learning (QML) has seen significant advancements, driven by recent improvements in Noisy Intermediate-Scale Quantum (NISQ) devices. Leveraging quantum principles such as entanglement and superposition, quantum convolutional neural networks (QCNNs) have demonstrated promising results in classifying both quantum and classical data. This study examines QCNNs in the context of image classification and proposes a novel strategy to enhance feature processing and a QCNN architecture for improved classification accuracy. First, a selective feature re-encoding strategy is proposed, which directs the quantum circuits to prioritize the most informative features, thereby effectively navigating the crucial regions of the Hilbert space to find the optimal solution space. Secondly, a novel parallel-mode QCNN architecture is designed to simultaneously incorporate features extracted by two classical methods, Principal Component Analysis (PCA) and Autoencoders, within a unified training scheme. The joint optimization involved in the training process allows the QCNN to benefit from complementary feature representations, enabling better mutual readjustment of model parameters. To assess these methodologies, comprehensive experiments have been performed using the widely used MNIST and Fashion MNIST datasets for binary classification tasks. Experimental findings reveal that the selective feature re-encoding method significantly improves the quantum circuit's feature processing capability and performance. Furthermore, the jointly optimized parallel QCNN architecture consistently outperforms the individual QCNN models and the traditional ensemble approach involving independent learning followed by decision fusion, confirming its superior accuracy and generalization capabilities.

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arXiv2024

Patch-Based End-to-End Quantum Learning Network for Reduction and Classification of Classical Data

In the noisy intermediate scale quantum (NISQ) era, the control over the qubits is limited due to the errors caused by quantum decoherence, crosstalk, and imperfect calibration. Hence, it is necessary to reduce the size of the large-scale classical data, such as images, when they are to be processed by quantum networks. Conventionally input classical data are reduced in the classical domain using classical networks such as autoencoders and, subsequently, analyzed in the quantum domain. These conventional techniques involve training an enormous number of parameters, making them computationally costly. In this paper, a dynamic patch-based quantum domain data reduction network with a classical attention mechanism is proposed to avoid such data reductions, and subsequently coupled with a novel quantum classifier to perform classification tasks. The architecture processes the classical data sequentially in patches and reduces them using a quantum convolutional-inspired reduction network and further enriches them using a self-attention technique, which utilizes a classical mask derived from simple statistical operations on the native classical data, after measurement. The reduced representation is passed through a quantum classifier, which re-encodes it into quantum states, processes them through quantum ansatzes, and finally measures them to predict classes. This training process involves a joint optimization scheme that considers both the reduction and classifier networks, making the reduction operation dynamic. The proposed architecture has been extensively tested on the publicly available Fashion MNIST dataset, and it has excellent classification performance using significantly reduced training parameters.

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arXiv2024

Quantum Convolutional Neural Networks with Interaction Layers for Classification of Classical Data

Quantum Machine Learning (QML) has come into the limelight due to the exceptional computational abilities of quantum computers. With the promises of near error-free quantum computers in the not-so-distant future, it is important that the effect of multi-qubit interactions on quantum neural networks is studied extensively. This paper introduces a Quantum Convolutional Network with novel Interaction layers exploiting three-qubit interactions, while studying the network's expressibility and entangling capability, for classifying both image and one-dimensional data. The proposed approach is tested on three publicly available datasets namely MNIST, Fashion MNIST, and Iris datasets, flexible in performing binary and multiclass classifications, and is found to supersede the performance of existing state-of-the-art methods.

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