Related papers: Classification Problem in a Quantum Framework
Quantum communication is often investigated in scenarios where only the dimension of Hilbert space is known. However, assigning a precise dimension is often an approximation of what is actually a higher-dimensional process. Here, we…
In this paper, we address the problem of designing a quantum encoder that maximizes the minimum output purity of a given decohering channel, where the minimum is taken over all possible pure inputs. This problem is cast as a max-min…
Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
Quantum computing is a new computational paradigm that promises applications in several fields, including machine learning. In the last decade, deep learning, and in particular Convolutional neural networks (CNN), have become essential for…
We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-valued data vectors of $d=\binom{n}{k}$ components into a subspace of fixed Hamming weight $k$. This represents a polynomial space compression of degree…
K-Nearest neighbor classifier (k-NNC) is simple to use and has little design time like finding k values in k-nearest neighbor classifier, hence these are suitable to work with dynamically varying data-sets. There exists some fundamental…
With the rapid advance of quantum machine learning, several proposals for the quantum-analogue of convolutional neural network (CNN) have emerged. In this work, we benchmark fully parameterized quantum convolutional neural networks (QCNNs)…
Quantum machine learning is at the crossroads of two of the most exciting current areas of research; quantum computing and classical machine learning. It explores the interaction between quantum computing and machine learning, investigating…
Consider an ill-posed inverse problem of estimating causal factors from observations, one of which is known to lie near some (un- known) low-dimensional, non-linear manifold expressed by a predefined Mercer-kernel. Solving this problem…
Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
Quantum machine learning (QML) is an emerging field that investigates the capabilities of quantum computers for learning tasks. While QML models can theoretically offer advantages such as exponential speed-ups, challenges in data loading…
In the NISQ (Noisy intermediate-scale quantum) area, Quantum computers can be utilized for deep learning by treating variational quantum circuits as neural network models. This can be achieved by first encoding the input data onto quantum…
Data sets that are specified by a large number of features are currently outside the area of applicability for quantum machine learning algorithms. An immediate solution to this impasse is the application of dimensionality reduction methods…
The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…
Detecting unseen ransomware is a critical cybersecurity challenge where classical machine learning often fails. While Quantum Machine Learning (QML) presents a potential alternative, its application is hindered by the dimensionality gap…
Vector quantization is a fundamental operation for data compression and vector search. To obtain high accuracy, multi-codebook methods represent each vector using codewords across several codebooks. Residual quantization (RQ) is one such…
Quantum sensor networks promise precision advantages over classical and single-sensor strategies, in particular when the estimator is non-local. We address the problem of finding such estimators through a framework we connote spatial…
In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is…