Related papers: A Quantum Spectral Framework for Solving PDEs
At present, in the face of the huge and complex data in cloud computing, the parallel computing ability of quantum computing is particularly important. Quantum principal component analysis algorithm is used as a method of quantum state…
Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers for certain problems. However, the physical qubits within a quantum computer are prone to noise and decoherence, which must be…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
Quantum neural networks (QNNs) leverage quantum entanglement and superposition to enable large-scale parallel linear computation, offering a potential solution to the scalability limits of classical deep learning. However, their practical…
Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…
Escalating cyber threats and the high-dimensional complexity of IoT traffic have outpaced classical anomaly detection methods. While deep learning offers improvements, computational bottlenecks limit real-time deployment at scale. We…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…
Network verification (NWV), broadly defined as the verification of properties of distributed protocols used in network systems, cannot be efficiently solved on classical hardware via brute force. Prior work has developed a variety of…
Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…
We propose a framework to solve non-linear and history-dependent mechanical problems based on a hybrid classical computer -- quantum annealer approach. Quantum Computers are anticipated to solve particular operations exponentially faster.…
This paper considers a version of the Wiener filtering problem for equalization of passive quantum linear quantum systems. We demonstrate that taking into consideration the quantum nature of the signals involved leads to features typically…
Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to…
As in classical reversible computing, Quantum Arithmetic is typically seen as a set of tools that process binary data encoded into a quantum register to set the value of another quantum register. This article presents another approach to…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…
We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level set method, these new quantum algorithms for nonlinear…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
Quantum computing has demonstrated potential for solving complex optimization problems; however, its application to spatial regionalization remains underexplored. Spatial contiguity, a fundamental constraint requiring spatial entities to…
A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential…