Related papers: A Quantum Linear Systems Pathway for Solving Diffe…
Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are…
Detecting and quantifying quantum entanglement remain significant challenges in the noisy intermediate-scale quantum (NISQ) era. This study presents the implementation of quantum support vector machines (QSVMs) on IBM quantum devices to…
From weather to neural networks, modeling is not only useful for understanding various phenomena, but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their…
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit…
Quantum computing holds immense potential for solving classically intractable problems by leveraging the unique properties of quantum mechanics. The scalability of quantum architectures remains a significant challenge. Multi-core quantum…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
In this study, we propose the Quantum Gradient Flow Algorithm (QGFA), a novel quantum algorithm for solving symmetric positive definite (SPD) linear systems based on the variational formulation and time-evolution dynamics. Conventional…
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
This work presents a fully quantum approach to support vector machine (SVM) learning by integrating gate-based quantum kernel methods with quantum annealing-based optimization. We explore the construction of quantum kernels using various…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
Recent advancements in quantum computing (QC) and machine learning (ML) have garnered significant attention, leading to substantial efforts toward the development of quantum machine learning (QML) algorithms to address a variety of complex…
Polynomial systems over the binary field have important applications, especially in symmetric and asymmetric cryptanalysis, multivariate-based post-quantum cryptography, coding theory, and computer algebra. In this work, we study the…
We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multiscale hyperbolic heat system with quantum algorithms (hence…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
Quantum computers face inherent scaling challenges, a fact that necessitates investigation of distributed quantum computing systems, whereby scaling is achieved through interconnection of smaller quantum processing units. However,…
The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference…