Related papers: Generic and Scalable Differential Equation Solver …
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…
Variational quantum eigensolver (VQE), aiming at determining the ground state energy of a quantum system described by a Hamiltonian on noisy intermediate scale quantum (NISQ) devices, is among the most significant applications of…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
Quantum computing has demonstrated the potential to solve computationally intensive problems more efficiently than classical methods. Many software engineering tasks, such as test case selection, static analysis, code clone detection, and…
Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and 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…
Quantum algorithms offer a compelling new avenue for addressing difficult NP-complete optimization problems, such as the Generalized Assignment Problem (GAP). Given the operational constraints of contemporary Noisy Intermediate-Scale…
Current quantum computers are limited in the number of qubits and coherence time, constraining the algorithms executable with sufficient fidelity. The variational quantum eigensolver (VQE) is an algorithm to find an approximate ground state…
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over…
Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex…
This paper presents a tool that simplifies quantum software development by unifying circuit design, code generation, and execution within a single cross-platform environment that supports iterative development. Implemented as open source,…
Characterizing quantum phases-of-matter at finite-temperature is essential for understanding complex materials and large-scale thermodynamic phenomena. Here, we develop algorithmic protocols for simulating quantum thermodynamics on quantum…
Quantum computing is entering a transformative phase with the emergence of logical quantum processors, which hold the potential to tackle complex problems beyond classical capabilities. While significant progress has been made, applying…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
Variational Quantum optimization algorithms, such as the Variational Quantum Eigensolver (VQE) or the Quantum Approximate Optimization Algorithm (QAOA), are among the most studied quantum algorithms. In our work, we evaluate and improve an…
Quantum Phase Estimation (QPE) is a cardinal algorithm in quantum computing that plays a crucial role in various applications, including cryptography, molecular simulation, and solving systems of linear equations. However, the standard…
Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To-date, experimental demonstrations of algorithms such as…
Great efforts have been dedicated in recent years to explore practical applications for noisy intermediate-scale quantum (NISQ) computers, which is a fundamental and challenging problem in quantum computing. As one of the most promising…
Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…
The Variational Quantum Eigensolver (VQE) is a promising algorithm for quantum computing applications in chemistry and materials science, particularly in addressing the limitations of classical methods for complex systems. This study…