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Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
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…
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…
The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
Quantum computing holds the promise of solving computational mechanics problems in polylogarithmic time, meaning computational time scales as $\mathscr{O}((\log N)^c)$, where $N$ is the problem size and $c$ a constant. We propose a quantum…
Solving high-dimensional partial differential equations (PDEs) is a major challenge in scientific computing. We develop a new numerical method for solving elliptic-type PDEs by adapting the Q-learning algorithm in reinforcement learning.…
For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with an end-to-end practical applications -- in this instance, fluid dynamics. We debut here a high performance…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
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…
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…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown…
The efficient resolution of optimization problems is one of the key issues in today's industry. This task relies mainly on classical algorithms that present scalability problems and processing limitations. Quantum computing has emerged to…
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally…