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In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation…
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…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
Solving optimization problems is a key task for which quantum computers could possibly provide a speedup over the best known classical algorithms. Particular classes of optimization problems including semi-definite programming (SDP) and…
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…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
We present a novel variational quantum framework for nonlinear partial differential equation (PDE) constrained optimization problems. The proposed work extends the recently introduced bi-level variational quantum PDE constrained…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…