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To solve nonlinear partial differential equations (PDEs) is one of the most common but important tasks in not only basic sciences but also many practical industries. We here propose a quantum variational (QuVa) PDE solver with the aid of…
We propose a physics-informed quantum algorithm to solve nonlinear and multidimensional differential equations (DEs) in a quantum latent space. We suggest a strategy for building quantum models as state overlaps, where exponentially large…
Quantum linear-system algorithms (QLSAs) have rigorous worst-case complexity guarantees, but their runtimes are often chosen from spectral information assumed in advance. What is largely lacking is an a posteriori progress flag: most QLSA…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Quantum Interior Point Methods (QIPMs) have been attracting significant interests recently due to their potential of solving optimization problems substantially faster than state-of-the-art conventional algorithms. In general, QIPMs use…
Nonlinear differential equations exhibit rich phenomena in many fields but are notoriously challenging to solve. Recently, Liu et al. [1] demonstrated the first efficient quantum algorithm for dissipative quadratic differential equations…
We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic…
Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum…
We present a novel variational quantum framework for linear partial differential equation (PDE) constrained optimization problems. Such problems arise in many scientific and engineering domains. For instance, in aerodynamics, the PDE…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
We present a detailed numerical study of an alternative approach, named Quantum Non-Demolition Measurement (QNDM), to efficiently estimate the gradients or the Hessians of a quantum observable. This is a key step and a resource-demanding…
Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods as a function of the problem dimension. At the same time, the known quantum algorithms scale very unfavorably…
Differential equations are a crucial mathematical tool used in a wide range of applications. If the solution to an initial value problem (IVP) can be transformed into an oracle, it can be utilized in various fields such as search and…
Reducing the dimension of nonlinear data is crucial in data processing and visualization. The locally linear embedding algorithm (LLE) is specifically a representative nonlinear dimensionality reduction method with well maintaining the…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…
In numerical approaches to solving differential equations on a lattice, a representation of the derivative operator that correctly matches the continuum behaviour of functions of momentum up to the band limit must be non-local. We present…
Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…
Improving renewable energy resource utilization efficiency is crucial to reducing carbon emissions, and multi-parametric programming has provided a systematic perspective in conducting analysis and optimization toward this goal in smart…
In this paper, we propose and study neural network based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…