Related papers: Quantum Algorithms for Nonlinear Differential Equa…
We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
We develop a convergence theory for non-monotone approximation schemes for fully nonlinear parabolic partial differential equations. Modern computational methods such as kernel-based collocation, spectral methods, physics-informed neural…
We analyze the Schr\"odingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schr\"odingerization technique, introduced in [31], transforms any linear ordinary and partial…
We present a probabilistic quantum algorithm for preparing mixed states which, in expectation, are proportional to the solutions of Lyapunov equations -- linear matrix equations ubiquitous in the analysis of classical and quantum dynamical…
We develop the framework for a non-intrusive, quadrature-based method for approximate balanced truncation (QuadBT) of linear systems with quadratic outputs, thus extending the applicability of QuadBT, which was originally designed for…
The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
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…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized version of the Koopman-von Neumann formulation of nonlinear…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
Dynamical systems with quadratic outputs have recently attracted significant attention. In this paper, we consider bilinear dynamical systems, a special class of weakly nonlinear systems, with a quadratic output. We develop various…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states…
We propose random non-Hermitian Hamiltonians to model the generic stochastic nonlinear dynamics of a quantum state in Hilbert space. Our approach features an underlying linearity in the dynamical equations, ensuring the applicability of…