Related papers: Quantum framework for parameterizing partial diffe…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…
The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years,…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
In recent years, parameterized quantum circuits have become a major tool to design quantum algorithms for optimization problems. The challenge in fully taking advantage of a given family of parameterized circuits lies in finding a good set…
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…
Inverse problems involving partial differential equations (PDEs) with discontinuous coefficients are fundamental challenges in modeling complex spatiotemporal systems with heterogeneous structures and uncertain dynamics. Traditional…
We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-form), to the study of quantum machine learning algorithms and derive general results that are applicable to a variety of input models,…
The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Recently, Zhu et al. (PLDI 2020) have formulated differentiable quantum programming with bounded…
Quantum optimization has gained increasing attention as advances in quantum hardware enable the exploration of problem instances approaching real-world scale. Among existing approaches, variational quantum algorithms and quantum annealing…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
This work studies quantum algorithms to solve high-dimensional stochastic differential equations (SDEs) $\mathrm{d} \mathbf{X}_t = A(t) \mathbf{X}_t \mathrm{d} t + B(t) \mathrm{d} \mathbf{W}_t$. Aiming for a speed-up in the dimension $N$ of…
This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations,…
We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…
We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…
Many real-world problems, like modelling environment dynamics, physical processes, time series etc., involve solving Partial Differential Equations (PDEs) parameterised by problem-specific conditions. Recently, a deep learning architecture…
To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity so that render the…
Parametric quantum circuits play a crucial role in the performance of many variational quantum algorithms. To successfully implement such algorithms, one must design efficient quantum circuits that sufficiently approximate the solution…
Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…