Related papers: Quantum framework for parameterizing partial diffe…
The paper investigates the techniques of quantum computation in metrological predictions, with a particular emphasis on enhancing prediction potential through variational parameter estimation. The applicability of quantum simulations and…
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
Dual encoders have been used for question-answering (QA) and information retrieval (IR) tasks with good results. Previous research focuses on two major types of dual encoders, Siamese Dual Encoder (SDE), with parameters shared across two…
We describe a numerical framework that uses random sampling to efficiently capture low-rank local solution spaces of multiscale PDE problems arising in domain decomposition. In contrast to existing techniques, our method does not rely on…
The study of parameter-dependent partial differential equations (parametric PDEs) with countably many parameters has been actively studied for the last few decades. In particular, it has been well known that a certain type of parametric…
We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form $\m{A}x=\lambda\m{B}x$, where the matrices $\m{A}$ and/or $\m{B}$ may depend on a scalar parameter.…
We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are…
A large body of recent work has begun to explore the potential of parametrized quantum circuits (PQCs) as machine learning models, within the framework of hybrid quantum-classical optimization. In particular, theoretical guarantees on the…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
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…
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…
Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems using parameterized quantum circuits (PQCs). The design of these circuits influences the ability 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 computers are a revolutionary class of computational platforms with applications in combinatorial and global optimization, machine learning, and other domains involving computationally hard problems. While these machines typically…
Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications…
We study and extend the semidefinite programming (SDP) hierarchies introduced in [Phys. Rev. Lett. 115, 020501] for the characterization of the statistical correlations arising from finite dimensional quantum systems. First, we introduce…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…