Related papers: Quantum-inspired space-time PDE solver and dynamic…
The D-Wave quantum annealer has emerged as a novel computational architecture that is attracting significant interest, but there have been only a few practical algorithms exploiting the power of quantum annealers. Here we present a model…
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…
Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…
The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…
We propose a novel multi-scale message passing neural network algorithm for learning the solutions of time-dependent PDEs. Our algorithm possesses both temporal and spatial multi-scale resolution features by incorporating multi-scale…
Computational Fluid Dynamics (CFD) is central to science and engineering, but faces severe scalability challenges, especially in high-dimensional, multiscale, and turbulent regimes. Traditional numerical methods often become prohibitively…
We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing…
The matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a…
Quantum computing has long promised to revolutionize the way we solve complex problems. At the same time, tensor networks are widely used across various fields due to their computational efficiency and capacity to represent intricate…
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor…
We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal…
With the growing interest in quantum computing, the emergence of quantum supremacy has marked a pivotal milestone in the field. As a result, numerous quantum programming languages (QPLs) have been introduced to support the development of…
Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various…
Ultra-short pulses propagating in nonlinear nanophotonic waveguides can simultaneously leverage both temporal and spatial field confinement, promising a route towards single-photon nonlinearities in an all-photonic platform. In this…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
This article develops how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order…
Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide…
Dynamical decoupling (DD) is a widely-used quantum control technique that takes advantage of temporal symmetries in order to partially suppress quantum errors without the need resource-intensive error detection and correction protocols.…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
In this article, we develop a systematic approach of the invariant subspace method combined with variable transformation to find the generalized separable exact solutions of the nonlinear two-component system of time-fractional PDEs…