Related papers: Carleman linearization approach for chemical kinet…
We introduce the FCHL19 representation for atomic environments in molecules or condensed-phase systems. Machine learning models based on FCHL19 are able to yield predictions of atomic forces and energies of query compounds with chemical…
With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
This work is devoted to the development and analysis of a linearization algorithm for microscopic elliptic equations, with scaled degenerate production, posed in a perforated medium and constrained by the homogeneous Neumann-Dirichlet…
Many quantum algorithms, such as Harrow-Hassidim-Lloyd (HHL) algorithm, depend on oracles that efficiently encode classical data into a quantum state. The encoding of the data can be categorized into two types; analog-encoding where the…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
We reiterate the contribution made by Harrow, Hassidim, and Llyod to the quantum matrix equation solver with the emphasis on the algorithm description and the error analysis derivation details. Moreover, the behavior of the amplitudes of…
This paper aims to reconstruct the initial condition of a hyperbolic equation with an unknown damping coefficient. Our approach involves approximating the hyperbolic equation's solution by its truncated Fourier expansion in the time domain…
Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…
This chapter provides an introduction to Hybrid High-Order (HHO) methods. These are new generation numerical methods for PDEs with several advantageous features: the support of arbitrary approximation orders on general polyhedral meshes,…
The role of entanglement is discussed in the Harrow-Hassidim-Lloyd (HHL) algorithm. We compute all tripartite entanglement at every steps of the HHL algorithm. The tripartite entanglement is generated in the first quantum phase estimation…
Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
Comparisons of higher-order predictions within the Standard Model of Particle Physics (SM) to data are central to high-energy collider experiments like the Large Hadron Collider (LHC). Processes with multiple kinematic scales, such as…
We explore the Carlemann linearization of the collision term of the lattice Boltzmann formulation, as a first step towards formulating a quantum lattice Boltzmann algorithm. Specifically, we deal with the case of a single, incompressible…
We assess the convergence of the Carleman linearization of advection-diffusion-reaction (ADR) equations with a logistic nonlinearity. It is shown that five Carleman iterates provide a satisfactory approximation of the original ADR across a…
A new open-source cluster finding library ''Common Clusterization Library'' (CCL) is proposed to describe the clusters production when applied to the transport codes. The new library was applied to the Parton-Hadron-Quantum-Molecular…
Quantum computation consists of a quantum state corresponding to a solution, and measurements with some observables. To obtain a solution with an accuracy $\epsilon$, measurements $O(n/\epsilon^2)$ are required, where $n$ is the size of a…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
One of the most computationally challenging problems expected for the High-Luminosity Large Hadron Collider (HL-LHC) is determining the trajectory of charged particles during event reconstruction. Algorithms used at the LHC today rely on…