We propose P-order (Power-order), a unified, norm-independent framework for quantifying the convergence rates of iterative methods. Standard analyses based on Q-order are norm-dependent and require some uniformity of ...
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Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interes...
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Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interest using minimal quantum resources. In this work, we will use eigenvector continuation to build a subspace from the low-lying states of a set of Hamiltonians. The basis vectors are prepared using truncated versions of standard state preparation methods such as imaginary-time evolution (ITE), adiabatic state preparation (ASP), and variational quantum eigensolver. By using these truncated methods combined with eigenvector continuation, we can directly improve upon them, obtaining more accurate ground-state energies at a reduced cost. We use several spin systems to demonstrate convergence even when methods like ITE and ASP fail, such as ASP in the presence of level crossings and ITE with vanishing energy gaps. We also showcase the noise resilience of this approach beyond the gains already made by having shallower quantum circuits. Our findings suggest that eigenvector continuation can be used to improve existing state preparation methods in the near term.
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank line...
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This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial d...
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We determine the Euclidean distance degrees of the three most common manifolds arising in manifold optimization: flag, Grassmann, and Stiefel manifolds. For the Grassmannian, we will also determine the Euclidean dista...
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We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The ...
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This paper establishes sharp dimension-free concentration inequalities and expectation bounds for the deviation of the sum of simple random tensors from its expectation. As part of our analysis, we use generic chainin...
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The stopping power of warm dense plasmas for electrons is a critical aspect in the study of hot electron transport. An externally applied strong magnetic field can significantly influence electron transport behavior d...
The stopping power of warm dense plasmas for electrons is a critical aspect in the study of hot electron transport. An externally applied strong magnetic field can significantly influence electron transport behavior due to various factors. However, the impact of external magnetic fields on the motion of incident particles is often overlooked. Through molecular dynamics simulations using the electron force field (eFF) method, this study investigates the stopping process of individual hot electrons in warm dense deuterium plasma under an applied longitudinal magnetic field. Results show that, at typical laboratory magnetic field intensities, the magnetic field significantly alters electron trajectories without notable effects on average stopping power, trajectory length, or scattering angle. Even with increased magnetic field intensity beyond 500 kT, it doesn’t affect the total kinetic energy loss of incident electrons but reduces stopping power by compressing the scattering angle distribution width. Due to the increase in the scattering angle distribution width with intensified fluctuations in high-temperature targets, the impact of the additional magnetic field on stopping power becomes more pronounced with an increase in target temperature.
In this paper, we investigate the stability and time-step constraints for solving advection-diffusion equations using exponential time differencing (ETD) Runge–Kutta (RK) methods in time and discontinuous Galerkin (D...
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This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multi...
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