Related papers: An implicit ODE-based numerical solver for the sim…
Our goal is to study optical signatures of quantum vacuum nonlinearities in strong macroscopic electromagnetic fields provided by high-intensity laser beams. The vacuum emission scheme is perfectly suited for this task as it naturally…
The 1+1D O(3) non-linear {\sigma}-model is a model system for future quantum lattice simulations of other asymptotically-free theories, such as non-Abelian gauge theories. We find that utilizing dimensional reduction can make efficient use…
Analytic results for (Q)ED processes in external fields are limited to a few special cases, such as plane waves. However, the strong focussing of intense laser fields implies a need to go beyond the plane wave model. By exploiting…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
We develop an analog classical simulation algorithm of noiseless quantum dynamics. By formulating the Schr\"{o}dinger equation into a linear system of real-valued ordinary differential equations (ODEs), the probability amplitudes of a…
The numerical simulation of the 3D incompressible Euler equation is analyzed with respect to different integration methods. The numerical schemes we considered include spectral methods with different strategies for dealiasing and two…
Quantum photon effects in vacuum provide an interesting setting to test quantum electrodynamics, serving as a source for predictions about physics beyond the Standard Model. In this paper, we investigate these effects by calculating the…
Upcoming high-intensity laser systems will be able to probe the quantum-induced nonlinear regime of electrodynamics. So far unobserved QED phenomena such as the discovery of a nonlinear response of the quantum vacuum to macroscopic…
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 known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
With the aim of progressing toward a practical implementation of an effective quantum-electrodynamics (QED) theory of atoms and molecules, which includes the effects of vacuum polarization through the creation of virtual electron-positron…
Some of the basic notions of nonlinear optics are summarized and then applied to the case of the Dirac vacuum, as described by the Heisenberg-Euler effective one-loop Lagrangian. The theoretical and experimental basis for the appearance of…
Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…
The invention of laser immediately enabled us to detect nonlinearities of photon interaction in matter, as manifested for example by Franken et al.'s detection of second harmonic generation and the excitation of the Brillouin forward…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While, the zeroth order linearization approximation to the operators is normally used, here first and second order…