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The Heisenberg-Euler theory of the quantum vacuum supplements Maxwell's theory of electromagnetism with nonlinear light-light interactions. These originate in vacuum fluctuations, a key prediction of quantum theory, and can be triggered by…
The quantum vacuum constitutes a fascinating medium of study, in particular since near-future laser facilities will be able to probe the nonlinear nature of this vacuum. There has been a large number of proposed tests of the low-energy,…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
We study all-optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum, using the collision of two focused high-intensity laser pulses as an example. The experimental signatures of quantum…
New processes associated with the nonlinear optical properties of the electromagnetic vacuum, as predicted by quantum electrodynamics are described. We consider the presence of a static and a rotating magnetic field. The cases of harmonic…
Up to date, quantum electrodynamics (QED) is the most precisely tested quantum field theory. Nevertheless, particularly in the high-intensity regime it predicts various phenomena that so far have not directly been accessible in all-optical…
We study the conditions required to distinguish laser-induced nonlinear quantum electrodynamics (QED) effects in vacuum from competing signals due to interactions of laser pulses with ionized residual gas. The latter is inevitably present…
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a…
Optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum can be conveniently described in terms of stimulated photon emission processes induced by strong classical, space-time dependent…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…
We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level set method, these new quantum algorithms for nonlinear…
State-of-the-art numerical simulations of quantum electrodynamical (QED) processes in strong laser fields rely on a semiclassical combination of classical equations of motion and QED rates, which are calculated in the locally constant field…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
Vacuum polarization, a key prediction of quantum theory, can cause a variety of intriguing phenomena that can be triggered by high-intensity laser pulses. The Heisenberg-Euler theory of the quantum vacuum supplements Maxwell's theory of…
The QED effective action encodes nonlinear interactions due to quantum vacuum polarization effects. While much is known for the special case of electrons in a constant electromagnetic field (the Euler-Heisenberg case), much less is known…
A new non-perturbative method of solution of the nonlinear Heisenberg equations in the finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schrodinger picture method, is based on a finite operator…
The process of photon-photon scattering in vacuum is investigated analytically in the long-wavelength limit within the framework of the Euler-Heisenberg Lagrangian. In order to solve the nonlinear partial differential equations (PDEs)…