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The nonlinear optical response of a system of molecules often contains contributions whereby the products of lower-order processes in two separate molecules give signals that appear on top of a genuine direct higher-order process with a…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…
Quantum electrodynamics predicts the vacuum to behave as a non-linear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard…
Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic…
We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
We propose a novel technique that promises hope of being the first to directly detect a polarization in the quantum electrodynamic (QED) vacuum. The technique is based upon the use of ultra-short pulses of light circulating in low…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied…
Non-equilibrium steady states are a focal point of research in the study of open quantum systems. Previous variational algorithms for searching these steady states have suffered from resource-intensive implementations due to vectorization…
We propose quantum algorithms for complex-valued nonlinear partial differential equations in the strongly nonlinear regime, where the dynamics is governed by vortex cores, phase singularities, and nonlinear vortex interactions. Examples…
We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity. The stochastic part of the system is modeled by a Gaussian…
Solving high-dimensional partial differential equations (PDEs) is a major challenge in scientific computing. We develop a new numerical method for solving elliptic-type PDEs by adapting the Q-learning algorithm in reinforcement learning.…
We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…
Coupling light to ensembles of strongly interacting particles has emerged as a promising route toward achieving few photon nonlinearities. One specific way to implement this kind of nonlinearity is to interface light with highly excited…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schr\"odingersation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…