Related papers: An implicit ODE-based numerical solver for the sim…
Many important systems across biology, engineering, physics, and economics are characterized by polynomial ordinary differential equations (ODEs), yet analytical solutions are rare. We develop a framework for identifying and solving a broad…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…
High intense electromagnetic fields can be unique probes to study natures of macroscopic vacua by themselves. Combining accelerators with the intense field can provide more fruitful probes which can neither be achieved by only intense…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
We analyze the propagation of light in the context of nonlinear electrodynamics, as it occurs in modified QED vacua. We show that the corresponding characteristic equation can be described in terms of a modification of the effective…
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
A numerical study of the Einstein field equations, based on the 3+1 foliation of the spacetime, is presented. A pseudo-spectral technique has been employed for simulations in vacuum, within two different formalisms, namely the…
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…
Cavity quantum electrodynamics (QED), the study of the interaction between quantized emitters and photons confined in an optical cavity, is an important tool for quantum science in computing, networking, and synthetic matter. In atomic…
High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties,…
As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
We provide a recipe for the digitalization of linear and nonlinear quantum optics in networks of superconducting qubits. By combining digital techniques with boson-qubit mappings we address relevant problems which are typically considered…
Quantum algorithms for computing classical nonlinear maps are widely known for toy problems but might not suit potential applications to realistic physics simulations. Here, we propose how to compute a general differentiable invertible…
Including the effect of the molecular environment in the numerical modeling of time-resolved electronic spectroscopy remains an important challenge in computational spectroscopy. In this contribution, we present a general approach for the…
Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds…
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…