Related papers: Singular Perturbation Approximations for a Class o…
As quantum optical phenomena are based on Maxwell's equations, and it is becoming important to understand quantum optical phenomena at short distances, so it is important to analyze quantum optics using short distance corrected Maxwell's…
In this review we give a brief overview of quantum simulation as applied to the study of complex systems. In particular, we cover the basic ideas of quantum simulation, neuromorphic computation, the Sachdev-Ye-Kitaev model, as well as…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Making measurements on single quantum systems is considered difficult, almost impossible if the state is a-priori unknown. Protective measurements suggest a possibility to measure single quantum systems and gain some new information in the…
Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This solves the long standing problem of quantizing the resonances and chaotic regions generically appearing in…
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…
We present an algorithm that exploits quantum parallelism to simulate randomness in a quantum system. In our scheme, all possible realizations of the random parameters are encoded quantum mechanically in a superposition state of an…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is…
Linear optics quantum computing (LOQC) is a leading candidate for the implementation of large scale quantum computers. Here quantum information is encoded into the quantum states of light and computation proceeds via a linear optics…
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.…
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined…
In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this…
In this paper, we present a collection of results on the observability of quantum mechanical systems, in the case the output is the result of a discrete nonselective measurement. By defining an effective observable we extend previous…
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…
Quantum sensing encompasses highly promising techniques with diverse applications including noise-reduced imaging, super-resolution microscopy as well as imaging and spectroscopy in challenging spectral ranges. These detection schemes use…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
A phase space treatment of special relativity of quantum systems is developed. In this approach a quantum particle remains localized if subject to inertial transformations, the localization occurring in a finite phase space area. Unlike…
We use the method of homological quantum reduction to construct a deformation quantization on singular symplectic quotients in the situation, where the coefficients of the moment map define a complete intersection. Several examples are…