Related papers: Twisted Pseudodifferential Calculus and Applicatio…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct…
This memoir is a summary of recent work, including collaborations with Erik van Erp, Christian Voigt and Marco Matassa, compiled for the "Habilitation \`a diriger des recherches". We present various different approaches to constructing…
A pseudodifferential calculus for parameter-dependent operators on smooth manifolds with boundary in the spirit of Boutet de Monvel's algebra is constructed. The calculus contains, in particular, the resolvents of realizations of…
A central roadblock in the realization of variational quantum eigensolvers on quantum hardware is the high overhead associated with measurement repetitions, which hampers the computation of complex problems, such as the simulation of mid-…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
We prove a semiclassical resolvent estimate for a broad class of non-self-adjoint, non-elliptic pseudodifferential operators in the low-lying spectral regime. The proof relies on improved ellipticity properties for the symbol of the…
Let $G$ be a unimodular type I second countable locally compact group and $\hat G$ its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on $G\times\hat G$, and its relations to…
The Lewis and Riesenfeld method has been investigated, by Ramos et al in Ref.[1], for quantum systems governed by time-dependent PT symmetric Hamiltonians and particularly where the quantum system is a particle submitted to action of a…
This paper is based on talks delivered in summer 2008 at the Conference on Motives, QFT and Pseudodifferential Operators in Boston, and at the Trimester programme Geometry and Physics, Hausdorff Institute for Mathematics in Bonn The paper…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…
The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on $\mathbb{R}^{n}\oplus\mathbb{R}^{n}$. In this paper we will show that the replacement of this structure by an arbitrary symplectic…
In this study, we propose a generalized pseudoclassical theory for the kicked rotor model in an attempt to discern the footprints of the classical dynamics in the deep quantum regime. Compared with the previous pseudoclassical theory that…
A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…
We present analytic solutions to the evolution in generalized tight-binding models, which consider complex first-neighbor couplings with equal amplitude and arbitrary phases. Our findings provide a powerful tool for efficiently calculating…
In this paper, we introduce and study a class of pseudo-differential operators on the lattice $\mathbb{Z}^n$. More preciously, we consider a weighted symbol class $M_{\rho, \Lambda}^m(\mathbb{ Z}^n\times \mathbb{T}^n), m\in \mathbb{R}$…
This is a review of some coordinate-free calculi of pseudodifferential operators developed in the last years. As an application, we use a coordinate-free calculus to obtain new results on the behaviour of the spectral projections of a…
Extracting the Hamiltonian of interacting quantum-information processing systems is a keystone problem in the realization of complex phenomena and large-scale quantum computers. The remarkable growth of the field increasingly requires…
In previous articles, a magnetic pseudodifferential calculus and a family of C*-algebras associated with twisted dynamical systems were introduced and the connections between them have been established. We extend this formalism to symbol…
Quantum computers could potentially simulate the dynamics of systems such as polyatomic molecules on a much larger scale than classical computers. We investigate a general quantum computational algorithm that simulates the time evolution of…