Related papers: Discrete Time Quantum Mechanics
An alternative approach to lattice gauge theory has been under development for the past decade. It is based on discretizing the operator Heisenberg equations of motion in such a way as to preserve the canonical commutation relations at each…
In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
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…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard…
We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
Discrete combinatorial optimization consists in finding the optimal configuration that minimizes a given discrete objective function. An interpretation of such a function as the energy of a classical system allows us to reduce the…
The recently introduced consistent discrete lattice formulation of canonical general relativity produces a discrete theory that is constraint-free. This immediately allows to overcome several of the traditional obstacles posed by the…
We propose a technique to design control algorithms for a class of finite dimensional quantum systems so that the control law does not present discontinuities. The class of models considered admits a group of symmetries which allows us to…
Efficient continuous time quantum Monte Carlo (CT-QMC) algorithms that do not suffer from time discretization errors have become the state-of-the-art for most discrete quantum models. They have not been widely used yet for fermionic quantum…
We propose an improved scheme of perturbation theory based on our exact solution [An Min Wang, quant-ph/0611216] in general quantum systems independent of time. Our elementary start-point is to introduce the perturbing parameter as late as…
This thesis is split into two parts, which are united in the sense that they involve applying ideas from quantum information to fundamental physics. The first part is focused on examining discrete-time models in quantum computation…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…
The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
Path integrals are usually formulated in discrete Euclidean time using the Trotter formula. We propose a new method to study discrete quantum systems, in which we work directly in the Euclidean time continuum. The method is of general…