Related papers: Does universal controllability of physical systems…
Thermodynamics is a macroscopic physical theory whose two very general laws are independent of any underlying dynamical laws and structures. Nevertheless, its generality enables us to understand a broad spectrum of phenomena in physics,…
Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case it corresponds to having a time-dependent Hamiltonian. However, the quantum…
A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY…
We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…
How well can quantum computers simulate classical dynamical systems? There is increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond Hamiltonian simulation, but so far exact resource estimates are not…
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…
We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…
The relationship between the thermodynamic and computational characteristics of dynamical physical systems has been a major theoretical interest since at least the 19th century, and has been of increasing practical importance as the…
This paper examines the claim that cellular automata (CA) belonging to Class III (in Wolfram's classification) are capable of (Turing universal) computation. We explore some chaotic CA (believed to belong to Class III) reported over the…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both…
Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with…
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter', and features a global symmetry. One then…
The hardware and software foundations laid in the first half of the 20th Century enabled the computing technologies that have transformed the world, but these foundations are now under siege. The current computing paradigm, which is the…
Control of open quantum systems is an essential ingredient to the realization of contemporary quantum science and technology. We demonstrate such control by employing a thermodynamically consistent framework, taking into account the fact…
We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists…
We describe a new statistical pattern in the chaotic dynamics of closed inflationary cosmologies, associated with the partition of the Hamiltonian rotational motion energy and hyperbolic motion energy pieces, in a linear neighborhood of the…
We develop a general optimization strategy for performing a chosen unitary or non-unitary task on an open quantum system. The goal is to design a controlled time-dependent system Hamiltonian by variationally minimizing or maximizing a…
Hamiltonian quantum gates controlled by classical electromagnetic fields form the basis of any realistic model of quantum computers. In this letter, we derive a lower bound on the field energy required to implement such gates and relate…
A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…