Quantum Systems from Random Probabilistic Automata

• URL: http://arxiv.org/abs/2405.09829v1
• Date: Thu, 16 May 2024 06:06:04 GMT
• Title: Quantum Systems from Random Probabilistic Automata
• Authors: A. Kreuzkamp, C. Wetterich,
• Abstract summary: Probabilistic cellular automata with deterministic updating are quantum systems. We find particular initial probability which distributions reemerge periodically after a certain number of time steps. Conservation of energy and momentum are essential ingredients for the understanding of the evolution of our probabilistic automata.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial configurations. The properties of the deterministic updating are randomly distributed over space and time. We are interested in a possible continuum limit for a very large number of cells. As an example we consider bits with two colors, moving to the left or right on a linear chain. At randomly distributed scattering points, they change direction and color. A numerical simulation reveals the typical features of quantum systems. We find particular initial probability distributions which reemerge periodically after a certain number of time steps, as produced by the periodic evolution of energy eigenstates in quantum mechanics. Using a description in terms of wave functions allows to introduce statistical observables for momentum and energy. They characterize the probabilistic information without taking definite values for a given bit configuration, with a conceptual status similar to temperature in classical statistical thermal equilibrium. Conservation of energy and momentum are essential ingredients for the understanding of the evolution of our stochastic probabilistic automata. This evolution resembles in some aspects a single Dirac fermion in two dimensions with a random potential.

Related papers

• On spooky action at a distance and conditional probabilities [0.0]
  We make explicit the analogy between the classical notion of non-independent probability distribution and the quantum notion of entangled state.<n>In the classical case, afet observing one of the random variables, the underlying sample space and the probability distribution change.<n>In the quantum case, when and event pertaining to one of the components is observed, the post-measurement state captures, both, the change in the state of the system and implicitly the new probability distribution.
  arXiv  Detail & Related papers  (2026-01-20T11:42:47Z)
• Expectation-Realization Interpretation of Quantum Superposition [8.869712776184477]
  I show that a quantum superposition should be understood as an expectation over possible eigenstates weighted by wave-like probabilities.<n>A measurement is indeed an activity employing a certain event to convert a quantum effect into a macroscopic outcome.
  arXiv  Detail & Related papers  (2025-11-06T08:01:16Z)
• Bayes or Heisenberg: Who(se) Rules? [28.888157650952675]
  We show that quantum systems can be reformulated as probabilistic equations expressed in terms of probabilistic state vectors.<n>These representations can, in turn, be approximated by the neural network dynamics of the Brain (TB) model.
  arXiv  Detail & Related papers  (2025-10-14T14:27:18Z)
• Quantum Probability via the Method of Arbitrary Functions [0.0]
  We argue that in a toy model of quantum measurement the Born rule probabilities can be derived from the unitary Schr"odinger dynamics. Our results establish the Born rule as a type of universal limiting behavior that is independent of the precise initial dynamical parameters.
  arXiv  Detail & Related papers  (2024-09-24T21:00:11Z)
• The probabilistic world II : Quantum mechanics from classical statistics [0.0]
  A simple neuromorphic computer based on neurons in an active or quiet state within a probabilistic environment can learn the unitary transformations of an entangled two-qubit system. Our explicit constructions constitute a proof that no-go theorems for the embedding of quantum mechanics in classical statistics are circumvented.
  arXiv  Detail & Related papers  (2024-08-09T14:02:55Z)
• Continuously Monitored Quantum Systems beyond Lindblad Dynamics [68.8204255655161]
  We study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state.
  arXiv  Detail & Related papers  (2023-05-06T18:09:17Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality [69.62715388742298]
  We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs) We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
  arXiv  Detail & Related papers  (2022-03-08T14:47:39Z)
• Fermionic quantum field theories as probabilistic cellular automata [0.0]
  A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata. Probabilistic cellular automata on a one-dimensional lattice are equivalent to two - dimensional quantum field theories for fermions.
  arXiv  Detail & Related papers  (2021-11-12T14:01:23Z)
• Quantum fermions from classical bits [0.0]
  A simple cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. The automaton acts deterministically on bit configurations.
  arXiv  Detail & Related papers  (2021-06-29T15:47:40Z)
• Machine learning time-local generators of open quantum dynamics [18.569079917372736]
  In the study of closed many-body quantum systems one is often interested in the evolution of a subset of degrees of freedom. In the simplest case the evolution of the reduced state of the system is governed by a quantum master equation with a time-independent, i.e. Markovian, generator. Here we are interested in understanding to which extent a neural network function approximator can predict open quantum dynamics from an underlying unitary dynamics.
  arXiv  Detail & Related papers  (2021-01-21T13:10:01Z)
• Quantum dynamics on a lossy non-Hermitian lattice [12.373452169290541]
  We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice. Quantum walker initially located on one of the non-leaky sites will finally disappear after a length of evolution time. The intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of edge states.
  arXiv  Detail & Related papers  (2020-11-15T03:51:13Z)
• The probabilistic world [0.0]
  We show that cellular automata are quantum systems in a formulation with discrete time steps and real wave functions. The quantum formalism for classical statistics is a powerful tool which allows us to implement for generalized Ising models the momentum observable.
  arXiv  Detail & Related papers  (2020-11-04T14:05:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.