Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model

• URL: http://arxiv.org/abs/2207.09465v3
• Date: Wed, 5 Jul 2023 20:55:56 GMT
• Title: Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model
• Authors: Kevin Slagle and John Preskill
• Abstract summary: We formulate a conceptually new model in which quantum mechanics emerges from classical mechanics. We analytically estimate how much the model deviates from quantum mechanics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We formulate a conceptually new model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian $H$ acting on $n$ qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately -- but to arbitrary precision -- described by Schr\"{o}dinger's equation and $H$. The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wavefunction. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. We analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.

Related papers

• Phase-space gaussian ensemble quantum camouflage [0.0]
  We extend the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum. For gaussian statistical ensembles, the exact phase-space profile of the quantum fluctuations over the classical trajectories are found.
  arXiv  Detail & Related papers  (2024-09-24T18:14:07Z)
• 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)
• Equivalence between finite state stochastic machine, non-dissipative and dissipative tight-binding and Schroedinger model [0.0]
  The concept of dissipation in most general case is incorporated into tight-binding and Schroedinger model. The existence of Aharonov-Bohm effect in quantum systems can also be reproduced by the classical epidemic model.
  arXiv  Detail & Related papers  (2022-08-20T22:43:11Z)
• Localized non-relativistic quantum systems in curved spacetimes: a general characterization of particle detector models [0.0]
  We provide a consistent way of describing a localized non-relativistic quantum system undergoing a timelike trajectory in a curved spacetime. This framework naturally provides a recipe for mapping a quantum theory defined in a non-relativistic background to a theory around a timelike trajectory in curved spacetimes. We then apply our formalism to particle detector models, that is, to the case where the non-relativistic quantum system is coupled to a quantum field in a curved background.
  arXiv  Detail & Related papers  (2022-06-02T18:00:31Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• The classical limit of Schr\"{o}dinger operators in the framework of Berezin quantization and spontaneous symmetry breaking as emergent phenomenon [0.0]
  A strict deformation quantization is analysed on the classical phase space $bR2n$. The existence of this classical limit is in particular proved for ground states of a wide class of Schr"odinger operators. The support of the classical state is included in certain orbits in $bR2n$ depending on the symmetry of the potential.
  arXiv  Detail & Related papers  (2021-03-22T14:55:57Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Quantum and semi-classical aspects of confined systems with variable mass [0.3149883354098941]
  We explore the quantization of classical models with position-dependent mass terms constrained to a bounded interval in the canonical position. For a non-separable function $Pi(q,p)$, a purely quantum minimal-coupling term arises in the form of a vector potential for both the quantum and semi-classical models.
  arXiv  Detail & Related papers  (2020-05-28T18:50:24Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

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.