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

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.