Quantum State Transfer through Noisy Quantum Cellular Automata

TL;DR

This paper models quantum state transfer in noisy quantum cellular automata, demonstrating that perfect transfer is possible under certain conditions and providing a framework for analyzing both unitary and open quantum evolutions.

Contribution

It introduces a class of noisy quantum cellular automata that incorporate classical stochastic dynamics and extends the model to include coherences and vacuum states.

Findings

Numerical simulations show perfect quantum state transfer is achievable in some cases.

The framework accounts for various forms of quantum noise in a homogeneous, local interaction setting.

Provides a natural description of both unitary and open quantum evolutions.

Abstract

We model the transport of an unknown quantum state on one dimensional qubit lattices by means of a quantum cellular automata evolution. We do this by first introducing a class of discrete noisy dynamics, in the first excitation sector, in which a wide group of classical stochastic dynamics is embedded within the more general formalism of quantum operations. We then extend the Hilbert space of the system to accommodate a global vacuum state, thus allowing for the transport of initial on-site coherences besides excitations, and determine the dynamical constraints that define the class of noisy quantum cellular automata in this subspace. We then study the transport performance through numerical simulations, showing that for some instances of the dynamics perfect quantum state transfer is attainable. Our approach provides one with a natural description of both unitary and open quantum evolutions, where the homogeneity and locality of interactions allow one to take into account several forms of quantum noise in a plausible scenario.