46 citations · 67 across the 3 of their papers we have counts for
6 papers
Causal dynamics of discrete manifolds
Pablo Arrighi, Clément Chouteau, Stefano Facchini +1
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in t…
Quantum walking in curved spacetime: discrete metric
Pablo Arrighi, Giuseppe Di Molfetta, Stefano Facchini
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuu…
Quantum walking in curved spacetime: dimensions, and beyond
Pablo Arrighi, Stefano Facchini
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, l…
Quantum walking in curved spacetime
Pablo Arrighi, Stefano Facchini, Marcelo Forets
A discrete-time Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar…
Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
Pablo Arrighi, Stefano Facchini, Marcelo Forets
We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)-dimensional discrete spacetime. The theory admits a diag…
Decoupled Quantum Walks, models of the Klein-Gordon and wave equations
Pablo Arrighi, Stefano Facchini
Decoupling a vectorial PDE consists in solving the system for each component, thereby obtaining scalar PDEs that prescribe the evolution of each component independently. We present…