Causal Fermions in Discrete Spacetime

TL;DR

This paper explores fermionic systems in discrete spacetime with strict causality, demonstrating their decomposition into local unitaries, their equivalence to quantum cellular automata, and their potential for efficient quantum simulation.

Contribution

It introduces a framework for causal fermionic systems in discrete spacetime, showing their decomposition, connection to quantum cellular automata, and simulation on quantum computers.

Findings

Decomposition of fermionic evolution into local unitaries

Equivalence to quantum cellular automata models

Efficient quantum simulation of causal fermions

Abstract

In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete spacetime can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete spacetime that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete spacetime can be efficiently simulated on a quantum computer.