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In this paper, we consider fermionic systems in discrete space-time 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 space-time 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 space-time 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 space-time can be efficiently simulated on a quantum computer.
|Number of pages||15|
|Journal||Physical Review A: Atomic, Molecular and Optical Physics|
|Publication status||Published - 3 Jan 2014|
- QUANTUM COMPUTER
Person: Academic , Member