Path-integral solution of the one-dimensional Dirac quantum cellular automaton
arXiv:1406.1021 · doi:10.1016/j.physleta.2014.09.020
Abstract
Quantum cellular automata have been recently considered as a fundamental approach to quantum field theory, resorting to a precise automaton, linear in the field, for the Dirac equation in one dimension. In such linear case a quantum automaton is isomorphic to a quantum walk, and a convenient formulation can be given in terms of transition matrices, leading to a new kind of discrete path integral that we solve analytically in terms of Jacobi polynomials versus the arbitrary mass parameter.
5 pages
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- Quantum State Transfer through Noisy Quantum Cellular Automata
- A perturbative approach to the solution of the Thirring quantum cellular automaton
- Mimicking the Hadamard discrete-time quantum walk with a time-independent Hamiltonian
- Simulating the discrete-time quantum walk dynamics with simultaneous coin and shift operators