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Dirac particle dynamics is encoded as a unitary path summation rule andimplemented on a qubit array, where the qubit array represents both spacetimeand the fermions contained therein. The unitary path summation rule gives aquantum algorithm to model a many-body system of Dirac particles in a gaugefield with Lorentz invariance down to the grid scale (Planck scale)--thelattice-based model neither suffers the Fermi-sign problem nor breaks Lorentzinvariance. Yet, for the Dirac Hamiltonian to generate the unitary evolution ofthe 4-spinor field at the Planck scale, there is time dilation between theshortest observable time near a single space point and that time measured atlong-wavelength scales. We find gravitational time dilation where the modelspace around each point (with an even number of qubits) is curved like thespace around a Schwarzschild black hole.

Quantum computational path summation for relativistic quantum mechanics  and a time dilation relation for a Dirac Hamiltonian generator on a qubit  array