  A quantum computer, i.e. utilizing the resources of quantum physics,
superposition of states and entanglement, could furnish an exponential gain in
computing time. A simulation using such resources is called a quantum
simulation. The advantage of quantum simulations over classical ones is well
established at the theoretical, i.e. software level. Their practical benefit
requires their implementation on a quantum hardware. The quantum computer, i.e.
the universal one (see below), has not seen the light of day yet, but the
efforts in this direction are both growing and diverse. Also, quantum
simulation has already been illustrated by numerous experimental proofs of
principle, thanks too small-size and specific-task quantum computers or
simulators. Quantum walks are particularly-studied quantum-simulation schemes,
being elementary bricks to conceive any quantum algorithm, i.e. to achieve
so-called universal quantum computation.
  The present thesis is a step more towards a simulation of quantum field
theories based on discrete-time quantum walks (DTQWs). Indeed, it is shown, in
certain cases, how DTQWs can simulate, in the continuum, the action of
Yang-Mills gauge fields on fermionic matter, and the retroaction of the latter
on the gauge-field dynamics. The suggested schemes preserve gauge invariance on
the spacetime lattice, i.e. not only in the continuum. In the (1+2)-dimensional
Abelian case, consistent lattice equivalents to both Maxwell's equations and
the current conservation are suggested. In the (1+1)-dimensional non-Abelian
case, a lattice version of the non-Abelian field strength is suggested.
Moreover, it is shown how this fermionic matter based on DTQWs can be coupled
to relativistic gravitational fields of the continuum, i.e. to curved
spacetimes, in 1+2 dimensions.
