  Waveguide QED simulators are analogue quantum simulators made by quantum
emitters interacting with one-dimensional photonic band-gap materials. One of
their remarkable features is that they can be used to engineer tunable-range
emitter interactions. Here, we demonstrate how these interactions can be a
resource to develop more efficient variational quantum algorithms for certain
problems. In particular, we illustrate their power in creating wavefunction
ans\"atze that capture accurately the ground state of quantum critical spin
models (XXZ and Ising) with less gates and optimization parameters than other
variational ans\"atze based on nearest-neighbor or infinite-range entangling
gates. Finally, we study the potential advantages of these waveguide ans\"atze
in the presence of noise. Overall, these results evidence the potential of
using the interaction range as a variational parameter and place waveguide QED
simulators as a promising platform for variational quantum algorithms.
