  Holonomic quantum computation uses non-Abelian geometric phases to realize
error resilient quantum gates. Nonadiabatic holonomic gates are particularly
suitable to avoid unwanted decoherence effects, as they can be performed at
high speed. By letting the computational system interact with a structured
environment, we show that the scope of error resilience of nonadiabatic
holonomic gates can be widened to include systematic parameter errors. Our
scheme maintains the geometric properties of the evolution and results in an
environment-assisted holonomic quantum map that can mimic the effect of a
holonomic gate. We demonstrate that the sensitivity to systematic errors can be
reduced in a proof-of-concept spin-bath model.
