Robust gates for holonomic quantum computation

Non Abelian geometric phases are attracting increasinginterest because of possible experimental application in quantumcomputation.

We study the effects of the environment (modelled as anensemble of harmonic oscillators) on a holonomic transformation andwrite the corresponding master equation.

The solution is analyticallyand numerically investigated and the behavior of the fidelity analyzed:fidelity revivals are observed and an optimal finite operation time isdetermined at which the gate is most robust against noise.