We study the stability of holonomic quantum computations with respect to errors in assignment of control parameters. The general expression for fidelity is obtaned.In the small errors limit the simple formulae for the fidelity decrease rate is derived.

For the system with one-dimensional spatially periodic potential we demonstrate that small periodic in time perturbation results in appearance of chaotic instanton solutions. We estimate parameter of local instability, width of stochastic layer and correlator for perturbed instanton solutions. Application of the instanton technique enables to calculate the amplitude of the tunneling, the form of the spectrum and the lower bound for width of the ground quasi-energy zone.

Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations.Comment: 7 page

No abstract

We consider one possible implementation of Hadamard gate for optical and ion trap holonomic quantum computers. The expression for its fidelity determining the gate stability with respect to the errors in the single-mode squeezing parameter control is analytically derived. We demonstrate by means of this expression the cancellation of the squeezing control errors up to the fourth order on their magnitude.