# Shift¶

class qctrl.dynamic.types.colored_noise_simulation.Shift(*, control, operator, noise=None)

A (possibly noisy) real control term for the colored noise simulation calculation of the form $$\left(1 + \beta_{\alpha_{k}}(t) \right) \alpha_{k}(t) A_{k}$$, where $$A_{k}$$ is a Hermitian operator, $$\alpha_{k}(t)$$ is a real-valued piecewise-constant function between 0 and $$\tau$$, and $$\beta_{\alpha_{k}}(t)$$ is the amplitude of its noise.

Variables
• control (List[qctrl.dynamic.types.RealSegmentInput]) – The list of segments, pairs of a duration and a value $$\{(\delta t_{\alpha_{k},n}, \alpha_{k,n})\}$$, that define the piecewise-constant control $$\alpha_{k}(t)$$. This means that $$\alpha_{k}(t) = \alpha_{k,n}$$ for $$t_{\alpha_{k},n-1} \leq t < t_{\alpha_{k},n}$$, where $$t_{\alpha_{k},0} = 0$$ and $$t_{\alpha_{k},n} = t_{\alpha_{k},n-1} + \delta t_{\alpha_{k},n}$$. You must provide at least one segment.

• operator (ndarray) – The Hermitian matrix $$A_{k}$$ that multiplies the real control.

• noise (qctrl.dynamic.types.colored_noise_simulation.Noise) – The noise amplitude $$\beta_{\alpha_{k}}(t)$$ associated to the term. If not provided, $$\beta_{\alpha_{k}}(t) = 0$$.