amplitude_amplification_utils

amplitude_amplification_utils ¶

calculate_fixed_point_amp_amp_angles(p_succ, eps_targ)

Compute the optimal number of iterations and reflection angles for fixed-point amplitude amplification.

Parameters:

Name	Type	Description	Default
`p_succ`	`float`	Initial probability of obtaining the good state.	required
`eps_targ`	`float`	Target error \(\epsilon\).	required

Returns:

Type	Description
`Tuple[List[float], List[float]]`	The first list (`alphas`) contains angles for reflections about the initial state, while the second list (`betas`) contains angles for reflections about the final state.

calculate_vanilla_amp_amp_angles(p_succ)

Compute the optimal number of iterations and reflection angles for fixed-point amplitude amplification.

Reference

Section 2.1 of "Quantum Amplitude Amplification and Estimation" (arXiv:quant-ph/0005055 ⧉).

Note

All angles are set to \(\pi\) except for the last, which is adjusted for exact final overlap.
The target state is obtained exactly (up to numerical precision).

Parameters:

Name	Type	Description	Default
`p_succ`	`float`	Initial probability of obtaining the good state.	required

Returns:

Type	Description
`Tuple[List[float], List[float]]`	Angles for amplitude amplification reflections.

get_final_reflection_angle(optimal_full_refls, p_succ)

Compute the optimal final angles for vanilla amplitude amplification.

Notes

The equation is complex, so optimization is used to determine the best angles.
Optimal angles minimize the difference in Eq. (12) from "Quantum Amplitude Amplification and Estimation" (arXiv:quant-ph/0005055 ⧉).

Parameters:

Name	Type	Description	Default
`optimal_full_refls`	`int`	Number of full reflections needed.	required
`p_succ`	`float`	Initial probability of obtaining the good state.	required

Returns:

Type	Description
`Tuple[List[float], List[float]]`	Tuple of angles (in degrees) for the final AA reflection. The first value is for reflection around the initial state, and the second for reflection around the good state.