FPOA

ampamp.fpoa

Fixed-Point Oblivious Amplitude Amplification module.

Provides the FOQAEngine to analyze and simulate LCU dynamics for oblivious amplitude amplification with fixed-point success guarantees.

FOQAEngine

Core engine for Fixed-Point Oblivious Amplitude Amplification.

Handles tripartite LCU dynamics and non-linear success recurrences.

__init__(theta)

Initializes the FOQA Engine.

Parameters:

Name	Type	Description	Default
theta	float	The fundamental geometric phase angle bound for the oblivious operation.	required

Raises:

Type	Description
ValueError	If theta is not within [0, pi/2).

build_lcu_split_operator(alpha_n)

Constructs the controlled-\(V_n\) operator for the tripartite system.

Parameters:

Name	Type	Description	Default
alpha_n	float	The current phase step angle \(\alpha_n\).	required

Returns:

Type	Description
ndarray	np.ndarray: The matrix representation of the split operator.

generate_constant_schedule(alpha, iterations) staticmethod

Generates a constant Zeno-like or underdamped schedule.

Parameters:

Name	Type	Description	Default
alpha	float	The constant phase angle to apply.	required
iterations	int	The total number of iterations.	required

Returns:

Type	Description
ndarray	np.ndarray: A constant phase sequence schedule array.

generate_mizel_schedule(c, iterations) staticmethod

Generates the optimal critical damping schedule: \(c/\sqrt{n+1}\).

Parameters:

Name	Type	Description	Default
c	float	The damping constant modifier.	required
iterations	int	The total number of iterations.	required

Returns:

Type	Description
ndarray	np.ndarray: The computed phase sequence schedule array.

simulate_recurrence(alpha_schedule)

Executes the non-linear FOQA recurrence relations.

Parameters:

Name	Type	Description	Default
alpha_schedule	ndarray	The schedule of phase angles \(\alpha_n\) to apply over iterations.	required

Returns:

Type	Description
ndarray	np.ndarray: The cumulative success probability array containing the likelihood of success at each step of the recurrence.