Foundations

ampamp.grover

GroverEngine

The core algebraic and circuit engine for Grover's Search.

Focuses on state synthesis and geometric calculations to amplify amplitudes of marked solution states optimally.

__init__(n_qubits, marked_indices)

Initializes the GroverEngine.

Parameters:

Name	Type	Description	Default
n_qubits	int	The number of qubits representing the problem space (\(N = 2^n\)).	required
marked_indices	list[int]	List indicating the integers representing the marked states in the problem subspace.	required

compute_success_prob(lambda_val, k) staticmethod

Analytic success probability calculation.

Computes the success probability \(P(k)\) after \(k\) Grover iterations given the solution density \(\lambda\). The probability formula is defined geometrically as \(P(k) = \sin^2((2k + 1) \theta / 2)\), where \(\theta = 2 \arcsin(\sqrt{\lambda})\).

Parameters:

Name	Type	Description	Default
lambda_val	float	The solution density fraction, \(M/N\).	required
k	int	The number of Grover iterations applied.	required

Returns:

Name	Type	Description
float	float	The probability of measuring a marked state.

Raises:

Type	Description
ValueError	If lambda_val is not within the inclusive bound [0, 1].

construct_circuit(iterations)

Synthesizes the full Grover circuit.

Links the oracle operator and diffusion operator for \(k\) iterations starting from the full uniformly mixed amplitude distribution \(|s\rangle\).

Parameters:

Name	Type	Description	Default
iterations	int	The amount of generalized Grover operator iterations to sequentially run \(Q = -A S_0 A^{-1} S_f\).	required

Returns:

Name	Type	Description
QuantumCircuit	QuantumCircuit	The synthesized Grover standard algorithm sequence.

get_diffusion()

Generates the Grover Diffusion operator (Inversion about mean).

Returns:

Name	Type	Description
QuantumCircuit	QuantumCircuit	An n-qubit circuit corresponding to \(2 |s\rangle\langle s| - I\),
	QuantumCircuit	where \(|s\rangle\) is the equal superposition state.

get_oracle()

Generates a Phase Oracle for the marked states.

Constructs a standard quantum phase oracle gate circuit that flips the sign of the marked states while leaving orthogonal unmarked states alone.

Returns:

Name	Type	Description
QuantumCircuit	QuantumCircuit	An n-qubit oracle circuit flipping the phase of marked states.