Discrete sine cosine transform

discrete_sine_cosine_transform

Functions:

Name	Description
qct_qst_type1	[Qmod Classiq-library function]
qct_qst_type2	[Qmod Classiq-library function]
qct_type2	[Qmod Classiq-library function]
qst_type2	[Qmod Classiq-library function]

qct_qst_type1

qct_qst_type1(x: QArray[QBit]) -> None

[Qmod Classiq-library function]

Applies the quantum discrete cosine (DCT) and sine (DST) transform of type 1 to the qubit array x. Corresponds to the matrix (with \(n\equiv\)x.len):

$$ \left( egin{array}{ccc|c} {} &{} &{} \ {}&{ m DCT}^{(1)}(2^{n-1}+1) & {}& 0\ {} &{} &{} \ \hline {} & 0 & {} & i{ m DST}^{(1)}(2^{n-1}-1) \end{array}

ight) $$

Parameters:

Name	Type	Description	Default
x	QArray[QBit]	The qubit array to apply the transform to.	required

qct_qst_type2

qct_qst_type2(x: QArray[QBit], q: QBit) -> None

[Qmod Classiq-library function]

Applies the quantum discrete cosine (DCT) and sine (DST) transform of type 2 to the qubit array x concatenated with q, with q being the MSB. Corresponds to the matrix (with \(n\equiv\)x.len+1):

$$ \left( egin{array}{c|c} { m DCT}^{(2)}(2^{n-1}) & 0\ \hline 0 & -{ m DST}^{(2)}(2^{n-1}) \end{array}

ight) $$

Parameters:

Name	Type	Description	Default
x	QArray[QBit]	The LSB part of the qubit array to apply the transform to.	required
q	QBit	The MSB of the qubit array to apply the transform to.	required

qct_type2

qct_type2(x: QArray[QBit]) -> None

[Qmod Classiq-library function]

Applies the quantum discrete cosine (DCT) transform of type 2, \({ m DCT}^{(2)}\), to the qubit array x.

Parameters:

Name	Type	Description	Default
x	QArray[QBit]	The qubit array to apply the transform to.	required

qst_type2

qst_type2(x: QArray[QBit]) -> None

[Qmod Classiq-library function]

Applies the quantum discrete sine (DST) transform of type 2, \({ m DST}^{(2)}\), to the qubit array x.

Parameters:

Name	Type	Description	Default
x	QArray[QBit]	The qubit array to apply the transform to.	required