Arithmetic

arithmetic

Functions:

Name	Description
unitary	[Qmod core-library function]
multiply	[Qmod core-library function]
multiply_constant	[Qmod core-library function]
canonical_multiply	[Qmod core-library function]
canonical_multiply_constant	[Qmod core-library function]

unitary

unitary(
    elements: CArray[CArray[CReal]],
    target: QArray[
        QBit, Literal["log(elements[0].len, 2)"]
    ],
) -> None

[Qmod core-library function]

Applies a unitary matrix on a quantum state.

Parameters:

Name	Type	Description	Default
elements	CArray[CArray[CReal]]	A 2d array of complex numbers representing the unitary matrix. This matrix must be unitary.	required
target	QArray[QBit, Literal['log(elements[0].len, 2)']]	The quantum state to apply the unitary on. Should be of corresponding size.	required

multiply

multiply(
    left: Const[QNum],
    right: Const[QNum],
    result: Output[QNum],
) -> None

[Qmod core-library function]

Multiplies two quantum numeric variables:

\[ \left|\text{left}\right\rangle \left|\text{right}\right\rangle \mapsto \left|\text{left}\right\rangle \left|\text{right}\right\rangle \left|\text{left} \cdot \text{right} \right\rangle \]

Parameters:

Name	Type	Description	Default
left	Const[QNum]	The first argument for the multiplication.	required
right	Const[QNum]	The second argument for the multiplication.	required
result	Output[QNum]	The quantum variable to hold the multiplication result.	required

multiply_constant

multiply_constant(
    left: CReal, right: Const[QNum], result: Output[QNum]
) -> None

[Qmod core-library function]

Multiplies a quantum numeric variable with a constant:

\[ \left|\text{right}\right\rangle \mapsto \left|\text{right}\right\rangle \left|\text{left} \cdot \text{right} \right\rangle \]

Parameters:

Name	Type	Description	Default
left	CReal	The constant argument for the multiplication.	required
right	Const[QNum]	The variable argument for the multiplication.	required
result	Output[QNum]	The quantum variable to hold the multiplication result.	required

canonical_multiply

canonical_multiply(
    left: Const[QArray],
    extend_left: CBool,
    right: Const[QArray],
    extend_right: CBool,
    result: QArray,
    trim_result_lsb: CBool,
) -> None

[Qmod core-library function]

Multiplies two quantum variables representing integers (signed or unsigned) into the result variable which is assumed to start in the \(|0\rangle\) state.

If trim_result_lsb is False, applies the transformation:

\[ \left|\text{left}\right\rangle \left|\text{right}\right\rangle \left|0\right\rangle \mapsto \left|\text{left}\right\rangle \left|\text{right}\right\rangle \left|\left( \text{left} \cdot \text{right} \right) \bmod 2^{\text{result.size}} \right\rangle \]

If trim_result_lsb is True, the function avoids computing the result's LSB and applies the transformation:

\[ \left|\text{left}\right\rangle \left|\text{right}\right\rangle \left|0\right\rangle \mapsto \left|\text{left}\right\rangle \left|\text{right}\right\rangle \left|\left( \text{left} \cdot \text{right} \right) \gg 1 \bmod 2^{\text{result.size}} \right\rangle \]

Parameters:

Name	Type	Description	Default
left	Const[QArray]	The first argument for the multiplication.	required
extend_left	CBool	Whether to sign-extend the left argument.	required
right	Const[QArray]	The second argument for the multiplication.	required
extend_right	CBool	Whether to sign-extend the right argument.	required
result	QArray	The quantum variable to hold the multiplication result.	required
trim_result_lsb	CBool	Whether to avoid computing the result's LSB.	required

canonical_multiply_constant

canonical_multiply_constant(
    left: CInt,
    right: Const[QArray],
    extend_right: CBool,
    result: QArray,
    trim_result_lsb: CBool,
) -> None

[Qmod core-library function]

Multiplies a quantum variable representing an integer (signed or unsigned) with a constant, into the result variable which is assumed to start in the \(|0\rangle\) state.

If trim_result_lsb is False, applies the transformation:

\[ \left|\text{right}\right\rangle \left|0\right\rangle \mapsto \left|\text{right}\right\rangle \left|\left( \text{left} \cdot \text{right} \right) \bmod 2^{\text{result.size}} \right\rangle \]

If trim_result_lsb is True, the function avoids computing the result's LSB and applies the transformation:

\[ \left|\text{right}\right\rangle \left|0\right\rangle \mapsto \left|\text{right}\right\rangle \left|\left( \text{left} \cdot \text{right} \right) \gg 1 \bmod 2^{\text{result.size}} \right\rangle \]

Parameters:

Name	Type	Description	Default
left	CInt	The constant argument for the multiplication.	required
right	Const[QArray]	The variable argument for the multiplication.	required
extend_right	CBool	Whether to sign-extend the right argument.	required
result	QArray	The quantum variable to hold the multiplication result.	required
trim_result_lsb	CBool	Whether to avoid computing the result's LSB.	required