paddle_quantum.gate.matrix

The library of gate matrices.

paddle_quantum.gate.matrix.h_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}H=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of H gate.

Return type:

Tensor

paddle_quantum.gate.matrix.s_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}S=\left[\begin{array}{cc}1& 0\\ 0& i\end{array}\right]\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of S gate.

Return type:

Tensor

paddle_quantum.gate.matrix.sdg_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}{S}^{†}=\left[\begin{array}{cc}1& 0\\ 0& -i\end{array}\right]\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of Sdg gate.

Return type:

Tensor

paddle_quantum.gate.matrix.t_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}T=\left[\begin{array}{cc}1& 0\\ 0& e^{\frac{i\pi }{4}}\end{array}\right]\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of T gate.

Return type:

Tensor

paddle_quantum.gate.matrix.tdg_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}{T}^{†}=\left[\begin{array}{cc}1& 0\\ 0& e^{-\frac{i\pi }{4}}\end{array}\right]\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of Sdg gate.

Return type:

Tensor

paddle_quantum.gate.matrix.x_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}X=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of X gate.

Return type:

Tensor

paddle_quantum.gate.matrix.y_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}Y=\left[\begin{array}{cc}0& -i\\ i& 0\end{array}\right]\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of Y gate.

Return type:

Tensor

paddle_quantum.gate.matrix.z_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}Z=\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of Z gate.

Return type:

Tensor

paddle_quantum.gate.matrix.p_gate(theta)

Generate the matrix

$$\begin{array}{r}P(\theta )=\left[\begin{array}{cc}1& 0\\ 0& e^{i\theta }\end{array}\right]\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of P gate.

Return type:

Tensor

paddle_quantum.gate.matrix.rx_gate(theta)

Generate the matrix

$$\begin{array}{r}{R}_X(\theta )=\left[\begin{array}{cc}\cos \frac{\theta }{2}& -i\sin \frac{\theta }{2}\\ -i\sin \frac{\theta }{2}& \cos \frac{\theta }{2}\end{array}\right]\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of R_X gate.

Return type:

Tensor

paddle_quantum.gate.matrix.ry_gate(theta)

Generate the matrix

$$\begin{array}{r}{R}_Y(\theta )=\left[\begin{array}{cc}\cos \frac{\theta }{2}& -\sin \frac{\theta }{2}\\ \sin \frac{\theta }{2}& \cos \frac{\theta }{2}\end{array}\right]\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of R_Y gate.

Return type:

Tensor

paddle_quantum.gate.matrix.rz_gate(theta)

Generate the matrix

$$\begin{array}{r}{R}_Z(\theta )=\left[\begin{array}{cc}{e}^{-i\frac{\theta }{2}}& 0\\ 0& e^{i\frac{\theta }{2}}\end{array}\right]\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of R_Z gate.

Return type:

Tensor

paddle_quantum.gate.matrix.u3_gate(theta)

Generate the matrix

$$\begin{array}{r}\begin{array}{c}{U}_3(\theta ,\varphi ,\lambda )=\left[\begin{array}{cc}\cos \frac{\theta }{2}& -e^{i\lambda }\sin \frac{\theta }{2}\\ e^{i\varphi }\sin \frac{\theta }{2}& e^{i(\varphi +\lambda )}\cos \frac{\theta }{2}\end{array}\right]\end{array}\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of U_3 gate.

Return type:

Tensor

paddle_quantum.gate.matrix.cnot_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}\begin{array}{rl}\mathit{CNOT}& =|0⟩⟨0|\otimes I+|1⟩⟨1|\otimes X\\ & =\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 1& 0\end{array}\right]\end{array}\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of CNOT gate.

Return type:

Tensor

paddle_quantum.gate.matrix.cy_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}\begin{array}{rl}\mathit{CY}& =|0⟩⟨0|\otimes I+|1⟩⟨1|\otimes Y\\ & =\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 0& -i\\ 0& 0& i& 0\end{array}\right]\end{array}\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of CY gate.

Return type:

Tensor

paddle_quantum.gate.matrix.cz_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}\begin{array}{rl}\mathit{CZ}& =|0⟩⟨0|\otimes I+|1⟩⟨1|\otimes Z\\ & =\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& -1\end{array}\right]\end{array}\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of CZ gate.

Return type:

Tensor

paddle_quantum.gate.matrix.swap_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}\begin{array}{c}\mathit{SWAP}=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 1& 0\\ 0& 1& 0& 0\\ 0& 0& 0& 1\end{array}\right]\end{array}\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of SWAP gate.

Return type:

Tensor

paddle_quantum.gate.matrix.cp_gate(theta)

Generate the matrix

$$\begin{array}{r}\begin{array}{c}\mathit{CP}(\theta )=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& e^{i\theta }\end{array}\right]\end{array}\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of CP gate.

Return type:

Tensor

paddle_quantum.gate.matrix.crx_gate(theta)

Generate the matrix

$$\begin{array}{r}\begin{array}{rl}{\mathit{CR}}_{\mathit{X}}& =|0⟩⟨0|\otimes I+|1⟩⟨1|\otimes R_X\\ & =\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& \cos \frac{\theta }{2}& -i\sin \frac{\theta }{2}\\ 0& 0& -i\sin \frac{\theta }{2}& \cos \frac{\theta }{2}\end{array}\right]\end{array}\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of CR_X gate.

Return type:

Tensor

paddle_quantum.gate.matrix.cry_gate(theta)

Generate the matrix

$$\begin{array}{r}\begin{array}{rl}{\mathit{CR}}_{\mathit{Y}}& =|0⟩⟨0|\otimes I+|1⟩⟨1|\otimes R_Y\\ & =\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& \cos \frac{\theta }{2}& -\sin \frac{\theta }{2}\\ 0& 0& \sin \frac{\theta }{2}& \cos \frac{\theta }{2}\end{array}\right]\end{array}\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of CR_Y gate.

Return type:

Tensor

paddle_quantum.gate.matrix.crz_gate(theta)

Generate the matrix

$$\begin{array}{r}\begin{array}{rl}{\mathit{CR}}_{\mathit{Z}}& =|0⟩⟨0|\otimes I+|1⟩⟨1|\otimes R_Z\\ & =\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& e^{-i\frac{\theta }{2}}& 0\\ 0& 0& 0& e^{i\frac{\theta }{2}}\end{array}\right]\end{array}\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of CR_Z gate.

Return type:

Tensor

paddle_quantum.gate.matrix.cu_gate(theta)

Generate the matrix

$$\begin{array}{r}\begin{array}{rl}\mathit{CU}& =\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& \cos \frac{\theta }{2}& -e^{i\lambda }\sin \frac{\theta }{2}\\ 0& 0& e^{i\varphi }\sin \frac{\theta }{2}& e^{i(\varphi +\lambda )}\cos \frac{\theta }{2}\end{array}\right]\end{array}\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of CU gate.

Return type:

Tensor

paddle_quantum.gate.matrix.rxx_gate(theta)

Generate the matrix

$$\begin{array}{r}\begin{array}{c}{\mathit{R}}_{\mathit{XX}}(\theta )=\left[\begin{array}{cccc}\cos \frac{\theta }{2}& 0& 0& -i\sin \frac{\theta }{2}\\ 0& \cos \frac{\theta }{2}& -i\sin \frac{\theta }{2}& 0\\ 0& -i\sin \frac{\theta }{2}& \cos \frac{\theta }{2}& 0\\ -i\sin \frac{\theta }{2}& 0& 0& \cos \frac{\theta }{2}\end{array}\right]\end{array}\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of RXX gate.

Return type:

Tensor

paddle_quantum.gate.matrix.ryy_gate(theta)

Generate the matrix

$$\begin{array}{r}\begin{array}{c}{\mathit{R}}_{\mathit{YY}}(\theta )=\left[\begin{array}{cccc}\cos \frac{\theta }{2}& 0& 0& i\sin \frac{\theta }{2}\\ 0& \cos \frac{\theta }{2}& -i\sin \frac{\theta }{2}& 0\\ 0& -i\sin \frac{\theta }{2}& \cos \frac{\theta }{2}& 0\\ i\sin \frac{\theta }{2}& 0& 0& cos\frac{\theta }{2}\end{array}\right]\end{array}\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of RYY gate.

Return type:

Tensor

paddle_quantum.gate.matrix.rzz_gate(theta)

Generate the matrix

$$\begin{array}{r}\begin{array}{c}{\mathit{R}}_{\mathit{ZZ}}(\theta )=\left[\begin{array}{cccc}{e}^{-i\frac{\theta }{2}}& 0& 0& 0\\ 0& e^{i\frac{\theta }{2}}& 0& 0\\ 0& 0& e^{i\frac{\theta }{2}}& 0\\ 0& 0& 0& e^{-i\frac{\theta }{2}}\end{array}\right]\end{array}\end{array}$$

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of RZZ gate.

Return type:

Tensor

paddle_quantum.gate.matrix.ms_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}\begin{array}{c}\mathit{MS}={\mathit{R}}_{\mathit{XX}}(-\frac{\pi }{2})=\frac{1}{\sqrt{2}}\left[\begin{array}{cccc}1& 0& 0& i\\ 0& 1& i& 0\\ 0& i& 1& 0\\ i& 0& 0& 1\end{array}\right]\end{array}\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of MS gate.

Return type:

Tensor

paddle_quantum.gate.matrix.cswap_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}\begin{array}{c}\mathit{CSWAP}=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right]\end{array}\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of CSWAP gate.

Return type:

Tensor

paddle_quantum.gate.matrix.toffoli_gate(dtype=None)

Generate the matrix

$$\begin{array}{r}\begin{array}{c}\mathit{CSWAP}=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0& 1& 0\end{array}\right]\end{array}\end{array}$$

Parameters:

dtype (str | None) – the dtype of this matrix. Defaults to None.

Returns:

the matrix of Toffoli gate.

Return type:

Tensor

paddle_quantum.gate.matrix.universal2_gate(theta)

Generate the matrix

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of universal two qubits gate.

Return type:

Tensor

paddle_quantum.gate.matrix.universal3_gate(theta)

Generate the matrix

Parameters:

theta (Tensor) – the parameter of this matrix.

Returns:

the matrix of universal three qubits gate.

Return type:

Tensor