paddle_quantum.gate.multi_qubit_gate

The source file of the classes for multi-qubit gates.

class paddle_quantum.gate.multi_qubit_gate.CNOT(qubits_idx=None, num_qubits=None, depth=1, cnot_idx=None)

Bases: Gate

A collection of CNOT gates.

For a 2-qubit quantum circuit, when qubits_idx is [0, 1], the matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | int | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• cnot_idx (List[int] | None) – CNOT gate index. Defaults to None.

paddle_quantum.gate.multi_qubit_gate.CX

alias of CNOT

class paddle_quantum.gate.multi_qubit_gate.CY(qubits_idx=None, num_qubits=None, depth=1)

Bases: Gate

A collection of controlled Y gates.

For a 2-qubit quantum circuit, when qubits_idx is [0, 1], the matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | int | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

class paddle_quantum.gate.multi_qubit_gate.CZ(qubits_idx=None, num_qubits=None, depth=1)

Bases: Gate

A collection of controlled Z gates.

For a 2-qubit quantum circuit, when qubits_idx is [0, 1], the matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | int | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

class paddle_quantum.gate.multi_qubit_gate.SWAP(qubits_idx=None, num_qubits=None, depth=1)

Bases: Gate

A collection of SWAP gates.

The matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | int | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

class paddle_quantum.gate.multi_qubit_gate.CP(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of controlled P gates.

For a 2-qubit quantum circuit, when qubits_idx is [0, 1], the matrix form of such a gate is:

$$\begin{array}{r}\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& e^{i\theta }\end{array}\right]\end{array}$$

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.

class paddle_quantum.gate.multi_qubit_gate.CRX(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of controlled rotation gates about the x-axis.

For a 2-qubit quantum circuit, when qubits_idx is [0, 1], the matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.

class paddle_quantum.gate.multi_qubit_gate.CRY(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of controlled rotation gates about the y-axis.

For a 2-qubit quantum circuit, when qubits_idx is [0, 1], the matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.

class paddle_quantum.gate.multi_qubit_gate.CRZ(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of controlled rotation gates about the z-axis.

For a 2-qubit quantum circuit, when qubits_idx is [0, 1], the matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.

class paddle_quantum.gate.multi_qubit_gate.CU(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of controlled single-qubit rotation gates.

For a 2-qubit quantum circuit, when qubits_idx is [0, 1], the matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.

class paddle_quantum.gate.multi_qubit_gate.RXX(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of RXX gates.

The matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.

class paddle_quantum.gate.multi_qubit_gate.RYY(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of RYY gates.

The matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.

class paddle_quantum.gate.multi_qubit_gate.RZZ(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of RZZ gates.

The matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.

class paddle_quantum.gate.multi_qubit_gate.MS(qubits_idx=None, num_qubits=None, depth=1)

Bases: Gate

A collection of Mølmer-Sørensen (MS) gates for trapped ion devices.

The matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | int | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

class paddle_quantum.gate.multi_qubit_gate.CSWAP(qubits_idx=None, num_qubits=None, depth=1)

Bases: Gate

A collection of CSWAP (Fredkin) gates.

The matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | int | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

class paddle_quantum.gate.multi_qubit_gate.CCX(qubits_idx=None, num_qubits=None, depth=1)

Bases: Gate

A collection of CCX (Toffoli) gates.

The matrix form of such a gate is:

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

Parameters:

• qubits_idx (Iterable | int | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

paddle_quantum.gate.multi_qubit_gate.Toffoli

alias of CCX

class paddle_quantum.gate.multi_qubit_gate.UniversalTwoQubits(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of universal two-qubit gates. One of such a gate requires 15 parameters.

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.

class paddle_quantum.gate.multi_qubit_gate.UniversalThreeQubits(qubits_idx=None, num_qubits=None, depth=1, param=None, param_sharing=False)

Bases: ParamGate

A collection of universal three-qubit gates. One of such a gate requires 81 parameters.

Parameters:

• qubits_idx (Iterable | str | None) – Indices of the qubits on which the gates are applied. Defaults to 'cycle'.

• num_qubits (int | None) – Total number of qubits. Defaults to None.

• depth (int | None) – Number of layers. Defaults to 1.

• param (Tensor | float | None) – Parameters of the gates. Defaults to None.

• param_sharing (bool | None) – Whether gates in the same layer share a parameter. Defaults to False.

Raises:

ValueError – The param must be paddle.Tensor or float.