paddle_quantum.channel.representation

The library of representations of channels

paddle_quantum.channel.representation.bit_flip_kraus(prob, dtype=None)

Kraus representation of a bit flip channel with form

$$E_0=\sqrt{1-p}I,E_1=\sqrt{p}X.$$

Parameters:

• prob (float | ndarray | Tensor) – probability $p$.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.phase_flip_kraus(prob, dtype=None)

Kraus representation of a phase flip channel with form

$$E_0=\sqrt{1-p}I,E_1=\sqrt{p}Z.$$

Parameters:

• prob (float | ndarray | Tensor) – probability $p$.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.bit_phase_flip_kraus(prob, dtype=None)

Kraus representation of a bit-phase flip channel with form

$$E_0=\sqrt{1-p}I,E_1=\sqrt{p}Y.$$

Parameters:

• prob (float | ndarray | Tensor) – probability $p$.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.amplitude_damping_kraus(gamma, dtype=None)

Kraus representation of an amplitude damping channel with form

$$\begin{array}{r}{E}_0=\left[\begin{array}{cc}1& 0\\ 0& \sqrt{1-\gamma }\end{array}\right],E_1=\left[\begin{array}{cc}0& \sqrt{\gamma }\\ 0& 0\end{array}\right].\end{array}$$

Parameters:

• gamma (float | ndarray | Tensor) – coefficient $\gamma$.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.generalized_amplitude_damping_kraus(gamma, prob, dtype=None)

Kraus representation of a generalized amplitude damping channel with form

$$\begin{array}{r}{E}_0=\sqrt{p}\left[\begin{array}{cc}1& 0\\ 0& \sqrt{1-\gamma }\end{array}\right],E_1=\sqrt{p}\left[\begin{array}{cc}0& \sqrt{\gamma }\\ 0& 0\end{array}\right],\\ E_2=\sqrt{1-p}\left[\begin{array}{cc}\sqrt{1-\gamma }& 0\\ 0& 1\end{array}\right],E_3=\sqrt{1-p}\left[\begin{array}{cc}0& 0\\ \sqrt{\gamma }& 0\end{array}\right].\end{array}$$

Parameters:

• gamma (float | ndarray | Tensor) – coefficient $\gamma$.

• prob (float | ndarray | Tensor) – probability $p$.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.phase_damping_kraus(gamma, dtype=None)

Kraus representation of a phase damping channel with form

$$\begin{array}{r}{E}_0=\left[\begin{array}{cc}1& 0\\ 0& \sqrt{1-\gamma }\end{array}\right],E_1=\left[\begin{array}{cc}0& 0\\ 0& \sqrt{\gamma }\end{array}\right].\end{array}$$

Parameters:

• gamma (float | ndarray | Tensor) – coefficient $\gamma$.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.depolarizing_kraus(prob, dtype=None)

Kraus representation of a depolarizing channel with form

$$E_0=\sqrt{1-3p/4}I,E_1=\sqrt{p/4}X,E_2=\sqrt{p/4}Y,E_3=\sqrt{p/4}Z.$$

Parameters:

• prob (float | ndarray | Tensor) – probability $p$.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.generalized_depolarizing_kraus(prob, num_qubits, dtype=None)

Kraus representation of a generalized depolarizing channel with form

$$E_0=\sqrt{1-(D-1)p/D}I,\text{ where }D=4^n,E_k=\sqrt{p/D}{\sigma }_k,\text{ for }0<k<D.$$

Parameters:

• prob (float) – probability $p$.

• num_qubits (int) – number of qubits $n$ of this channel.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.pauli_kraus(prob, dtype=None)

Kraus representation of a pauli channel

Parameters:

• prob (List[float] | ndarray | Tensor) – a list of three probabilities corresponding to X, Y, Z gate $p$.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.reset_kraus(prob, dtype=None)

Kraus representation of a reset channel with form

$$\begin{array}{r}{E}_0=\left[\begin{array}{cc}\sqrt{p}& 0\\ 0& 0\end{array}\right],E_1=\left[\begin{array}{cc}0& \sqrt{p}\\ 0& 0\end{array}\right],\\ E_2=\left[\begin{array}{cc}0& 0\\ \sqrt{q}& 0\end{array}\right],E_3=\left[\begin{array}{cc}0& 0\\ 0& \sqrt{q}\end{array}\right],\\ E_4=\sqrt{1-p-q}I.\end{array}$$

Parameters:

• prob (List[float] | ndarray | Tensor) – list of two probabilities of resetting to state $|0⟩$ and $|1⟩$.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators

Return type:

List[Tensor]

paddle_quantum.channel.representation.thermal_relaxation_kraus(const_t, exec_time, dtype=None)

Kraus representation of a thermal relaxation channel

Parameters:

• const_t (List[float] | ndarray | Tensor) – list of $T_1$ and $T_2$ relaxation time in microseconds.

• exec_time (List[float] | ndarray | Tensor) – quantum gate execution time in the process of relaxation in nanoseconds.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a list of Kraus operators.

Return type:

List[Tensor]

paddle_quantum.channel.representation.replacement_choi(sigma, dtype=None)

Choi representation of a replacement channel

Parameters:

• sigma (ndarray | Tensor | State) – output state of this channel.

• dtype (str | None) – data type. Defaults to be None.

Returns:

a Choi operator.

Return type:

Tensor