quairkit.database.representation
Representations of channels
-
quairkit.database.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]
-
quairkit.database.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]
-
quairkit.database.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]
-
quairkit.database.representation.amplitude_damping_kraus(gamma, dtype=
None)
Kraus representation of an amplitude damping channel with form
\[\begin{split}E_0 =
\begin{bmatrix}
1 & 0 \\
0 & \sqrt{1-\gamma}
\end{bmatrix},
E_1 =
\begin{bmatrix}
0 & \sqrt{\gamma} \\
0 & 0
\end{bmatrix}.\end{split}\]
- 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]
-
quairkit.database.representation.generalized_amplitude_damping_kraus(gamma, prob, dtype=
None)
Kraus representation of a generalized amplitude damping channel with form
\[\begin{split}E_0 = \sqrt{p} \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1-\gamma} \end{bmatrix},
E_1 = \sqrt{p} \begin{bmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{bmatrix},\\
E_2 = \sqrt{1-p} \begin{bmatrix} \sqrt{1-\gamma} & 0 \\ 0 & 1 \end{bmatrix},
E_3 = \sqrt{1-p} \begin{bmatrix} 0 & 0 \\ \sqrt{\gamma} & 0 \end{bmatrix}.\end{split}\]
- 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]
-
quairkit.database.representation.phase_damping_kraus(gamma, dtype=
None)
Kraus representation of a phase damping channel with form
\[\begin{split}E_0 =
\begin{bmatrix}
1 & 0 \\
0 & \sqrt{1-\gamma}
\end{bmatrix},
E_1 =
\begin{bmatrix}
0 & 0 \\
0 & \sqrt{\gamma}
\end{bmatrix}.\end{split}\]
- 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]
-
quairkit.database.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]
-
quairkit.database.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]
-
quairkit.database.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]
-
quairkit.database.representation.reset_kraus(prob, dtype=
None)
Kraus representation of a reset channel with form
\[\begin{split}E_0 =
\begin{bmatrix}
\sqrt{p} & 0 \\
0 & 0
\end{bmatrix},
E_1 =
\begin{bmatrix}
0 & \sqrt{p} \\
0 & 0
\end{bmatrix},\\
E_2 =
\begin{bmatrix}
0 & 0 \\
\sqrt{q} & 0
\end{bmatrix},
E_3 =
\begin{bmatrix}
0 & 0 \\
0 & \sqrt{q}
\end{bmatrix},\\
E_4 = \sqrt{1-p-q} I.\end{split}\]
- Parameters:
- prob : List[float] | ndarray | Tensor
list of two probabilities of resetting to state \(|0\rangle\) and \(|1\rangle\).
- dtype : str | None
data type. Defaults to be None.
- Returns:
a list of Kraus operators
- Return type:
List[Tensor]
-
quairkit.database.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]
-
quairkit.database.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