quairkit.operator.channel.common¶
The source file of the classes for common quantum channels.
-
class quairkit.operator.channel.common.BitFlip(prob, qubits_idx=
None)¶ A collection of bit flip channels.
Such a channel’s Kraus operators are
\[E_0 = \sqrt{1-p} I, E_1 = \sqrt{p} X.\]
-
class quairkit.operator.channel.common.PhaseFlip(prob, qubits_idx=
None)¶ A collection of phase flip channels.
Such a channel’s Kraus operators are
\[E_0 = \sqrt{1 - p} I, E_1 = \sqrt{p} Z.\]
-
class quairkit.operator.channel.common.BitPhaseFlip(prob, qubits_idx=
None)¶ A collection of bit phase flip channels.
Such a channel’s Kraus operators are
\[E_0 = \sqrt{1 - p} I, E_1 = \sqrt{p} Y.\]
-
class quairkit.operator.channel.common.AmplitudeDamping(gamma, qubits_idx=
None)¶ A collection of amplitude damping channels.
Such a channel’s Kraus operators are
\[\begin{split}E_0 = \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1-\gamma} \end{bmatrix}, E_1 = \begin{bmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{bmatrix}.\end{split}\]
-
class quairkit.operator.channel.common.GeneralizedAmplitudeDamping(gamma, prob, qubits_idx=
None)¶ A collection of generalized amplitude damping channels.
Such a channel’s Kraus operators are
\[\begin{split}E_0 = \sqrt{p} \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1-\gamma} \end{bmatrix}, E_1 = \sqrt{p} \begin{bmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{bmatrix},\\ E_2 = \sqrt{1-p} \begin{bmatrix} \sqrt{1-\gamma} & 0 \\ 0 & 1 \end{bmatrix}, E_3 = \sqrt{1-p} \begin{bmatrix} 0 & 0 \\ \sqrt{\gamma} & 0 \end{bmatrix}.\end{split}\]- Parameters:¶
- gamma : Tensor | float¶
Damping probability. Its value should be in the range \([0, 1]\).
- prob : Tensor | float¶
Excitation probability. Its value should be in the range \([0, 1]\).
- qubits_idx : Iterable[int] | int | str¶
Indices of the qubits on which the channels act. Defaults to list(range(# of acted qubits))
-
class quairkit.operator.channel.common.PhaseDamping(gamma, qubits_idx=
None)¶ A collection of phase damping channels.
Such a channel’s Kraus operators are
\[\begin{split}E_0 = \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1-\gamma} \end{bmatrix}, E_1 = \begin{bmatrix} 0 & 0 \\ 0 & \sqrt{\gamma} \end{bmatrix}.\end{split}\]
-
class quairkit.operator.channel.common.Depolarizing(prob, qubits_idx=
None)¶ A collection of depolarizing channels.
Such a channel’s Kraus operators are
\[E_0 = \sqrt{1-3p/4} I, E_1 = \sqrt{p/4} X, E_2 = \sqrt{p/4} Y, E_3 = \sqrt{p/4} Z.\]- Parameters:¶
Note
The implementation logic for this feature has been updated. The current version refers to formula (8.102) in Quantum Computation and Quantum Information 10th edition by M.A.Nielsen and I.L.Chuang. Reference: Nielsen, M., & Chuang, I. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511976667
-
class quairkit.operator.channel.common.GeneralizedDepolarizing(prob, qubits_idx, num_qubits=
None)¶ A generalized depolarizing channel.
Such a channel’s Kraus operators are
\[\begin{split}E_0 = \sqrt{1-(D - 1)p/D} I, \text{ where } D = 4^n, \\ E_k = \sqrt{p/D} \sigma_k, \text{ for } 0 < k < D.\end{split}\]
-
class quairkit.operator.channel.common.PauliChannel(prob, qubits_idx=
None)¶ A collection of Pauli channels.
- Parameters:¶
Note
The sum of three input probabilities should be less than or equal to 1.
-
class quairkit.operator.channel.common.ResetChannel(prob, qubits_idx=
None)¶ A collection of reset channels.
Such a channel reset the state to \(|0\rangle\) with a probability of p and to \(|1\rangle\) with a probability of q. Its Kraus operators are
\[\begin{split}E_0 = \begin{bmatrix} \sqrt{p} & 0 \\ 0 & 0 \end{bmatrix}, E_1 = \begin{bmatrix} 0 & \sqrt{p} \\ 0 & 0 \end{bmatrix},\\ E_2 = \begin{bmatrix} 0 & 0 \\ \sqrt{q} & 0 \end{bmatrix}, E_3 = \begin{bmatrix} 0 & 0 \\ 0 & \sqrt{q} \end{bmatrix},\\ E_4 = \sqrt{1-p-q} I.\end{split}\]- Parameters:¶
Note
The sum of two input probabilities should be less than or equal to 1.
-
class quairkit.operator.channel.common.ThermalRelaxation(const_t, exec_time, qubits_idx=
None)¶ A collection of thermal relaxation channels.
Such a channel simulates the mixture of the \(T_1\) and the \(T_2\) processes on superconducting devices.
- Parameters:¶
- const_t : Tensor | Iterable[float]¶
\(T_1\) and \(T_2\) relaxation time in microseconds.
- exec_time : Tensor | float¶
Quantum gate execution time in the process of relaxation in nanoseconds.
- qubits_idx : Iterable[int] | int | str¶
Indices of the qubits on which the channels act. Defaults to list(range(# of acted qubits))
Note
Relaxation time must satisfy \(T_2 \le T_1\). For reference please see https://arxiv.org/abs/2101.02109.
-
class quairkit.operator.channel.common.ReplacementChannel(sigma, system_idx=
None)¶ A collection of quantum replacement channels.
For a quantum state \(\sigma\), the corresponding replacement channel \(R\) is defined as
\[R(\rho) = \text{tr}(\rho)\sigma\]