toqito.channels.bitflip¶

Implements the bitflip quantum gate channel.

Module Contents¶

toqito.channels.bitflip.bitflip(input_mat=None, prob=0)[source]¶

Apply the bitflip quantum channel to a state or return the Kraus operators.

The bitflip channel is a quantum channel that flips a qubit from (|0rangle) to (|1rangle) and from (|1rangle) to (|0rangle) with probability (p). It is defined by the following operation:

[: mathcal{E}(rho) = (1-p) rho + p X rho X

]

where (X) is the Pauli-X (NOT) gate given by:

[: X = begin{pmatrix} 0 & 1 \ 1 & 0 end{pmatrix}

]

The Kraus operators for this channel are:

[: K_0 = sqrt{1-p} begin{pmatrix} 1 & 0 \ 0 & 1 end{pmatrix}, quad K_1 = sqrt{p} begin{pmatrix} 0 & 1 \ 1 & 0 end{pmatrix}

]

Examples

We can generate the Kraus operators for the bitflip channel with probability 0.3:

```python exec=”1” source=”above” from toqito.channels import bitflip

print(bitflip(prob=0.3)) ```

We can also apply the bitflip channel to a quantum state. For the state (|0rangle), the bitflip channel with probability 0.3 produces:

```python exec=”1” source=”above” import numpy as np from toqito.channels import bitflip

rho = np.array([[1, 0], [0, 0]]) # |0><0| print(bitflip(rho, prob=0.3)) ```

Parameters:

input_mat (numpy.ndarray | None) – A matrix or state to apply the channel to. If None, returns the Kraus operators.
prob (float) – The probability of a bitflip occurring.

Returns:

Either the Kraus operators of the bitflip channel if input_mat is None, or the result of applying the channel to input_mat.

Return type:

numpy.ndarray | list[numpy.ndarray]