mimiqcircuits.operations.noisechannel.mixedunitary¶

Classes

MixedUnitary(*args)

MixedUnitary(p,umatrices).

class mimiqcircuits.operations.noisechannel.mixedunitary.MixedUnitary(*args)[source]¶

Bases: krauschannel

MixedUnitary(p,umatrices).

Custom N-qubit mixed unitary channel specified by a list of \(2^N \times 2^N\) unitary matrices and a list of probabilities that add up to 1.

A mixed unitary noise channel is defined by:

\[\mathcal{E}(\rho) = \sum_k p_k U_k \rho U_k^\dagger,\]

where \(0 \leq p_k \leq 1\) and \(U_k\) are unitary matrices. The probabilities must fulfill \(\sum_k p_k = 1\).

If your Kraus matrices are not all proportional to unitaries, use KrausChannel() instead.

Note: Currently, only 1 and 2-qubit custom MixedUnitary channels are supported.

See also

Kraus ismixedunitary() krauschannel

Parameters:

p (list) – List of probabilities, must be positive real numbers and add up to 1.
umatrices (list) – List of complex-valued \(2^N \times 2^N\) matrices. The number of qubits is equal to \(N\).

The length of the lists p and umatrices must be equal.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> c = Circuit()
>>> c.push(MixedUnitary([0.9, 0.1], [Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [1, 0]])]), 0)
1-qubit circuit with 1 instruction:
└── MixedUnitary((0.9, "Custom([1 0; 0 1])"),(0.1, "Custom([0 1; 1 0])")) @ q[0]

>>> c.push(MixedUnitary([0.8, 0.2], [Matrix(GateID().matrix()), Matrix(GateRX(0.2).matrix())]), 1)
2-qubit circuit with 2 instructions:
├── MixedUnitary((0.9, "Custom([1 0; 0 1])"),(0.1, "Custom([0 1; 1 0])")) @ q[0]
└── MixedUnitary((0.8, "Custom([1.0 0; 0 1.0])"),(0.2, "Custom([0.995004165278026 -0.0 - 0.0998334166468282*I; -0.0 - 0.0998334166468282*I 0.995004165278026])")) @ q[1]

RescaleGate

>>> p1= 0.2
>>> p2 = 0.8
>>> U1 = Matrix([[1, 0], [0, 1]])  # Identity matrix
>>> U2 = Matrix([[0, 1], [1, 0]])  # Pauli-X matrix
>>> gate1 = GateCustom(U1)
>>> gate2 = GateCustom(U2)
>>> rescaled_gate1 = RescaledGate(gate1, sqrt(p1))
>>> rescaled_gate2 = RescaledGate(gate2, sqrt(p2))
>>> op = MixedUnitary([rescaled_gate1, rescaled_gate2])
>>> op
MixedUnitary((0.2, "Custom([1 0; 0 1])"), (0.8, "Custom([0 1; 1 0])"))
>>> c.push(op,1)
2-qubit circuit with 3 instructions:
├── MixedUnitary((0.9, "Custom([1 0; 0 1])"),(0.1, "Custom([0 1; 1 0])")) @ q[0]
├── MixedUnitary((0.8, "Custom([1.0 0; 0 1.0])"),(0.2, "Custom([0.995004165278026 -0.0 - 0.0998334166468282*I; -0.0 - 0.0998334166468282*I 0.995004165278026])")) @ q[1]
└── MixedUnitary((0.2, "Custom([1 0; 0 1])"),(0.8, "Custom([0 1; 1 0])")) @ q[1]

__init__(*args)[source]¶

evaluate(values)[source]¶

Evaluates symbolic parameters in the MixedUnitary using a dictionary of values.

Parameters:: values (dict) – A dictionary where keys are symbolic variables and values are the corresponding numerical values.
Returns:: A new MixedUnitary instance with evaluated parameters.
Return type:: MixedUnitary

krausmatrices()[source]¶

Returns the Kraus matrices associated with the given Kraus channel.

A mixed unitary channel is written as:

\[\mathcal{E}(\rho) = \sum_k p_k U_k \rho U_k^\dagger,\]

where \(U_k\) are the unitary matrices returned by this function.

If the Kraus channel is parametric, the matrix elements are wrapped in a symengine or sympy object.

Returns:: A list of symengine matrices representing the Kraus operators.
Return type:: list

probabilities()[source]¶

Returns the probabilities for each Kraus operator in a mixed unitary channel.

A mixed unitary channel is written as:

\[\mathcal{E}(\rho) = \sum_k p_k U_k \rho U_k^\dagger,\]

where \(p_k\) are the probabilities.

This method is valid only for mixed unitary channels.

Returns:: A list of probabilities for each Kraus operator.
Return type:: list

unitarymatrices()[source]¶

Unitary matrices associated with the given mixed unitary Kraus channel.

A mixed unitary channel is written as:

\[\mathcal{E}(\rho) = \sum_k p_k U_k \rho U_k^\dagger,\]

where \(U_k\) are the unitary matrices.

An error is raised if the channel is not mixed unitary (i.e., ismixedunitary(self)==False).

Note

If the Kraus channel is parametric, the matrix elements are wrapped in a symbolic object (e.g., from sympy or symengine). To manipulate expressions, use the appropriate symbolic manipulation libraries.