Kraus#

class qiskit.quantum_info.Kraus(data, input_dims=None, output_dims=None)[source]#

Bases: QuantumChannel

Kraus representation of a quantum channel.

For a quantum channel \(\mathcal{E}\), the Kraus representation is given by a set of matrices \([A_0,...,A_{K-1}]\) such that the evolution of a DensityMatrix \(\rho\) is given by

\[\mathcal{E}(\rho) = \sum_{i=0}^{K-1} A_i \rho A_i^\dagger\]

A general operator map \(\mathcal{G}\) can also be written using the generalized Kraus representation which is given by two sets of matrices \([A_0,...,A_{K-1}]\), \([B_0,...,A_{B-1}]\) such that

\[\mathcal{G}(\rho) = \sum_{i=0}^{K-1} A_i \rho B_i^\dagger\]

See reference [1] for further details.

References

C.J. Wood, J.D. Biamonte, D.G. Cory, Tensor networks and graphical calculus for open quantum systems, Quant. Inf. Comp. 15, 0579-0811 (2015). arXiv:1111.6950 [quant-ph]

Initialize a quantum channel Kraus operator.

প্যারামিটার:

data (QuantumCircuit | circuit.instruction.Instruction | BaseOperator | np.ndarray) -- data to initialize superoperator.
input_dims (tuple | None) -- the input subsystem dimensions.
output_dims (tuple | None) -- the output subsystem dimensions.

রেইজেস:

QiskitError -- if input data cannot be initialized as a list of Kraus matrices.

Additional Information:: If the input or output dimensions are None, they will be automatically determined from the input data. If the input data is a list of Numpy arrays of shape \((2^N,\,2^N)\) qubit systems will be used. If the input does not correspond to an N-qubit channel, it will assign a single subsystem with dimension specified by the shape of the input.

Attributes

atol = 1e-08#

data#: Return list of Kraus matrices for channel.

dim#: Return tuple (input_shape, output_shape).

num_qubits#: Return the number of qubits if a N-qubit operator or None otherwise.

qargs#: Return the qargs for the operator.

rtol = 1e-05#

settings#: Return settings.

Methods

adjoint()[source]#: Return the adjoint quantum channel.

নোট

This is equivalent to the matrix Hermitian conjugate in the SuperOp representation ie. for a channel \(\mathcal{E}\), the SuperOp of the adjoint channel \(\mathcal{{E}}^\dagger\) is \(S_{\mathcal{E}^\dagger} = S_{\mathcal{E}}^\dagger\).

compose(other, qargs=None, front=False)[source]#

Return the operator composition with another Kraus.

প্যারামিটার:

other (Kraus) -- a Kraus object.
qargs (list or None) -- Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
front (bool) -- If True compose using right operator multiplication, instead of left multiplication [default: False].

রিটার্নস:

The composed Kraus.

রিটার্ন টাইপ:

Kraus

রেইজেস:

QiskitError -- if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.

নোট

Composition (&) by default is defined as left matrix multiplication for matrix operators, while @ (equivalent to dot()) is defined as right matrix multiplication. That is that A & B == A.compose(B) is equivalent to B @ A == B.dot(A) when A and B are of the same type.

Setting the front=True kwarg changes this to right matrix multiplication and is equivalent to the dot() method A.dot(B) == A.compose(B, front=True).

conjugate()[source]#: Return the conjugate quantum channel.

নোট

This is equivalent to the matrix complex conjugate in the SuperOp representation ie. for a channel \(\mathcal{E}\), the SuperOp of the conjugate channel \(\overline{{\mathcal{{E}}}}\) is \(S_{\overline{\mathcal{E}^\dagger}} = \overline{S_{\mathcal{E}}}\).

copy()#: Make a deep copy of current operator.

dot(other, qargs=None)#

Return the right multiplied operator self * other.

প্যারামিটার:

other (Operator) -- an operator object.
qargs (list or None) -- Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).

রিটার্নস:

The right matrix multiplied Operator.

রিটার্ন টাইপ:

Operator

নোট

The dot product can be obtained using the @ binary operator. Hence a.dot(b) is equivalent to a @ b.

expand(other)[source]#

Return the reverse-order tensor product with another Kraus.

প্যারামিটার:

other (Kraus) -- a Kraus object.

রিটার্নস:

the tensor product \(b \otimes a\), where \(a\): is the current Kraus, and \(b\) is the other Kraus.

রিটার্ন টাইপ:

Kraus

input_dims(qargs=None)#: Return tuple of input dimension for specified subsystems.

is_cp(atol=None, rtol=None)#

Test if Choi-matrix is completely-positive (CP)

রিটার্ন টাইপ:: bool

is_cptp(atol=None, rtol=None)[source]#: Return True if completely-positive trace-preserving.

is_tp(atol=None, rtol=None)#

Test if a channel is trace-preserving (TP)

রিটার্ন টাইপ:: bool

is_unitary(atol=None, rtol=None)#

Return True if QuantumChannel is a unitary channel.

রিটার্ন টাইপ:: bool

output_dims(qargs=None)#: Return tuple of output dimension for specified subsystems.

power(n)#

Return the power of the quantum channel.

প্যারামিটার:: n (float) -- the power exponent.
রিটার্নস:: the channel \(\mathcal{{E}} ^n\).
রিটার্ন টাইপ:: SuperOp
রেইজেস:: QiskitError -- if the input and output dimensions of the SuperOp are not equal.

নোট

For non-positive or non-integer exponents the power is defined as the matrix power of the SuperOp representation ie. for a channel \(\mathcal{{E}}\), the SuperOp of the powered channel \(\mathcal{{E}}^\n\) is \(S_{{\mathcal{{E}}^n}} = S_{{\mathcal{{E}}}}^n\).

reshape(input_dims=None, output_dims=None, num_qubits=None)#

Return a shallow copy with reshaped input and output subsystem dimensions.

প্যারামিটার:

input_dims (None or tuple) -- new subsystem input dimensions. If None the original input dims will be preserved [Default: None].
output_dims (None or tuple) -- new subsystem output dimensions. If None the original output dims will be preserved [Default: None].
num_qubits (None or int) -- reshape to an N-qubit operator [Default: None].

রিটার্নস:

returns self with reshaped input and output dimensions.

রিটার্ন টাইপ:

BaseOperator

রেইজেস:

QiskitError -- if combined size of all subsystem input dimension or subsystem output dimensions is not constant.

tensor(other)[source]#

Return the tensor product with another Kraus.

প্যারামিটার:

other (Kraus) -- a Kraus object.

রিটার্নস:

the tensor product \(a \otimes b\), where \(a\): is the current Kraus, and \(b\) is the other Kraus.

রিটার্ন টাইপ:

Kraus

নোট

The tensor product can be obtained using the ^ binary operator. Hence a.tensor(b) is equivalent to a ^ b.

to_instruction()#

Convert to a Kraus or UnitaryGate circuit instruction.

If the channel is unitary it will be added as a unitary gate, otherwise it will be added as a kraus simulator instruction.

রিটার্নস:: A kraus instruction for the channel.
রিটার্ন টাইপ:: qiskit.circuit.Instruction
রেইজেস:: QiskitError -- if input data is not an N-qubit CPTP quantum channel.

to_operator()#

Try to convert channel to a unitary representation Operator.

রিটার্ন টাইপ:: Operator

transpose()[source]#: Return the transpose quantum channel.

নোট

This is equivalent to the matrix transpose in the SuperOp representation, ie. for a channel \(\mathcal{E}\), the SuperOp of the transpose channel \(\mathcal{{E}}^T\) is \(S_{mathcal{E}^T} = S_{\mathcal{E}}^T\).