# cirq.kraus_to_superoperator

Returns the matrix representation of the linear map with given Kraus operators.

### Used in the notebooks

Used in the tutorials

Quantum channel E: L(H1) -> L(H2) may be described by a collection of operators A_i, called Kraus operators, such that

$$E(\rho) = \sum_i A_i \rho A_i^\dagger.$$


Kraus representation is not unique. Alternatively, E may be specified by its superoperator matrix K(E) defined so that

$$K(E) vec(\rho) = vec(E(\rho))$$


where the vectorization map $$vec$$ rearranges d-by-d matrices into d**2-dimensional vectors. Superoperator matrix is unique for a given channel. It is also called the natural representation of a quantum channel.

The computation of the superoperator matrix from a Kraus representation involves the sum of Kronecker products of all Kraus operators. This has the cost of O(kd**4) where k is the number of Kraus operators and d is the dimension of the input and output Hilbert space.

kraus_operators Sequence of Kraus operators specifying a quantum channel.

Superoperator matrix of the channel specified by kraus_operators.

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