cirq.kraus_to_superoperator

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

cirq.kraus_to_superoperator(
    kraus_operators: Sequence[np.ndarray]
) -> np.ndarray

Used in the notebooks

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.