cirq.qis.superoperator_to_kraus

Returns a Kraus representation of a channel specified via the superoperator matrix.

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 most expensive step in the computation of a Kraus representation from a superoperator matrix is eigendecomposition. Therefore, the cost of the conversion is O(d**6) where d is the dimension of the input and output Hilbert space.

superoperator Superoperator matrix specifying a quantum channel.

Sequence of Kraus operators of the channel specified by superoperator.

ValueError If superoperator is not a valid superoperator matrix.