# cirq.DepolarizingChannel¶

class cirq.DepolarizingChannel(p: float)[source]

A channel that depolarizes a qubit.

__init__(p: float) → None[source]

The symmetric depolarizing channel.

This channel applies one of four disjoint possibilities: nothing (the
identity channel) or one of the three pauli gates. The disjoint
probabilities of the three gates are all the same, p / 3, and the
identity is done with probability 1 - p. The supplied probability must
be a valid probability or else this constructor will raise a ValueError.

This channel evolves a density matrix via

$$\rho \rightarrow (1 - p) \rho + (p / 3) X \rho X + (p / 3) Y \rho Y + (p / 3) Z \rho Z$$

Parameters

p – The probability that one of the Pauli gates is applied. Each of the Pauli gates is applied independently with probability p / 3.

Raises

ValueError – if p is not a valid probability.