phase_amplitude_damping_error#

phase_amplitude_damping_error(param_amp, param_phase, excited_state_population=0, canonical_kraus=True)[source]#

Return a single-qubit combined phase and amplitude damping quantum error channel.

The single-qubit combined phase and amplitude damping channel is described by the following Kraus matrices:

A0 = sqrt(1 - p1) * [[1, 0], [0, sqrt(1 - a - b)]]
A1 = sqrt(1 - p1) * [[0, sqrt(a)], [0, 0]]
A2 = sqrt(1 - p1) * [[0, 0], [0, sqrt(b)]]
B0 = sqrt(p1) * [[sqrt(1 - a - b), 0], [0, 1]]
B1 = sqrt(p1) * [[0, 0], [sqrt(a), 0]]
B2 = sqrt(p1) * [[sqrt(b), 0], [0, 0]]

where a = param_amp, b = param_phase, and p1 = excited_state_population. The equilibrium state after infinitely many applications of the channel is:

rho_eq = [[1 - p1, 0]], [0, p1]]
Parameters:

  • param_amp (double) – the amplitude damping error parameter.

  • param_phase (double) – the phase damping error parameter.

  • excited_state_population (double) – the population of \(|1\rangle\) state at equilibrium (default: 0).

  • canonical_kraus (bool) – Convert input Kraus matrices into the canonical Kraus representation (default: True)

Returns:

a quantum error object for a noise model.

Return type:

QuantumError

Raises:

NoiseError – If noise parameters are invalid.