  Quantum noise or decoherence is a major factor impacting the performance of
quantum technologies. On the qubit, an important quantum noise, often relevant
in practice, is the thermal noise or generalized amplitude damping noise,
describing the interaction with a thermal bath at an arbitrary temperature. A
qubit thermal noise however cannot be modeled nor directly simulated with a few
elementary Pauli operators, but instead requires specific operators. Our main
goal here is to construct a circuit model for simulating the thermal noise from
standard elementary qubit operators. Starting from a common quantum-operation
model based on Kraus operators and an associated qubit-environment model, we
derive a proper Stinespring dilated representation for the thermal noise. This
dilated unitary model is then decomposed in terms of simple elementary qubit
operators, and converted into a circuit based on elementary quantum gates. We
arrive at our targeted simulator circuit for the thermal noise, coming with
built-in easy control on the noise parameters. The noise simulator is then
physically implemented and tested on an IBM-Q quantum processor. The simulator
represents a useful addition to existing libraries of quantum circuits for
quantum processors, and it offers a new tool for investigating quantum signal
and information processing having to cope with thermal noise.
