Classical simulation of quantum dephasing and depolarizing noise

Dephasing decoherence induced by interaction of one qubit with a quantum bath can be simulated classically by random unitary evolution without the need for a bath and this random unitary evolution is equivalent to the quantum case. For a general dephasing model and a single-qubit system, we explicitly construct the noise functional and completely specify the random unitary evolution. To demonstrate the technique, we applied our results to three paradigmatic models: spin-boson, central spin, and quantum impurity. For multiple qubits, we identify a class of generalized quantum dephasing models that can be simulated classically. Finally we show that depolarizing quantum models can be simulated classically for all dimensionalities of the principal system.

Figure 1

Fields $h_1\left(t\right)$ and $h_2\left(t\right)$ for the spin-boson model.

Figure 2

Fields $h_1\left(t\right)$ and $h_2\left(t\right)$ for the quantum impurity model. The solid line shows coupling $v=3$ (quantum phase). The dotted line shows $v=2$ (crossover). The dashed line shows $v=0.6$ (classical phase). Note the oscillatory behavior of the stronger coupling, indicative of coherence oscillation.

Figure 3

The $z$ component of the Bloch vector as a function of time for single-qubit classical depolarization. Note that proper depolarization ends at the first root ($t\approx 0.77$).