Equivalent qubit dynamics under classical and quantum noise

We study the dynamics of quantum systems under classical and quantum noise, focusing on decoherence in qubit systems. Classical noise is described by a random process leading to a stochastic temporal evolution of a closed quantum system, whereas quantum noise originates from the coupling of the microscopic quantum system to its macroscopic environment. We derive deterministic master equations describing the average evolution of the quantum system under classical continuous-time Markovian noise and two sets of master equations under quantum noise. Strikingly, these three equations of motion are shown to be equivalent in the case of classical random telegraph noise and proper quantum environments. Hence fully quantum-mechanical models within the Born approximation can be mapped to a quantum system under classical noise. Furthermore, we apply the derived equations together with pulse optimization techniques to achieve high-fidelity one-qubit operations under random telegraph noise, and hence fight decoherence in these systems of great practical interest.

Figure 1

Fidelities for the NOT gate as functions of the correlation time ${\tau }_c$ for a $\pi$-pulse (dotted line), CORPSE (dashed-dotted line), short CORPSE (dashed line), and gradient optimization (solid line). The RTN strength $\Delta$ is set to (a) $0.125a_{\max }$ and (b) $0.25a_{\max }$. The gate fidelity for a gate $U$ is defined as $⟨\mathrm{Tr}\left[U{\rho }_0{U}^{†}\rho \right]⟩$, where the average is calculated over all pure initial states ${\rho }_0$, see Ref. 11.

Figure 2

Optimized pulse sequences yielding the highest gate fidelities for correlation times (a) $5\hslash ∕a_{\max }$, (b) $20\hslash ∕a_{\max }$, and (c) $50\hslash ∕a_{\max }$. The strength of the noise is chosen to be $\Delta =0.125a_{\max }$ corresponding to Fig. 1a.