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Register a new userOpen system model for quantum dynamical maps with classical noise and corresponding master equations
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We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases: commuting system and interaction Hamiltonians, the short-time limit, and the Markov approximation.
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Deep quantum neural networks may provide a promising way to achieve quantum learning advantage with noisy intermediate scale quantum devices. Here, we use deep quantum feedforward neural networks capable of universal quantum computation to represent the mixed states for open quantum many-body systems and introduce a variational method with quantum derivatives to solve the master equation for dynamics and stationary states. Owning to the special structure of the quantum networks, this approach enjoys a number of notable features, including the absence of barren plateaus, efficient quantum analogue of the backpropagation algorithm, resource-saving reuse of hidden qubits, general applicability independent of dimensionality and entanglement properties, as well as the convenient implementation of symmetries. As proof-of-principle demonstrations, we apply this approach to both one-dimensional transverse field Ising and two-dimensional $J_1-J_2$ models with dissipation, and show that it can efficiently capture their dynamics and stationary states with a desired accuracy.
Understanding system-bath correlations in open quantum systems is essential for various quantum information and technology applications. Derivations of most master equations (MEs) for the dynamics of open systems require approximations that mask dependence of the system dynamics on correlations, since the MEs focus on reduced system dynamics. Here we demonstrate that the most common MEs indeed contain hidden information about explicit system-environment correlation. We unfold these correlations by recasting the MEs into a universal form in which the system-bath correlation operator appears. The equations include the Lindblad, Redfield, second-order time-convolutionless, second-order Nakajima-Zwanzig, and second-order universal Lindblad-like cases. We further illustrate our results in an example, which implies that the second-order universal Lindblad-like equation captures correlation more accurately than other standard techniques.
We consider an open quantum system described by a Lindblad-type master equation with two times-scales. The fast time-scale is strongly dissipative and drives the system towards a low-dimensional decoherence-free space. To perform the adiabatic elimination of this fast relaxation, we propose a geometric asymptotic expansion based on the small positive parameter describing the time-scale separation. This expansion exploits geometric singular perturbation theory and center-manifold techniques. We conjecture that, at any order, it provides an effective slow Lindblad master equation and a completely positive parameterization of the slow invariant sub-manifold associated to the low-dimensional decoherence-free space. By preserving complete positivity and trace, two important structural properties attached to open quantum dynamics, we obtain a reduced-order model that directly conveys a physical interpretation since it relies on effective Lindbladian descriptions of the slow evolution. At the first order, we derive simple formulae for the effective Lindblad master equation. For a specific type of fast dissipation, we show how any Hamiltonian perturbation yields Lindbladian second-order corrections to the first-order slow evolution governed by the Zeno-Hamiltonian. These results are illustrated on a composite system made of a strongly dissipative harmonic oscillator, the ancilla, weakly coupled to another quantum system.
The problem of a driven quantum system coupled to a bath and coherently driven is usually treated using either of two approaches: Employing the common secular approximation in the lab frame (as usually done in the context of atomic physics) or in the rotating frame (prevailing in, e.g., the treatment of solid-state qubits). These approaches are applicable in different parts of the parameter space and yield different results. We show how to bridge between these two approaches by working in the rotating frame without employing the secular approximation with respect to the driving amplitude. This allows us to uncover novel behaviors in regimes which were previously inaccessible or inaccurately treated. New features such as the qualitative different evolution of the coherence, population inversion at a lower driving amplitude, and novel structure in the resonance fluorescence spectrum of the system are found. We argue that this generalized approach is essential for analyzing hybrid systems, with components that come from distinctly different regimes which can now be treated simultaneously, giving specific examples from recent experiments on quantum dots coupled to optical cavities, and single-spin electron paramagnetic resonance.
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact and versatile description. However, care needs to be taken when several noise processes act simultaneously or the Hamiltonian evolution of the system is modified. Here, we show that generators can be added at the master equation level without compromising physicality only under restrictive conditions. Moreover, even when adding generators results in legitimate dynamics, this does not generally correspond to the true evolution of the system. We establish a general condition under which direct addition of dynamical generators is justified, showing that it is ensured under weak coupling and for settings where the free system Hamiltonian and all system-environment interactions commute. In all other cases, we demonstrate by counterexamples that the exact evolution derived microscopically cannot be guaranteed to coincide with the dynamics naively obtained by adding the generators.
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