Unveiling noiseless clusters in complex quantum networks

Abstract

The transport and storage of quantum information, excitations, and entanglement, within and across complex quantum networks is crucially affected by the presence of noise induced by their surroundings. Generally, the interaction with the environment deteriorates quantum properties initially present, thus limiting the efficiency of any quantum-enhanced protocol or phenomenon. This is of key relevance, for example, in the design of quantum communication networks and for understanding and controlling quantum harvesting on complex systems. Here, we show that complex quantum networks, such as random and small-world ones, can admit noiseless clusters for collective dissipation. We characterize these noiseless structures in connection to their topology addressing their abundance, extension, and configuration, as well as their robustness to noise and experimental imperfections. We show that the network degree variance controls the probability to find noiseless modes and that these are mostly spanning an even number of nodes, like breathers. For imperfections across the network, a family of quasi-noiseless modes is also identified shielded by noise up to times decreasing linearly with frequency inhomogeneities. Large noiseless components are shown to be more resilient to the presence of detuning than to differences in their coupling strengths. Finally, we investigate the emergence of both stationary and transient quantum synchronization showing that this is a rather resilient phenomenon in these networks.

Synchronization and coalescence in a dissipative two-qubit system

“…Otherwise, as shown in this section, synchronization emerges in the presence of multiple frequencies and a slowly relaxing eigenmode; for this reason, we can refer specifically to non-degenerate subradiance. For vanishing relaxation (real part of the Liouvillian eigenvalues), a decoherence-free subspace arises that (for non-vanishing imaginary part of the corresponding eigenvalues) leads to stationary synchronization [4,5,66]. In the present case, this happens for instance in the absence of detuning and incoherent pumping, this being a situation generally hindered by disorder effects [5].…”

“…An example studied in the last decade is spontaneous synchronization emerging among different interacting quantum systems, reaching a synchronized dynamics determined by the coupling to some external environments [2]. Different approaches have been proposed to define and describe this phenomenon in the quantum regime [2], also considering a variety of systems such as harmonic oscillators [3–5], spins [6,7], biological [8] or optomechanical [9–11] systems, quantum van der Pol oscillators [12–16] or micromasers [17], and also exploring the effects of different system–bath configurations [18–20]. Synchronization signatures between mesoscopic ensembles of atomic systems have also been discussed in [21,22] using a semiclassical approach.…”

“…In particular, quantum synchronization can be induced by dissipation when time-scale separation occurs between the modes governing the dynamics [23], owing to the presence of a dominant collective excitation. Depending on the lifetime of this excitation, this synchronization can be either observed in a transient regime prior to thermalization or found in the stationary dynamics in the presence of decoherence-free channels [4,5,24,25]. From a mathematical point of view, when describing the open quantum system through a master equation, this dominant collective excitation emerges if one eigenmode of the Liouvillian has a decay rate much smaller than any other eigenmode.…”

Synchronization and non-Markovianity in open quantum systems

“…It emerges spontaneously, being enabled by several coupling mechanisms and in the absence of an external driver, differently from entrainment. While it has been well studied in the classical domain [3], it has recently become a focus of research in the quantum regime [4], where both entrainment [5][6][7][8][9][10][11][12] and spontaneous synchronization [13][14][15][16][17][18][19][20][21][22][23][24][25][26] have been explored in a variety of systems including spins, and harmonic and nonlinear oscillators, modeling platforms ranging from optomechanical systems to trapped ions and superconducting qubits. The presence of quantum correlations as a signature of synchronization, as well as the origin of these dynamical features, has been discussed [10,14,17,18,27].…”

Continuous Variables Graph States Shaped as Complex Networks: Optimization and Manipulation

“…Recurrent types of complex networks, like the scale-free networks, have been recovered in phenomena at different scales, where the functionality of the systems seems to be closely related to their structure [ 3 , 4 ]. More recently, complex networks have gained attention in the quantum realm, where several theoretical works [ 5 , 6 , 7 , 8 , 9 , 10 ] show that complex structures may play a role in quantum information technologies. It is clear that, as quantum architectures are reaching larger scales, their internal arrangement starts to play a significant role in their functionality.…”