Decoherence in chaotic systems: role of chaotic dynamics as energy and information reservoir.

Qingyu Li, Chiranjib Mukhopadhyay, Ludovico Minati +1 more

Quantum reservoir computing has emerged as a promising paradigm for harnessing quantum systems to process temporal data efficiently by bypassing the costly training of gradient-based learning methods. Here, we demonstrate the capability of this approach to predict and characterize chaotic dynamics in discrete nonlinear maps, exemplified through the logistic and Hénon maps. While achieving excellent predictive accuracy, we also demonstrate the optimization of training hyperparameters of the quantum reservoir based on the properties of the underlying map, thus paving the way for efficient forecasting with other discrete and continuous time-series data. Using closed-loop prediction of distant future steps, our protocol discriminates between chaotic and nonchaotic phases without prior knowledge of the underlying map or the nature of the time series. Furthermore, the framework exhibits robustness against decoherence when trained and shows insensitivity to reservoir Hamiltonian variations as well as robustness to finite-sampling error. These results highlight quantum reservoir computing as a scalable and noise-resilient tool for modeling complex dynamical systems, with immediate applicability in near-term quantum hardware.

Fernando Cucchietti, Horacio M. Pastawski, Rodolfo A. Jalabert

Hans-Thomas Elze

Michael B. Mensky

Decoherence aiid dissipation of a quantum system occurs due to its entanglement with the environment (reservoir) . In the course of interaction of the system with the reservoir information about the system is 'recorded' in the state of the reservoir. This is why influence of the reservoir on the system (i.e. the system's decoherence and dissipation) may be accounted in the framework of quantum theory of continuous measurements. Constructing such a theory with the help of restricted path integrals (RPI) gives a model-independent theory of decoherence and dissipation. The special role of information in decoherence and dissipation is explicitly revealed by this approach. This makes it possible to apply the RPI approach for the analysis of decoherence in quantum informatic devices.

Nikola Burić

Bongsu Kim, Oscar Lee, Sangjun Jeon +1 more

Physical reservoir computing offers an energy-efficient alternative to conventional neural networks, where the material-specific intrinsic memory capacity in a physical system plays an indispensable role. Substituting temporal memory with spatial degrees of freedom, we demonstrate that the memory capacity can be created extrinsically in systems with no intrinsic memory by exploiting the computational space-time tradeoff. Our approach utilizes multidimensional input nodes to function as a spatial memory axis, thereby replacing the dependency on intrinsic history-dependent dynamics in the reservoir. Our scheme is validated in a multi-terminal quantum dot system, whose discrete energy levels provide strong nonlinearity and complexity crucial for reservoir computing, while its short relaxation time leaves no room for intrinsic memory. Numerically, the quantum dot reservoir with a tunable extrinsic memory shows high performance on both chaotic future prediction and nonlinear transformation tasks. Furthermore, from the analysis of quantum state trajectory acquired from task operations, the geometric understanding of the extrinsic memory capacity, nonlinearity, and complexity is provided and their correlations are systematically investigated.