RESUMEN
When reasoning about causes of sustainability problems and possible solutions, sustainability scientists rely on disciplinary-based understanding of cause-effect relations. These disciplinary assumptions enable and constrain how causal knowledge is generated, yet they are rarely made explicit. In a multidisciplinary field like sustainability science, lack of understanding differences in causal reasoning impedes our ability to address complex sustainability problems. To support navigating the diversity of causal reasoning, we articulate when and how during a research process researchers engage in causal reasoning and discuss four common ideas about causation that direct it. This articulation provides guidance for researchers to make their own assumptions and choices transparent and to interpret other researchers' approaches. Understanding how causal claims are made and justified enables sustainability researchers to evaluate the diversity of causal claims, to build collaborations across disciplines, and to assess whether proposed solutions are suitable for a given problem.
RESUMEN
Most existing results in the analysis of quantum reservoir computing (QRC) systems with classical inputs have been obtained using the density matrix formalism. This paper shows that alternative representations can provide better insight when dealing with design and assessment questions. More explicitly, system isomorphisms are established that unify the density matrix approach to QRC with the representation in the space of observables using Bloch vectors associated with Gell-Mann bases. It is shown that these vector representations yield state-affine systems previously introduced in the classical reservoir computing literature and for which numerous theoretical results have been established. This connection is used to show that various statements in relation to the fading memory property (FMP) and the echo state property (ESP) are independent of the representation and also to shed some light on fundamental questions in QRC theory in finite dimensions. In particular, a necessary and sufficient condition for the ESP and FMP to hold is formulated using standard hypotheses, and contractive quantum channels that have exclusively trivial semi-infinite solutions are characterized in terms of the existence of input-independent fixed points.
RESUMEN
Reservoir computing has emerged as a powerful machine learning paradigm for harvesting nontrivial information processing out of disordered physical systems driven by sequential inputs. To this end, the system observables must become nonlinear functions of the input history. We show that encoding the input to quantum or classical fluctuations of a network of interacting harmonic oscillators can lead to a high performance comparable to that of a standard echo state network in several nonlinear benchmark tasks. This equivalence in performance holds even with a linear Hamiltonian and a readout linear in the system observables. Furthermore, we find that the performance of the network of harmonic oscillators in nonlinear tasks is robust to errors both in input and reservoir observables caused by external noise. For any reservoir computing system with a linear readout, the magnitude of trained weights can either amplify or suppress noise added to reservoir observables. We use this general result to explain why the oscillators are robust to noise and why having precise control over reservoir memory is important for noise robustness in general. Our results pave the way toward reservoir computing harnessing fluctuations in disordered linear systems.
RESUMEN
Closed quantum systems exhibit different dynamical regimes, like many-body localization or thermalization, which determine the mechanisms of spread and processing of information. Here we address the impact of these dynamical phases in quantum reservoir computing, an unconventional computing paradigm recently extended into the quantum regime that exploits dynamical systems to solve nonlinear and temporal tasks. We establish that the thermal phase is naturally adapted to the requirements of quantum reservoir computing and report an increased performance at the thermalization transition for the studied tasks. Uncovering the underlying physical mechanisms behind optimal information processing capabilities of spin networks is essential for future experimental implementations and provides a new perspective on dynamical phases.