Online quantum time series processing with random oscillator networks.

Reservoir computing is a powerful machine learning paradigm for online time series processing. It has reached state-of-the-art performance in tasks such as chaotic time series prediction and continuous speech recognition thanks to its unique combination of high computational power and low training cost which sets it aside from alternatives such as traditionally trained recurrent neural networks, and furthermore is amenable to implementations in dedicated hardware, potentially leading to extremely compact and efficient reservoir computers. Recently the use of random quantum systems has been proposed, leveraging the complexity of quantum dynamics for classical time series processing. Extracting the output from a quantum system without disturbing its state too much is problematic however, and can be expected to become a bottleneck in such approaches. Here we propose a reservoir computing inspired approach to online processing of time series consisting of quantum information, sidestepping the measurement problem. We illustrate its power by generalizing two paradigmatic benchmark tasks from classical reservoir computing to quantum information and introducing a task without a classical analogue where a random system is trained to both create and distribute entanglement between systems that never directly interact. Finally, we discuss partial generalizations where only the input or only the output time series is quantum.

High-Performance Reservoir Computing With Fluctuations in Linear Networks.

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.

Dynamical Phase Transitions in Quantum Reservoir Computing.

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.

Local probe for connectivity and coupling strength in quantum complex networks.

We develop a local probe to estimate the connectivity of complex quantum networks. Our results show how global properties of different classes of complex networks can be estimated - in quantitative manner with high accuracy - by coupling a probe to a single node of the network. Here, our interest is focused on probing the connectivity, i.e. the degree sequence, and the value of the coupling constant within the complex network. The scheme combines results on classical graph theory with the ability to develop quantum probes for networks of quantum harmonic oscillators. Whilst our results are proof-of-principle type, within the emerging field of quantum complex networks they may have potential applications for example to the efficient transfer of quantum information or energy or possibly to shed light on the connection between network structure and dynamics.

Complex quantum networks as structured environments: engineering and probing.

We consider structured environments modeled by bosonic quantum networks and investigate the probing of their spectral density, structure, and topology. We demonstrate how to engineer a desired spectral density by changing the network structure. Our results show that the spectral density can be very accurately detected via a locally immersed quantum probe for virtually any network configuration. Moreover, we show how the entire network structure can be reconstructed by using a single quantum probe. We illustrate our findings presenting examples of spectral densities and topology probing for networks of genuine complexity.