Information Processing Capacity of Spin-Based Quantum Reservoir Computing Systems

The dynamical behaviour of complex quantum systems can be harnessed for information processing. With this aim, quantum reservoir computing (QRC) with Ising spin networks was recently introduced as a quantum version of classical reservoir computing. In turn, reservoir computing is a neuro-inspired machine learning technique that consists in exploiting dynamical systems to solve nonlinear and temporal tasks. We characterize the performance of the spin-based QRC model with the Information Processing Capacity (IPC), which allows to quantify the computational capabilities of a dynamical system beyond specific tasks. The influence on the IPC of the input injection frequency, time multiplexing, and different measured observables encompassing local spin measurements as well as correlations, is addressed. We find conditions for an optimum input driving and provide different alternatives for the choice of the output variables used for the readout. This work establishes a clear picture of the computational capabilities of a quantum network of spins for reservoir computing. Our results pave the way to future research on QRC both from the theoretical and experimental points of view.

[1]  Harald Haas,et al.  Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication , 2004, Science.

[2]  Toshiyuki Yamane,et al.  Recent Advances in Physical Reservoir Computing: A Review , 2018, Neural Networks.

[3]  Daniel Brunner,et al.  Parallel photonic information processing at gigabyte per second data rates using transient states , 2013, Nature Communications.

[4]  Naftali Tishby,et al.  Machine learning and the physical sciences , 2019, Reviews of Modern Physics.

[5]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[6]  M. C. Soriano,et al.  Gaussian states provide universal and versatile quantum reservoir computing , 2020, 2006.04821.

[7]  Harry Buhrman,et al.  The quantum technologies roadmap: a European community view , 2018, New Journal of Physics.

[8]  Keisuke Fujii,et al.  Boosting Computational Power through Spatial Multiplexing in Quantum Reservoir Computing , 2018, Physical Review Applied.

[9]  Evangelos Spiliotis,et al.  The M4 Competition: Results, findings, conclusion and way forward , 2018, International Journal of Forecasting.

[10]  Kohei Nakajima,et al.  Machine learning with controllable quantum dynamics of a nuclear spin ensemble in a solid , 2018, 1806.10910.

[11]  Henry Markram,et al.  Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations , 2002, Neural Computation.

[12]  Benjamin Schrauwen,et al.  An experimental unification of reservoir computing methods , 2007, Neural Networks.

[13]  Damien Querlioz,et al.  Neuromorphic computing with nanoscale spintronic oscillators , 2017, Nature.

[14]  L. Appeltant,et al.  Information processing using a single dynamical node as complex system , 2011, Nature communications.

[15]  M. C. Soriano,et al.  Advances in photonic reservoir computing , 2017 .

[16]  Julie Grollier,et al.  Quantum neuromorphic computing , 2020 .

[17]  Archil Avaliani,et al.  Quantum Computers , 2004, ArXiv.

[18]  Herbert Jaeger,et al.  Reservoir computing approaches to recurrent neural network training , 2009, Comput. Sci. Rev..

[19]  Pedram Khalili Amiri,et al.  Quantum computers , 2003 .

[20]  Erik Cambria,et al.  Recent Trends in Deep Learning Based Natural Language Processing , 2017, IEEE Comput. Intell. Mag..

[21]  Jan Danckaert,et al.  Real-time Audio Processing with a Cascade of Discrete-Time Delay Line-Based Reservoir Computers , 2017, Cognitive Computation.

[22]  Herbert Jaeger,et al.  The''echo state''approach to analysing and training recurrent neural networks , 2001 .

[23]  Jan Danckaert,et al.  Delay-Based Reservoir Computing: Noise Effects in a Combined Analog and Digital Implementation , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[25]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[26]  Jaideep Pathak,et al.  Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach. , 2018, Physical review letters.

[27]  Benjamin Schrauwen,et al.  Information Processing Capacity of Dynamical Systems , 2012, Scientific Reports.

[28]  Juan-Pablo Ortega,et al.  Echo state networks are universal , 2018, Neural Networks.

[29]  Jean-Pierre Martens,et al.  Large Vocabulary Continuous Speech Recognition With Reservoir-Based Acoustic Models , 2014, IEEE Signal Processing Letters.

[30]  Jiayin Chen,et al.  Learning nonlinear input–output maps with dissipative quantum systems , 2019, Quantum Information Processing.

[31]  Michiel Hermans,et al.  Online Training of an Opto-Electronic Reservoir Computer Applied to Real-Time Channel Equalization , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Claudio Gallicchio,et al.  Echo State Property of Deep Reservoir Computing Networks , 2017, Cognitive Computation.

[33]  Andrzej Opala,et al.  Quantum reservoir processing , 2018, npj Quantum Information.

[34]  Geoffrey E. Hinton.  Deep Learning-A Technology With the Potential to Transform Health Care. , 2018, JAMA.

[35]  Laurent Larger,et al.  High-Speed Photonic Reservoir Computing Using a Time-Delay-Based Architecture: Million Words per Second Classification , 2017 .

[36]  Naoki Yamamoto,et al.  Temporal Information Processing on Noisy Quantum Computers , 2020, ArXiv.