Hybrid quantum-classical reservoir computing for simulating chaotic systems

Forecasting chaotic systems is a notably complex task, which in recent years has been approached with reasonable success using reservoir computing (RC), a recurrent network with fixed random weights (the reservoir) used to extract the spatio-temporal information of the system. This work presents a hybrid quantum reservoir-computing (HQRC) framework, which replaces the reservoir in RC with a quantum circuit. The modular structure and measurement feedback in the circuit are used to encode the complex system dynamics in the reservoir states, from which classical learning is performed to predict future dynamics. The noiseless simulations of HQRC demonstrate valid prediction times comparable to state-of-the-art classical RC models for both the Lorenz63 and double-scroll chaotic paradigmatic systems and adhere to the attractor dynamics long after the forecasts have deviated from the ground truth.

[1]  F. Heyder,et al.  Reduced-order modeling of two-dimensional turbulent Rayleigh-Bénard flow by hybrid quantum-classical reservoir computing , 2023, Physical Review Research.

[2]  Samuel Yen-Chi Chen,et al.  Optimizing quantum noise-induced reservoir computing for nonlinear and chaotic time series prediction , 2023, Scientific reports.

[3]  Patrick J. Coles,et al.  Theory for Equivariant Quantum Neural Networks , 2022, PRX Quantum.

[4]  K. Nakajima,et al.  Quantum Noise-Induced Reservoir Computing , 2022, ArXiv.

[5]  D. Brunner,et al.  Hands-on reservoir computing: a tutorial for practical implementation , 2022, Neuromorph. Comput. Eng..

[6]  M. C. Soriano,et al.  Time-series quantum reservoir computing with weak and projective measurements , 2022, npj Quantum Information.

[7]  J. Schumacher,et al.  Hybrid quantum-classical reservoir computing of thermal convection flow , 2022, Physical Review Research.

[8]  M. Spannowsky,et al.  Completely Quantum Neural Networks , 2022, Physical Review A.

[9]  Stephen G. Penny,et al.  A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics , 2022, Neural Networks.

[10]  S. Yelin,et al.  Quantum Reservoir Computing Using Arrays of Rydberg Atoms , 2021, PRX Quantum.

[11]  K. Pradel,et al.  Natural quantum reservoir computing for temporal information processing , 2021, Scientific Reports.

[12]  G. Ribeill,et al.  Nonlinear input transformations are ubiquitous in quantum reservoir computing , 2021, Neuromorph. Comput. Eng..

[13]  Erik Bollt,et al.  Next generation reservoir computing , 2021, Nature Communications.

[14]  Miguel C. Soriano,et al.  Opportunities in Quantum Reservoir Computing and Extreme Learning Machines , 2021, Advanced Quantum Technologies.

[15]  M. Cerezo,et al.  Variational quantum algorithms , 2020, Nature Reviews Physics.

[16]  Annie E. Paine,et al.  Solving nonlinear differential equations with differentiable quantum circuits , 2020, Physical Review A.

[17]  Joni Dambre,et al.  A training algorithm for networks of high-variability reservoirs , 2020, Scientific Reports.

[18]  L. C. G. Govia,et al.  Quantum reservoir computing with a single nonlinear oscillator , 2020, Physical Review Research.

[19]  Jaideep Pathak,et al.  Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics , 2019, Neural Networks.

[20]  Marcello Benedetti,et al.  Parameterized quantum circuits as machine learning models , 2019, Quantum Science and Technology.

[21]  Dirk Oliver Theis,et al.  Input Redundancy for Parameterized Quantum Circuits , 2019, Frontiers in Physics.

[22]  Maria Schuld,et al.  Quantum Machine Learning in Feature Hilbert Spaces. , 2018, Physical review letters.

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

[24]  Rupak Biswas,et al.  Quantum Machine Learning , 2018 .

[25]  Keisuke Fujii,et al.  Quantum circuit learning , 2018, Physical Review A.

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

[27]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[28]  Jaideep Pathak,et al.  Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data. , 2017, Chaos.

[29]  Rupak Biswas,et al.  From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz , 2017, Algorithms.

[30]  S. Lloyd,et al.  Quantum gradient descent and Newton’s method for constrained polynomial optimization , 2016, New Journal of Physics.

[31]  Hans-J. Briegel,et al.  Quantum-enhanced machine learning , 2016, Physical review letters.

[32]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[33]  Alán Aspuru-Guzik,et al.  A variational eigenvalue solver on a photonic quantum processor , 2013, Nature Communications.

[34]  B. Schrauwen,et al.  2007 Special Issue: An experimental unification of reservoir computing methods , 2007 .

[35]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[36]  Bozhkov Lachezar,et al.  Echo State Network , 2017, Encyclopedia of Machine Learning and Data Mining.

[37]  Mantas Lukosevicius,et al.  A Practical Guide to Applying Echo State Networks , 2012, Neural Networks: Tricks of the Trade.

[38]  Benjamin Schrauwen,et al.  An overview of reservoir computing: theory, applications and implementations , 2007, ESANN.

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