Boosting Computational Power through Spatial Multiplexing in Quantum Reservoir Computing

Quantum reservoir computing provides a framework for exploiting the natural dynamics of quantum systems as a computational resource. It can implement real-time signal processing and solve temporal machine learning problems in general, which requires memory and nonlinear mapping of the recent input stream using the quantum dynamics in computational supremacy region, where the classical simulation of the system is intractable. A nuclear magnetic resonance spin-ensemble system is one of the realistic candidates for such physical implementations, which is currently available in laboratories. In this paper, considering these realistic experimental constraints for implementing the framework, we introduce a scheme, which we call a spatial multiplexing technique, to effectively boost the computational power of the platform. This technique exploits disjoint dynamics, which originate from multiple different quantum systems driven by common input streams in parallel. Accordingly, unlike designing a single large quantum system to increase the number of qubits for computational nodes, it is possible to prepare a huge number of qubits from multiple but small quantum systems, which are operationally easy to handle in laboratory experiments. We numerically demonstrate the effectiveness of the technique using several benchmark tasks and quantitatively investigate its specifications, range of validity, and limitations in detail.

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

[2]  Nils Bertschinger,et al.  Real-Time Computation at the Edge of Chaos in Recurrent Neural Networks , 2004, Neural Computation.

[3]  Chrisantha Fernando,et al.  Pattern Recognition in a Bucket , 2003, ECAL.

[4]  Audrius V. Avizienis,et al.  Emergent Criticality in Complex Turing B‐Type Atomic Switch Networks , 2012, Advanced materials.

[5]  Timothy F. Havel,et al.  NMR Based Quantum Information Processing: Achievements and Prospects , 2000, quant-ph/0004104.

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

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

[8]  Andrew S. Cassidy,et al.  A million spiking-neuron integrated circuit with a scalable communication network and interface , 2014, Science.

[9]  Claudio R. Mirasso,et al.  Analytical and numerical studies of noise-induced synchronization of chaotic systems. , 2001, Chaos.

[10]  Keisuke Fujii,et al.  Harnessing disordered quantum dynamics for machine learning , 2016, 1602.08159.

[11]  Haeberlen Ulrich,et al.  High resolution NMR in solids : selective averaging , 1976 .

[12]  Edward Ott,et al.  Attractor reconstruction by machine learning. , 2018, Chaos.

[13]  Helmut Hauser,et al.  A soft body as a reservoir: case studies in a dynamic model of octopus-inspired soft robotic arm , 2013, Front. Comput. Neurosci..

[14]  Hitoshi Kubota,et al.  Macromagnetic Simulation for Reservoir Computing Utilizing Spin Dynamics in Magnetic Tunnel Junctions , 2018, Physical Review Applied.

[15]  L Pesquera,et al.  Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing. , 2012, Optics express.

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

[17]  Tao Li,et al.  Information processing via physical soft body , 2015, Scientific Reports.

[18]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[19]  Dieter Suter,et al.  Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins , 2014, Science.

[20]  Jonathan A. Jones.  Quantum computing with NMR. , 2010, Progress in nuclear magnetic resonance spectroscopy.

[21]  Jun Li,et al.  Enhancing quantum control by bootstrapping a quantum processor of 12 qubits , 2017, 1701.01198.

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

[23]  Dieter Suter,et al.  Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins , 2015, Science.

[24]  Tao Li,et al.  Exploiting the Dynamics of Soft Materials for Machine Learning , 2018, Soft robotics.

[25]  Timothy F. Havel,et al.  Benchmarking quantum control methods on a 12-qubit system. , 2006, Physical review letters.

[26]  Hitoshi Kubota,et al.  Evaluation of memory capacity of spin torque oscillator for recurrent neural networks , 2018, Japanese Journal of Applied Physics.

[27]  Helmut Hauser,et al.  Exploiting short-term memory in soft body dynamics as a computational resource , 2014, Journal of The Royal Society Interface.

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

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

[30]  L. Vandersypen,et al.  NMR techniques for quantum control and computation , 2004, quant-ph/0404064.

[31]  Amir F. Atiya,et al.  New results on recurrent network training: unifying the algorithms and accelerating convergence , 2000, IEEE Trans. Neural Networks Learn. Syst..

[32]  Cyrus P. Master,et al.  Quantum simulation of spin ordering with nuclear spins in a solid-state lattice , 2007 .