Coherence influx is indispensable for quantum reservoir computing
Echo state property (ESP) is a fundamental property that allows an input-driven dynamical system to perform information processing tasks. Recently, extensions of ESP to potentially nonstationary systems and subsystems, that is, nonstationary ESP and subset/subspace ESP, have been proposed. In this paper, we theoretically and numerically analyze the sufficient and necessary conditions for a quantum system to satisfy nonstationary ESP and subset/subspace nonstationary ESP. Based on extensive usage of the Pauli transfer matrix (PTM) form, we find that (1) the interaction with a quantum-coherent environment, termed $\textit{coherence influx}$, is indispensable in realizing nonstationary ESP, and (2) the spectral radius of PTM can characterize the fading memory property of quantum reservoir computing (QRC). Our numerical experiment, involving a system with a Hamiltonian that entails a spin-glass/many-body localization phase, reveals that the spectral radius of PTM can describe the dynamical phase transition intrinsic to such a system. To comprehensively understand the mechanisms under ESP of QRC, we propose a simplified model, multiplicative reservoir computing (mRC), which is a reservoir computing (RC) system with a one-dimensional multiplicative input. Theoretically and numerically, we show that the parameters corresponding to the spectral radius and coherence influx in mRC directly correlates with its linear memory capacity (MC). Our findings about QRC and mRC will provide a theoretical aspect of PTM and the input multiplicativity of QRC. The results will lead to a better understanding of QRC and information processing in open quantum systems.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Robust and Efficient Quantum Reservoir Computing with Discrete Time Crystal
The rapid development of machine learning and quantum computing has placed quantum machine learning at the forefront of research. However, existing quantum machine learning algorithms based on quantum variational algorit…
Quantum Machine LearningBinary ClassificationImage ClassificationOptimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics
In the current Noisy Intermediate Scale Quantum (NISQ) era, the presence of noise deteriorates the performance of quantum computing algorithms. Quantum Reservoir Computing (QRC) is a type of Quantum Machine Learning algo…
DenoisingQuantum Machine LearningTime SeriesTime Series Forecasting+1Temporal Information Processing on Noisy Quantum Computers
The combination of machine learning and quantum computing has emerged as a promising approach for addressing previously untenable problems. Reservoir computing is an efficient learning paradigm that utilizes nonlinear dy…
speech-recognitionSpeech RecognitionReservoir Computing Using Measurement-Controlled Quantum Dynamics
Physical reservoir computing (RC) is a machine learning algorithm that employs the dynamics of a physical system to forecast highly nonlinear and chaotic phenomena. In this paper, we introduce a quantum RC system that em…
Level Generation with Quantum Reservoir Computing
Reservoir computing is a form of machine learning particularly suited for time series analysis, including forecasting predictions. We take an implementation of \emph{quantum} reservoir computing that was initially design…
Time SeriesTime Series Analysis