更改

== Classical reservoir computing ==

== Classical reservoir computing ==

= = = 经典的油藏计算 = =  

= = = 经典的储备池计算 = =  

=== Reservoir ===

=== Reservoir ===

=== Readout ===

=== Readout ===

= = = 读出 = =  

= = = 读出 层= =  

The readout is a neural network layer that performs a linear transformation on the output of the reservoir.<ref name=":4" /> The weights of the readout layer are trained by analyzing the spatiotemporal patterns of the reservoir after excitation by known inputs, and by utilizing a training method such as a [[linear regression]] or a [[Ridge regression]].<ref name=":4" /> As its implementation depends on spatiotemporal reservoir patterns, the details of readout methods are tailored to each type of reservoir.<ref name=":4" /> For example, the readout for a reservoir computer using a container of liquid as its reservoir might entail observing spatiotemporal patterns on the surface of the liquid.<ref name=":4" />

The readout is a neural network layer that performs a linear transformation on the output of the reservoir.<ref name=":4" /> The weights of the readout layer are trained by analyzing the spatiotemporal patterns of the reservoir after excitation by known inputs, and by utilizing a training method such as a [[linear regression]] or a [[Ridge regression]].<ref name=":4" /> As its implementation depends on spatiotemporal reservoir patterns, the details of readout methods are tailored to each type of reservoir.<ref name=":4" /> For example, the readout for a reservoir computer using a container of liquid as its reservoir might entail observing spatiotemporal patterns on the surface of the liquid.<ref name=":4" />

==== Gaussian states of interacting quantum harmonic oscillators ====

==== Gaussian states of interacting quantum harmonic oscillators ====

= = = 相互作用量子谐振子的高斯态 = = =  

= = = 相互作用的量子谐振子的高斯态 = = =  

Gaussian states are a paradigmatic class of states of [[Continuous-variable quantum information|continuous variable quantum systems]].<ref>{{cite arXiv|last1=Ferraro|first1=Alessandro|last2=Olivares|first2=Stefano|last3=Paris|first3=Matteo G. A.|date=2005-03-31|title=Gaussian states in continuous variable quantum information|eprint=quant-ph/0503237}}</ref> Although they can nowadays be created and manipulated in, e.g, state-of-the-art optical platforms,<ref>{{Cite journal|last1=Roslund|first1=Jonathan|last2=de Araújo|first2=Renné Medeiros|last3=Jiang|first3=Shifeng|last4=Fabre|first4=Claude|last5=Treps|first5=Nicolas|date=2013-12-15|title=Wavelength-multiplexed quantum networks with ultrafast frequency combs|url=https://www.nature.com/articles/nphoton.2013.340|journal=Nature Photonics|language=en|volume=8|issue=2|pages=109–112|doi=10.1038/nphoton.2013.340|arxiv=1307.1216|s2cid=2328402|issn=1749-4893}}</ref> naturally robust to [[Quantum decoherence|decoherence]], it is well-known that they are not sufficient for, e.g., universal [[quantum computing]] because transformations that preserve the Gaussian nature of a state are linear.<ref>{{Cite journal|last1=Bartlett|first1=Stephen D.|last2=Sanders|first2=Barry C.|last3=Braunstein|first3=Samuel L.|last4=Nemoto|first4=Kae|date=2002-02-14|title=Efficient Classical Simulation of Continuous Variable Quantum Information Processes|url=https://link.aps.org/doi/10.1103/PhysRevLett.88.097904|journal=Physical Review Letters|volume=88|issue=9|pages=097904|doi=10.1103/PhysRevLett.88.097904|pmid=11864057|arxiv=quant-ph/0109047|bibcode=2002PhRvL..88i7904B|s2cid=2161585}}</ref> Normally, linear dynamics would not be sufficient for nontrivial reservoir computing either. It is nevertheless possible to harness such dynamics for reservoir computing purposes by considering a network of interacting [[quantum harmonic oscillator]]s and injecting the input by periodical state resets of a subset of the oscillators. With a suitable choice of how the states of this subset of oscillators depends on the input, the observables of the rest of the oscillators can become nonlinear functions of the input suitable for reservoir computing; indeed, thanks to the properties of these functions, even universal reservoir computing becomes possible by combining the observables with a polynomial readout function.<ref name=":5" /> In principle, such reservoir computers could be implemented with controlled multimode [[Optical parametric oscillator|optical parametric processes]],<ref>{{Cite journal|last1=Nokkala|first1=J.|last2=Arzani|first2=F.|last3=Galve|first3=F.|last4=Zambrini|first4=R.|last5=Maniscalco|first5=S.|last6=Piilo|first6=J.|last7=Treps|first7=N.|last8=Parigi|first8=V.|date=2018-05-09|title=Reconfigurable optical implementation of quantum complex networks|url=https://doi.org/10.1088%2F1367-2630%2Faabc77|journal=New Journal of Physics|language=en|volume=20|issue=5|pages=053024|doi=10.1088/1367-2630/aabc77|arxiv=1708.08726|bibcode=2018NJPh...20e3024N|s2cid=119091176|issn=1367-2630}}</ref> however efficient extraction of the output from the system is challenging especially in the quantum regime where [[Measurement in quantum mechanics#State change due to measurement|measurement back-action]] must be taken into account.

Gaussian states are a paradigmatic class of states of [[Continuous-variable quantum information|continuous variable quantum systems]].<ref>{{cite arXiv|last1=Ferraro|first1=Alessandro|last2=Olivares|first2=Stefano|last3=Paris|first3=Matteo G. A.|date=2005-03-31|title=Gaussian states in continuous variable quantum information|eprint=quant-ph/0503237}}</ref> Although they can nowadays be created and manipulated in, e.g, state-of-the-art optical platforms,<ref>{{Cite journal|last1=Roslund|first1=Jonathan|last2=de Araújo|first2=Renné Medeiros|last3=Jiang|first3=Shifeng|last4=Fabre|first4=Claude|last5=Treps|first5=Nicolas|date=2013-12-15|title=Wavelength-multiplexed quantum networks with ultrafast frequency combs|url=https://www.nature.com/articles/nphoton.2013.340|journal=Nature Photonics|language=en|volume=8|issue=2|pages=109–112|doi=10.1038/nphoton.2013.340|arxiv=1307.1216|s2cid=2328402|issn=1749-4893}}</ref> naturally robust to [[Quantum decoherence|decoherence]], it is well-known that they are not sufficient for, e.g., universal [[quantum computing]] because transformations that preserve the Gaussian nature of a state are linear.<ref>{{Cite journal|last1=Bartlett|first1=Stephen D.|last2=Sanders|first2=Barry C.|last3=Braunstein|first3=Samuel L.|last4=Nemoto|first4=Kae|date=2002-02-14|title=Efficient Classical Simulation of Continuous Variable Quantum Information Processes|url=https://link.aps.org/doi/10.1103/PhysRevLett.88.097904|journal=Physical Review Letters|volume=88|issue=9|pages=097904|doi=10.1103/PhysRevLett.88.097904|pmid=11864057|arxiv=quant-ph/0109047|bibcode=2002PhRvL..88i7904B|s2cid=2161585}}</ref> Normally, linear dynamics would not be sufficient for nontrivial reservoir computing either. It is nevertheless possible to harness such dynamics for reservoir computing purposes by considering a network of interacting [[quantum harmonic oscillator]]s and injecting the input by periodical state resets of a subset of the oscillators. With a suitable choice of how the states of this subset of oscillators depends on the input, the observables of the rest of the oscillators can become nonlinear functions of the input suitable for reservoir computing; indeed, thanks to the properties of these functions, even universal reservoir computing becomes possible by combining the observables with a polynomial readout function.<ref name=":5" /> In principle, such reservoir computers could be implemented with controlled multimode [[Optical parametric oscillator|optical parametric processes]],<ref>{{Cite journal|last1=Nokkala|first1=J.|last2=Arzani|first2=F.|last3=Galve|first3=F.|last4=Zambrini|first4=R.|last5=Maniscalco|first5=S.|last6=Piilo|first6=J.|last7=Treps|first7=N.|last8=Parigi|first8=V.|date=2018-05-09|title=Reconfigurable optical implementation of quantum complex networks|url=https://doi.org/10.1088%2F1367-2630%2Faabc77|journal=New Journal of Physics|language=en|volume=20|issue=5|pages=053024|doi=10.1088/1367-2630/aabc77|arxiv=1708.08726|bibcode=2018NJPh...20e3024N|s2cid=119091176|issn=1367-2630}}</ref> however efficient extraction of the output from the system is challenging especially in the quantum regime where [[Measurement in quantum mechanics#State change due to measurement|measurement back-action]] must be taken into account.

* Extreme learning machines

* Extreme learning machines

= = = = 深度学习 = = 极限学习机器

深度学习  

 

极限学习机器

== References ==

== References ==