text
stringlengths
0
8.13M
00 .. 89 00 ..1 89
00 .. 67 xk-15 0000 .... 4567
0.5 00..23
0000 .... 01234 0 . 01
9600t Qe Rac Cher 9800 10000 tim 10 e20 s0 tep 10400 10600 10800 11000 0 0.1 0.2 0.3 0 x.4 k 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 x0.6 k0. -7 60.8 0.9 1
(d) Hénon map
1 1
0.9 0.9
0.8 0.8
0.7 0.7
0.6 0.6
00 .. 45 xk-1 00 .. 45
0.3 0.3
0.2 teacher 0.2
0.1 QRC 0.1
0 9600 9800 10000 10200 10400 10600 10800 11000 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
timestep xk
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
9900 9950 10000 10050 10100
timestep
FIG.4. Demonstrationsofchaoticattractoremulations. (a)Lorenzattractor. (b)Mackey-Glasssystem. (c)Ro¨sslerattractor.
(d) H´enon map. The dotted line shows the time step when the system is switched from teacher forced state to autonomous
state. In the right side, delayed phase diagrams of learned dynamics are shown.
V. CONCLUSION AND DISCUSSION stand the power of a quantum enhanced feature space.
ACKNOWLEDGEMENT
Here we reviewed quantum reservoir computing and
related approaches, quantum extreme learning machine
and quantum circuit learning. The idea of quantum KF is supported by KAKENHI No.16H02211, JST
reservoir computing comes from the spirit of reservoir PRESTO JPMJPR1668, JST ERATO JPMJER1601,
computing, i.e., outsourcing information processing to andJSTCRESTJPMJCR1673. KNissupportedbyJST
natural physical systems. This idea is best suited to PRESTOGrantNumberJPMJPR15E7,Japan,byJSPS
quantum machine learning on near-term quantum de- KAKENHI Grant Numbers JP18H05472, JP16KT0019,
vices in NISQ (noisy intermediate quantum) era. Since and JP15K16076. KN would like to acknowledge Dr.
reservoir computing uses complex physical systems as a Quoc Hoan Tran for his helpful comments. This work is
feature space to construct a model by the simple linear supported by MEXT Quantum Leap Flagship Program
regression, this approach would be a good way to under- (MEXT Q-LEAP) Grant No. JPMXS0118067394.
[1] R.P. Feynman, Simulating physics with computers, Int. [2] M.A. Nielsen and I. L. Chuang, Quantum computation
J. Theor. Phys. 21, 467 (1982). and quantum information, (Cambridge university press
12
2010). [24] L.Appeltant,M.C.Soriano,G.VanderSande,J.Danck-
[3] K. Fujii, Quantum Computation with Topological Codes aert,S.Massar,J.Dambre,B.Schrauwen,C.R.Mirasso,
-From Qubit to Topological Fault-Tolerance-, Springer- and I. Fischer, Information processing using a single dy-
Briefs in Mathematical Physics (Springer-Verlag 2015). namical node as complex system. Nat. Commun. 2, 468
[4] P. W. Shor, Algorithms for quantum computation: Dis- (2011).
cretelogarithmsandfactoring,InProceedingsofthe35th [25] D. Woods and T. J. Naughton, Photonic neural net-
Annual Symposium on Foundations of Computer Sci- works., Nat. Phys. 8, 257 (2012).
ence, 124 (1994). [26] L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J.
[5] R. Barends et al., Superconducting quantum circuits at M.Gutierrez,L.Pesquera,C.R.Mirasso,andI.Fischer,
thesurfacecodethresholdforfaulttolerance,Nature508, PhotonicinformationprocessingbeyondTuring: anopto-
500 (2014). electronicimplementationofreservoircomputing,Optics
[6] J.Kellyetal.,Statepreservationbyrepetitiveerrordetec- Express 20, 3241 (2012).
tion in a superconducting quantum circuit, Nature 519, [27] Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B.
66 (2015). Schrauwen, M. Haelterman, and S. Massar, Optoelec-
[7] J. Preskill, Quantum Computing in the NISQ era and tronic Reservoir Computing, Sci. Rep. 2, 287 (2012).
beyond., Quantum 2, 79 (2018). [28] D.Brunner,M.C.Soriano,C.R.Mirasso,andI.Fischer,
[8] S. Boixo et al., Characterizing quantum supremacy in Parallel photonic information processing at gigabyte per
near-term devices., Nature Physics 14, 595 (2018). second data rates using transient states, Nat. Commun.
[9] J.I.CiracandP.Zoller,Goalsandopportunitiesinquan- 4, 1364 (2013).
tum simulation, Nat. Phys. 8, 264 (2012). [29] K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers,
[10] I.Bloch,J.Dalibard,andS.Nascimb`ene,Quantum sim- G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre,
ulations with ultracold quantum gases, Nat. Phys. 8, 267 andP.Bienstman,Experimental demonstration of reser-
(2012). voircomputingonasiliconphotonicschipNat.Commun.
[11] I.M.Georgescu,S.Ashhab,andF.Nori,Quantum sim- 5, 3541 (2014).
ulation, Rev. of Mod. Phys. 86, 153 (2014). [30] A. Z. Stieg, A. V. Avizienis, H. O. Sillin, C. Martin-
[12] T. Kadowaki and H. Nishimori, Quantum annealing in Olmos, M. Aono, and J. K. Gimzewski Emergent criti-
thetransverseIsingmodel,Phys.Rev.E58,5355(1998). cality in complex turing B-type atomic switch networks,
[13] E.Farhi,J.Goldstone,S.Gutmann,J.Lapan,A.Lund- Adv. Mater. 24, 286 (2012).
gren, and D. Preda, A quantum adiabatic evolution al- [31] H.Hauser,A.J.Ijspeert,R.M.Fu¨chslin,R.Pfeifer,and
gorithm applied to random instances of an NP-complete W.Maass,Towards a theoretical foundation for morpho-
problem, Science 292, 472 (2001). logical computation with compliant bodies Biol. Cybern.
[14] T.F.Rønnow,Z.Wang,J.Job,S.Boixo,S.V.Isakov,D. 105, 355 (2011).
Wecker,J.M.Martinis,D.A.Lidar,M.TroyerDefining [32] K.Nakajima,H.Hauser,R.Kang,E.Guglielmino,D.G.
and detecting quantum speedup,Science345,420(2014). Caldwell, and R. Pfeifer, Computing with a Muscular-
[15] S. Boixo, T. F. Rønnow, S. V. Isakov, Z. Wang, D. Hydrostat System, Proceedings of 2013 IEEE Interna-
Wecker,D.A.Lidar,J.M.Martinis,andM.Troyer,Evi- tionalConferenceonRoboticsandAutomation(ICRA),
denceforquantumannealingwithmorethanonehundred 1496 (2013).
qubits, Nat. Phys. 10, 218 (2014). [33] K. Nakajima, H. Hauser, R. Kang, E. Guglielmino, D.
[16] T. Morimae, K. Fujii, and J. F. Fitzsimons, Hardness G. Caldwell, and R. Pfeifer, A soft body as a reservoir:
of classically simulating the one-clean-qubit model,Phys. case studies in a dynamic model of octopus-inspired soft
Rev. Lett. 112, 130502 (2014). robotic arm Front. Comput. Neurosci. 7, 1 (2013).
[17] K. Fujii, H. Kobayashi, T. Morimae, H. Nishimura, S. [34] K.Nakajima,T.Li,H.Hauser,andR.Pfeifer,Exploiting
Tamate, and S. Tani, Power of Quantum Computation short-term memory in soft body dynamics as a computa-
withFewCleanQubits,Proceedingsof43rdInternational tionalresource,J.R.Soc.Interface11,20140437(2014).
ColloquiumonAutomata,Languages,andProgramming [35] K. Nakajima, H.Hauser, T. Li, andR. Pfeifer, Informa-
(ICALP 2016), pp.13:1-13:14. tion processing via physical soft body, Sci. Rep. 5, 10487
[18] K.FujiiandS.Tamate,Computationalquantum-classical (2015).
boundary of complex and noisy quantum systems, Sci. [36] K. Caluwaerts, J. Despraz, A. I¸s¸cen, A. P. Sabelhaus,
Rep. 6, 25598 (2016). J. Bruce, B. Schrauwen, and V. SunSpiral, Design and
[19] M. Rabinovich, R. Huerta, and G. Laurent, Transient control of compliant tensegrity robots through simula-
dynamics for neural processing Science 321, 48 (2008). tions and hardware validation, J. R. Soc. Interface 11,