Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size

[en] There is a worldwide effort toward quantum technology. Information processing, sensing, communication, and related areas are getting much of the attention. The advantages offered by the quantum domain are well recognized and acclaimed. Proposed implementations rely on systems operating at rather low temperatures and on the need to isolate the system from outside sources of noise. We discuss a theoretical scheme that suggests operating with a classical collection of quantum systems. An experimental demonstration of the principle is available. The ensemble is an array of size-disordered quantum dots addressed and probed by laser pulses. The algebraic approach encodes information in the coherences between quantum levels of the dots and demonstrates resilience to size disorder.Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nanosystems are not quite identical, and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N2 logic variables per N level system. This is how massive parallelism is achieved in that there are N2 potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N2 expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot (QD) dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semiconducting QDs suggests that the dimer coherences can be probed at room temperature.There are no data underlying this work.

Research Center/Unit :

MolSys - Molecular Systems - ULiège

Disciplines :

Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others

Author, co-author :

Gattuso, Hugo ; Université de Liège - ULiège > Département de chimie (sciences) > Laboratoire de chimie physique théorique

Levine, R. D.

Remacle, Françoise ; Université de Liège - ULiège > Département de chimie (sciences) > Laboratoire de chimie physique théorique

Language :

English

Title :

Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size

Publication date :

2020

Journal title :

Proceedings of the National Academy of Sciences of the United States of America

ISSN :

0027-8424

eISSN :

1091-6490

Volume :

117

Issue :

Pages :

21022

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://www.pnas.org/content/117/35/21022.abstract

European Projects :

H2020 - 766563 - COPAC - Coherent Optical Parallel Computing

Name of the research project :

MONACOMP

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique
EC - European Commission

Available on ORBi :

since 26 January 2021

Statistics

Number of views

58 (4 by ULiège)

Number of downloads

3 (3 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

L. Gyongyosi, S. Imre, A survey on quantum computing technology. Comput. Sci. Rev. 31, 51–71 (2019).
National Academies of Sciences, Engineering, and Medicine, Quantum Computing: Progress and Prospects, E. Grumbling, M. Horowitz, Eds. (The National Academies Press, Washington, DC, 2019), p. 272.
S. Lloyd, M. Mohseni, P. Rebentrost, Quantum principal component analysis. Nat. Phys. 10, 631–633 (2014).
P. Rebentrost, B. Gupt, T. R. Bromley, Quantum computational finance: Monte Carlo pricing of financial derivatives. Phys. Rev. A (Coll. Park) 98, 022321 (2018).
R. Xia, S. Kais, Quantum machine learning for electronic structure calculations. Nat. Commun. 9, 4195 (2018).
M. Schuld, I. Sinayskiy, F. Petruccione, Prediction by linear regression on a quantum computer. Phys. Rev. A (Coll. Park) 94, 022342 (2016).
S. Kais, Ed., Quantum Information and Computation for Chemistry, (Wiley and Sons, Hoboken, NJ, 2014), Vol. vol. 154.
J. Yuen-Zhou, J. J. Krich, I. Kassal, A. S. Johnson, A. Aspuru-Guzik, Ultrafast spectroscopy: Quantum Information and Wavepackets, (IOP Publishing, Bristol, 2014).
S. Mukamel, Principles of Nonlinear Optical Spectroscopy, (Oxford Series in Optical and Imaging Sciences, Oxford University Press, 1995).
M. Cho, Two-Dimensional Optical Spectroscopy, (CRC Press, Boca Raton, 2009).
P. Hamm, M. T. Zanni, Concepts and Methods of 2D Infrared Spectroscopy, (Cambridge University Press, Cambridge, 2011).
B. Fresch et al., Parallel and multivalued logic by the two-dimensional photon-echo response of a rhodamine−DNA complex. J. Phys. Chem. Lett. 6, 1714–1718 (2015).
B. Fresch, D. Hiluf, E. Collini, R. D. Levine, F. Remacle, Molecular decision trees realized by ultrafast electronic spectroscopy. Proc. Natl. Acad. Sci. U.S.A. 110, 17183–17188 (2013).
T.-M. Yan, B. Fresch, R. D. Levine, F. Remacle, Information processing in parallel through directionally resolved molecular polarization components in coherent multidimensional spectroscopy. J. Chem. Phys. 143, 064106 (2015).
D. B. Turner, Y. Hassan, G. D. Scholes, Exciton superposition states in CdSe nanocrystals measured using broadband two-dimensional electronic spectroscopy. Nano Lett. 12, 880–886 (2012).
S. Dong et al., Observation of an excitonic quantum coherence in CdSe nanocrystals. Nano Lett. 15, 6875–6882 (2015).
E. Cassette, R. D. Pensack, B. Mahler, G. D. Scholes, Room-temperature exciton coherence and dephasing in two-dimensional nanostructures. Nat. Commun. 6, 6086 (2015).
E. M. Janke et al., Origin of broad emission spectra in InP quantum dots: Contributions from structural and electronic disorder. J. Am. Chem. Soc. 140, 15791–15803 (2018).
J. R. Caram et al., Exploring size and state dynamics in CdSe quantum dots using two-dimensional electronic spectroscopy. J. Chem. Phys. 140, 084701 (2014).
J. R. Caram et al., Persistent inter-excitonic quantum coherence in CdSe quantum dots. J. Phys. Chem. Lett. 5, 196–204 (2014).
G. B. Griffin et al., Two-dimensional electronic spectroscopy of CdSe nanoparticles at very low pulse power. J. Chem. Phys. 138, 014705 (2013).
C. Y. Wong, G. D. Scholes, Biexcitonic fine structure of CdSe nanocrystals probed by polarization-dependent two-dimensional photon echo spectroscopy. J. Phys. Chem. A 115, 3797–3806 (2011).
N. Lenngren et al., Hot electron and hole dynamics in thiol-capped CdSe quantum dots revealed by 2D electronic spectroscopy. Phys. Chem. Chem. Phys. 18, 26199–26204 (2016).
E. Collini et al., Quantum phenomena in nanomaterials: Coherent superpositions of fine structure states in CdSe nanocrystals at room temperature. J. Phys. Chem. C 123, 31286–31293 (2019).
V. I. Klimov, Ed., Nanocrystal Quantum Dots, (CRC Press, Boca Raton, ed. 2, 2010).
F. Remacle, R. D. Levine, Architecture with designer atoms: Simple theoretical considerations. Proc. Natl. Acad. Sci. U.S.A. 97, 553–558 (2000).
E. Collini, Spectroscopic signatures of quantum-coherent energy transfer. Chem. Soc. Rev. 42, 4932–4947 (2013).
F. D. Fuller, J. P. Ogilvie, Experimental implementations of two-dimensional fourier transform electronic spectroscopy. Annu. Rev. Phys. Chem. 66, 667–690 (2015).
J. C. Dean, G. D. Scholes, Coherence spectroscopy in the condensed phase: Insights into molecular structure, environment, and interactions. Acc. Chem. Res. 50, 2746–2755 (2017).
T. A. A. Oliver, Recent advances in multidimensional ultrafast spectroscopy. R. Soc. Open Sci. 5, 171425 (2018).
J. R. Caram, G. S. Engel, Extracting dynamics of excitonic coherences in congested spectra of photosynthetic light harvesting antenna complexes. Faraday Discuss. 153, 93–104 (2011).
G. Panitchayangkoon et al., Direct evidence of quantum transport in photosynthetic light-harvesting complexes. Proc. Natl. Acad. Sci. U.S.A. 108, 20908–20912 (2011).
Z. Hu, G. S. Engel, S. Kais, Double-excitation manifold’s effect on exciton transfer dynamics and the efficiency of coherent light harvesting. Phys. Chem. Chem. Phys. 20, 30032–30040 (2018).
S.-H. Yeh, R. D. Hoehn, M. A. Allodi, G. S. Engel, S. Kais, Elucidation of near-resonance vibronic coherence lifetimes by nonadiabatic electronic-vibrational state character mixing. Proc. Natl. Acad. Sci. U.S.A. 116, 18263–18268 (2019).
Y. Alhassid, The statistical theory of quantum dots. Rev. Mod. Phys. 72, 895–968 (2000).
T. A. Brody et al., Random-matrix physics: Spectrum and strength fluctuations. Rev. Mod. Phys. 53, 385–479 (1981).
E. Cohen et al., Fast energy transfer in CdSe quantum dot layered structures: Controlling coupling with covalent-bond organic linkers. J. Phys. Chem. C 122, 5753–5758 (2018).
L. Brus, Electronic wave functions in semiconductor clusters: Experiment and theory. J. Phys. Chem. 90, 2555–2560 (1986).
K. Leung, S. Pokrant, K. B. Whaley, Exciton fine structure in CdSe nanoclusters. Phys. Rev. B Condens. Matter Mater. Phys. 57, 12291–12301 (1998).
A. L. Efros, M. Rosen, The electronic structure of semi-conducting nanocrystal. Ann. Rev. Mater. Sci. 30, 475–521 (2000).
A. L. Efros et al., Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states. Phys. Rev. B Condens. Matter 54, 4843–4856 (1996).
S. Lee, L. Jönsson, J. W. Wilkins, G. W. Bryant, G. Klimeck, Electron-hole correlations in semiconductor quantum dots with tight-binding wave functions. Phys. Rev. B Condens. Matter Mater. Phys. 63, 195318 (2001).
L. W. Wang, A. Zunger, High-energy excitonic transitions in CdSe quantum dots. J. Phys. Chem. B 102, 6449–6454 (1998).
O. V. Prezhdo, Photoinduced dynamics in semiconductor quantum dots: Insights from time-domain ab initio studies. Acc. Chem. Res. 42, 2005–2016 (2009).
J. M. Luttinger, W. Kohn, Motion of electrons and holes in perturbed periodic fields. Phys. Rev. 97, 869–883 (1955).
A. L. Efros, Luminescence polarization of CdSe microcrystals. Phys. Rev. B Condens. Matter 46, 7448–7458 (1992).
H. Gattuso, B. Fresch, D. R. Levine, F. Remacle, Coherent exciton dynamics in ensembles of size-dispersed CdSe quantum dot dimers probed via ultrafast spectroscopy: A quantum computational study. Appl. Sci. 10, 1328 (2020).
J. Hinze, Ed., The Unitary Group for the Evaluation of the Electronic Energy Matrix Elements, (Springer-Verlag, Berlin, 1981), Vol. 22.
R. Gilmore, Lie Groups, Lie Algebras and Some of Their Applications, (Mineola, Dover, 2012).
Y. Alhassid, R. D. Levine, Connection between the maximal entropy and the scattering theoretic analyses of collision processes. Phys. Rev. A 18, 89–116 (1978).
A. J. F. Siegert, On the approach to statistical equilibrium. Phys. Rev. 76, 1708–1714 (1949).
R. I. Cukier, K. E. Shuler, On the microscopic conditions for linear macroscopic laws. J. Chem. Phys. 57, 302–311 (1972).
Wikipedia, Cumulants (2020). https://en.wikipedia.org/wiki/Cumulant. Accessed 7 April 2020.
M. Abramovitz, I. Stegun, A Handbook of Mathematical Functions, (Dover, New York, 1972).