Abstract
A brief introduction to quantum computing is provided and the potential use of molecules as the platform is discussed. The basic building blocks (quantum bits, quantum gates, and quantum algorithms) are described in order to emphasize the requirements for realizing a quantum computer, and, the advantages quantum computation has over its classical counterpart. We outline the three key steps to quantum computation: (1) initialization, (2) manipulation, and (3) readout. The possible use of internal molecular states as quantum bits and shaped laser fields to implement the quantum gates is introduced. The application to molecular quantum computing is connected to the more general problem of the control of quantum dynamics using tailored laser fields determined theoretically with optimal control theory or genetic algorithms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Messiah A (1962) Quantum mechanics, vol 1. Wiley, New York
Cohen-Tannoudji C, Diu B, Laloe F (1992) Quantum mechanics. Wiley, New York
Basdevant J-L, Dalibard J (2005) Quantum mechanics. Springer, Heidelberg
Tannor DJ (2007) Introduction to Quantum Dynamics: A Time-Dependent Perspective. University Science Books, Sausalito, CA
Fox M (2006) Quantum optics: An introduction. Oxford University Press, Oxford
Cohen-Tannoudji C, Grynberg G, Aspect A, Fabre C (2010) Introduction to quantum optics: From the semi-classical approach to quantized light. Cambridge University Press, Cambridge
Pauling L, Wilson EB (1985) Introduction to quantum mechanics with applications to chemistry. Dover Publications, New York
Smith VH, Schaefer HF, Morokuma K (eds) (1986) Applied quantum chemistry. Springer, Heidelberg
Marcus RA (1965) On the theory of electron-transfer reactions. VI. Unified treatment for homogeneous and electrode reactions. J Chem Phys 43:679
Marcus RA (1993) Electron transfer reactions in chemistry. Theory and experiment. Rev Mod Phys 65:599
Onuhic JN, Wolynes PG (1988) Classical and quantum pictures of reaction dynamics in condensed matter: Resonances, dephasing, and all that. J Phys Chem 92:6495
Herzberg G (1992) Molecular spectra and molecular structure. Krieger, Malabar
Zuev PS, Sheridan RS, Albu TV, Truhlar DG, Hrovat DA, Borden WT (2003) Carbon tunneling from a single quantum state. Science 299:867
McMahon RJ (2003) Chemical reactions involving quantum tunneling. Science 299:833
Espinosa-GarcÃa J, Corchado JC, Truhlar DG (1997) The importance of quantum effects for C-H bond activation reactions. J Am Chem Soc 119:9891
Wonchoba SE, Hu W-P, Truhlar DG (1995) Surface diffusion of H on Ni(100). Interpretation of the transition temperature. Phys Rev B 51:9985
Hiraoka K, Sato T, Takayama T (2001) Tunneling reactions in interstellar ices. Science 292:869
Cha Y, Murray CJ, Klinman JP (1989) Hydrogen tunneling in enzyme-reaction. Science 243:1325
Kohen A, Cannio R, Bartolucci S, Klinman JP (1999) Enzyme dynamics and hydrogen tunnelling in a thermophilic alcohol dehydrogenase. Nature 399:496
Truhlar DG, Gao J, Alhambra C, Garcia-Viloca M, Corchado J, Sánchez ML, Villà J (2002) The incorporation of quantum effects in enzyme kinetics modeling. Acc Chem Res 35:341
Truhlar DG, Gao J, Alhambra C, Garcia-Viloca M, Corchado J, Sánchez ML, Villà J (2004) Ensemble-averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed-phase reactions. Int J Quant Chem 100:1136
Hammer-Schiffer S (2002) Impact of enzyme motion on activity. Biochemistry 41:13335
Antoniou D, Caratzoulas S, Mincer J, Schwartz SD (2002) Barrier passage and protein dynamics in enzymatically catalyzed reactions. Eur J Biochem 269:3103
Ball P (2012) The dawn of quantum biology. Nature 474:272
Domcke W, Yarkony DR, Köppel H (eds) (2004) Conical intersections, electronic strucutre, dynamics and spectroscopy. World Scientific, New Jersey
Domcke W, Yarkony DR, Köppel H (eds) (2004) Conical intersections, theory, computation and experiment. World Scientific, New Jersey
Worth GA, Cederbaum LS (2001) Mediation of ultrafast electron transfer in biological systems by conical intersections. Chem Phys Lett 338:219–223
González-Luque M, Garavelli M, Bernardi F, Mechán M, Robb MA, Olivucci M (2010) Computational. Proc Natl Acad Sci USA 97:9379
Polli D, Altoè P, Weingart O, Spillane KM, Manzoni C, Brida D, Tomasello G, Orlandi G, Kukura P, Mathies RA, Garavelli M, Cerullo G (2010) Conical intersection dynamics of the primary photoisomerization event in vision. Nature 467:440
Lan Z, Frutos LM, Sobolewski AL, Domcke W (2008) Photochemistry of hydrogen-bonded aromatic pairs: quantum dynamical calculations for the pyrrole-pyridine complex. Proc Natl Acad Sci USA 105:12707
Schultz T, Samoylova E, Radloff W, Hertel IV, Sobolewski AL, Domcke W (2004) Efficient deactivation of a model base pair via excited-state hydrogen transfer. Science 306:1765
Wolynes PG (2009) Some quantum weirdness in physiology. Proc Natl Acad Sci USA 106:17247–17248
Engel GS, Calhoun TR, Read EL, Ahn T-K, Mancal T, Cheng Y-C, Blankenship RE, Fleming GR (2007) Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446:782–786
Lee H, Cheng Y-C, Fleming GR (2007) Coherence dynamics in photosynthesis: Protein protection of excitonic coherence. Science 316:1462
Collini E, Wong CY, Wilk KE, Curmi PMG, Brumer P, Scholes GD (2010) Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463:644
Wang Q, Schoenlein RW, Peteanu LA, Shank RA (1994) Vibrationnaly coherent photochemistry in the femtosecond primary event of vision. Science 266:422–424
Brumer P, Shapiro M (2012) Molecular response in one-photon absorption via natural thermal light vs. pulsed laser excitation. Proc Natl Acad Sci USA 109:19575
Gross A, Scheffer M (1998) Ab initio quantum and molecular dynamics of the dissociative adsorption on Pd(100). Phys Rev B 57:2493
Marx D, Parrinello M (1996) The effect of quantum and thermal fluctuations on the structure of the floppy molecule C2H3 +. Science 271:179
Arndt M, Nairz O, Voss-Andreae J, Keller C, van der Zouw G, Zeillinger A (1999) Wave-particle duality of c60 molecules. Nature 401:680
Gerlich S, Eibenberger S, Tomand M, Nimmrichter S, Hornberger K, Fagan PJ, Tüxen J, Mayor M, Arndt M (2011) Quantum interference of large organic molecules. Nat Phys 2:263
Chatzidimitriou-Dreismann A, Arndt M (2004) Quantum mechanics and chemistry: The relevance of nonlocality and entanglement for molecules. Angew Chem Int Ed 335:144
Chergui M (ed) (1996) Femtochemistry. World Scientific, Singapore
Zewail AH (1994) Femtochemistry: ultrafast dynamics of the chemical bond. World Scientific, Singapore
Ihee H, Lobastov V, Gomez U, Goodson B, Srinivasan R, Ruan C-Y, Zewail AH (2001) Science 291:385
Drescher M, Hentschel M, Kienberger R, Uiberacker M, Scrinzi A, Westerwalbesloh T, Kleineberg U, Heinzmann U, Krausz F (2002) Time-resolved atomic inner-shell spectroscopy. Nature 419:803
Goulielmakis E, Loh Z-H, Wirth A, Santra R, Rohringer N, Yakovlev VS, Zherebtsov S, Pfeifero T, Azzeer AM, Kling MF, Leone SR, Krausz F (2010) Real-time observation of valence electron motion. Nature 466:739
Krausz F, Ivanov M (2009) Attosecond physics. Rev Mod Phys 81:163–234
Kling MF, Siedschlag C, Verhoef AJ, Khan JI, Schultze M, Uphues T, Ni Y, Uiberacker M, Drescher M, Krausz F, Vrakking MJJ (2006) Control of electron localization in molecular dissociation. Science 312:246
Stolow A, Jonas DM (2004) Muldimensional snapshots of chemical dynamics. Science 305:1575
Kahra S, Leschhorn G, Kowalewski M, Schiffrin A, Bothschafter E, Fuss W, de Vivie-Riedle R, Ernstorfer R, Krausz F, Kienberger R, Schaetz T (2012) Controlled delivery of single molecules into ultra-short laser pulses: a molecular conveyor belt. Nat Phys 8:238
Asssion A, Baumert T, Bergt M, Brixner T, Kiefer B, Seyfried V, Strehle M, Gerber G (1998) Control of chemical reactions by feedback-optimized phase-shaped femtocecond laser pulses. Science 282:919
Brixner T, Damreuer NH, Niklaus P, Gerber G (2001) Photoselective adaptative femtosecond quantum control in the liquid phase. Nature 414:57
Herek JL, Wohlleben W, Cogdell RJ, Zeidler D, Motzus M (2002) Quantum control of energy flow in light harvesting. Nature 417:533
Levis RJ, Menkir GM, Rabitz H (2001) Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses. Science 292:709
Daems D, Guérin S, Hertz E, Jauslin HR, Lavorel B, Faucher O (2005) Field-free two-direction alignement alternation of linear molecules by elliptic laser pulses. Phys Rev Lett 95:063005
Madsen CB, Madsen LB, Viftrup SS, Johansson MP, Poulsen TB, Holmegaard L, Kumarappan V, Jorgensen KA, Stapelfeldt H (2009) Manipulating the torsion of molecules by strong laser pulses. Phys Rev Lett 102:073007
Holmegaard L, Hansen JL, Kalhøj L, Kragh SL, Stapelfeldt H, Filsinger F, Küpper J, Meijer G, Dimitrovski D, Martiny C, Madsen LB (2010) Photoelectron angular distributions from strong-field ionization of oriented molecules. Nat Phys 6:428
Bisgaard CZ, Clarkin OJ, Wu G, Lee AMD, Gessner O, Hayden CC, Stolow A (2009) Time-resolved molecular frame dynamics of fixed-in-space CS2 molecules. Science 323:1464
Bethlem HL, Berden G, Crompvoets FM, Jongma RT, van Roij AJA, Meijer G (2000) Electrostatic trapping of ammonia molecules. Nature 406:491
Clary DC (1998) Quantum theory of chemical reaction dynamics. Science 279:1879
Schnieder L, Seekamp-Rahn K, Borkowski J, Wrede E, Welge KH, Aoiz FJ, Bañares L, D’Mello MJ, Herrero VJ, Rábanos VS, Wyatt RE (1995) Experimental studies and theoretical predictions for the H + D2 → HD + D reaction. Science 269:207
Qui M, Ren Z, Che L, Dai D, Harich SA, Wang X, Yang X, Xu C, Xie D, Gustafsson M, Skodje RT, Sun Z, Zhang DH (2006) Observation of Feshbach resonances in the F + H2 → HF + H reaction. Science 311:1440
Dong W, Xiao C, Wang T, Dai D, Yang X, Zhang DH (2010) Transition-state spectroscopy of partial wave resonances in the F + HD. Science 327:1501
Dyke TR, Howard BJ, Klemperer W. Radiofrequency and microwave spectrum of the hydrogen fluoride dimer; a nonrigid molecule. J Chem Phys 56:2442
Howard BJ, Dyke TR, Klemperer W (1984) The molecular beam spectrum and the structure of the hydrogen fluoride dimer. J Chem Phys 81:5417
Fellers RS, Leforestier C, Braly LB, Brown MG, Saykally RJ (1999) Spectroscopic Determination of the Water Pair Potential. Science 284:945
Saykally RJ, Blake GA (1993) Molecular interactions and hydrogen bond tunneling dynamics: Some new perspectives. Science 259:1570
Miller WH (1974) Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants. J Chem Phys 61:1823–1834
Miller WH (1993) Beyond transition-state theory: a rigorous quantum theory of chemical reaction rates. Acc Chem Res 26(4):174
Thoss M, Miller WH, Stock G (2000) Semiclassical description of nonadiabatic quantum dynamics: Application to the S1 – S2 conical intersection in pyrazine. J Chem Phys 112:10282–10292
Acknowledgements
The authors thank the Alberta Ingenuity Fund (New Faculty Award) and the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant) for financial support. We thank the Canadian Foundation for Innovation (New Opportunities Fund) for support of the computational infrastructure on which this work was carried out. R.R.Z. acknowledges financial support of NSERC via a PGS-D2 scholarship.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Brown, A., Zaari, R.R. (2014). The Dynamics of Quantum Computing in Molecules. In: Gatti, F. (eds) Molecular Quantum Dynamics. Physical Chemistry in Action. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45290-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-45290-1_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45289-5
Online ISBN: 978-3-642-45290-1
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)