Advertisement

Toward prethreshold gate-based quantum simulation of chemical dynamics: using potential energy surfaces to simulate few-channel molecular collisions

  • Andrew T. Sornborger
  • Phillip Stancil
  • Michael R. Geller
Article
  • 107 Downloads

Abstract

One of the most promising applications of an error-corrected universal quantum computer is the efficient simulation of complex quantum systems such as large molecular systems. In this application, one is interested in both the electronic structure such as the ground state energy and dynamical properties such as the scattering cross section and chemical reaction rates. However, most theoretical work and experimental demonstrations have focused on the quantum computation of energies and energy surfaces. In this work, we attempt to make the prethreshold (not error-corrected) quantum simulation of dynamical properties practical as well. We show that the use of precomputed potential energy surfaces and couplings enables the gate-based simulation of few-channel but otherwise realistic molecular collisions. Our approach is based on the widely used Born–Oppenheimer approximation for the structure problem coupled with a semiclassical method for the dynamics. In the latter the electrons are treated quantum mechanically but the nuclei are classical, which restricts the collisions to high energy or temperature (typically above \(\approx 10\) eV). By using operator splitting techniques optimized for the resulting time-dependent Hamiltonian simulation problem, we give several physically realistic collision examples, with 3–8 channels and circuit depths < 1000.

Keywords

Quantum computation Quantum simulation Gate-based quantum simulation Molecular collisions Molecular dynamics 

Notes

Acknowledgements

This work was supported by the National Science Foundation under CDI Grant DMR-1029764.

References

  1. 1.
    Tseng, C.H., Somaroo, S., Sharf, Y., Knill, E., Laflamme, R., Havel, T.F., Cory, D.G.: Quantum simulation of a three-body-interaction Hamiltonian on an NMR quantum computer. Phys. Rev. A 61, 012302 (1999)ADSCrossRefGoogle Scholar
  2. 2.
    Somaroo, S., Tseng, C.H., Havel, T.F., Laflamme, R., Cory, D.G.: Quantum simulations on a quantum computer. Phys. Rev. Lett. 82, 5381–5383 (1999)ADSCrossRefGoogle Scholar
  3. 3.
    Khitrin, A.K., Fung, B.M.: NMR simulation of an eight-state quantum system. Phys. Rev. A 64, 032306 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    Negrevergne, C., Somma, R., Ortiz, G., Knill, E., Laflamme, R.: Liquid-state NMR simulations of quantum many-body problems. Phys. Rev. A 71, 032344 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    Peng, X.H., Du, J.F., Suter, D.: Quantum phase transition of ground-state entanglement in a Heisenberg spin chain simulated in an NMR quantum computer. Phys. Rev. A 71, 012307 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    Brown, K.R., Clark, R.J., Chuang, I.L.: Limitations of quantum simulation examined by a pairing Hamiltonian using nuclear magnetic resonance. Phys. Rev. Lett. 97, 050504 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    Peng, X.H., Zhang, J.F., Du, J.F., Suter, D.: Quantum simulation of a system with competing two- and three-body interactions. Phys. Rev. Lett. 103, 140501 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    Du, J.F., Xu, N.Y., Peng, X.H., Wang, P.F., Wu, S.F., Lu, D.W.: NMR implementation of a molecular hydrogen quantum simulation with adiabatic state preparation. Phys. Rev. Lett. 104, 030502 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    Edwards, E.E., Korenblit, S., Kim, K., Islam, R., Chang, M.-S., Freericks, J.K., Lin, G.-D., Duan, L.-M., Monroe, C.: Quantum simulation and phase diagram of the transverse field ising model with three atomic spins. Phys. Rev. B 82, 060412 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Kinoshita, T., Wenger, T., Weiss, D.S.: Observation of a one-dimensional Tonks–Girardeau gas. Science 305, 1125–1128 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    Friedenauer, A., Schmitz, H., Glueckert, J.T., Porras, D., Schaetz, T.: Simulating a quantum magnet with trapped ions. Nat. Phys. 4, 757–761 (2008)CrossRefGoogle Scholar
  12. 12.
    Gerritsma, R., Kirchmair, G., Zähringer, F., Solano, E., Blatt, R., Roos, C.F.: Quantum simulation of the Dirac equation. Nature 463, 68–71 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    Gerritsma, R., Lanyon, B.P., Kirchmair, G., Zähringer, F., Hempel, C., Casanova, J., García-Ripoll, J.J., Solano, E., Blatt, R., Roos, C.F.: Quantum simulation of the Klein paradox with trapped ions. Phys. Rev. Lett. 106, 060503 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    Lanyon, B.P., Hempel, C., Nigg, D., Müller, M., Gerritsma, R., Zähringer, F., Schindler, P., Barreiro, J.T., Rambach, M., Kirchmair, G., Hennrich, M., Zoller, P., Blatt, R., Roos, C.F.: Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    Lanyon, B.P., Whitfield, J.D., Gillett, G.G., Goggin, M.E., Almeida, M.P., Kassal, I., Biamonte, J.D., Mohseni, M., Powell, B.J., Barbieri, M., Aspuru-Guzik, A., White, A.G.: Towards quantum chemistry on a quantum computer. Nat. Chem. 2, 106–111 (2010)CrossRefGoogle Scholar
  16. 16.
    Shen, Y., Zhang, X., Zhang, S., Zhang, J.-N., Yung, M.-H., Kim, K.: Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure. Phys. Rev. A 95, 020501(R) (2017)ADSCrossRefGoogle Scholar
  17. 17.
    Ma, X.S., Dakic, B., Naylor, W., Zeilinger, A., Walther, P.: Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems. Nat. Phys. 7, 399–405 (2011)CrossRefGoogle Scholar
  18. 18.
    Kassal, I., Whitfield, J.D., Perdomo-Ortiz, A., Yung, M.-H., Aspuru-Guzik, A.: Simulating chemistry using quantum computers. Annu. Rev. Phys. Chem. 62, 185–207 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    Wang, Y., Dolde, F., Biamonte, J., Babbush, R., Bergholm, V., Yang, S., Jakobi, I., Neumann, P., Aspuru-Guzik, A., Whitfield, J.D., Wrachtrup, J.: Quantum simulation of helium hydride cation in a solid-state spin register. ACS Nano 9, 7769–7774 (2015)CrossRefGoogle Scholar
  20. 20.
    O’Malley, P.J.J., Babbush, R., Kivlichan, I.D., Romero, J., McLean, J.R., Barends, R., Kelly, J., Roushan, P., Tranter, A., Ding, N., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Fowler, A.G., Jeffrey, E., Lucero, E., Megrant, A., Mutus, J.Y., Neeley, M., Neill, C., Quintana, C., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Coveney, P.V., Love, P.J., Neven, H., Aspuru-Guzik, A., Martinis, J.M.: Scalable quantum simulation of molecular energies. Phys. Rev. X 6, 031007 (2016)Google Scholar
  21. 21.
    Kandala, A., Mezzacapo, A., Temme, K., Takita,M., Chow, J.M., Gambetta, J.M.: Hardware-efficient quantum optimizer for small molecules and quantum magnets. arXiv:1704.05018 (2017)
  22. 22.
    Colless, J.I., Ramasesh, V.V., Dahlen, D., Blok, M.S., McClean,J.R., Carter, J., de Jong, W.A., Siddiqi, I.: Robust determination of molecular spectra on a quantum processor. arXiv:1707.06408 (2017)
  23. 23.
    Berry, D.W., Ahokas, G., Cleve, R., Sanders, B.C.: Efficient quantum algorithms for simulating sparse hamiltonians. Commun. Math. Phys. 270, 359 (2007)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Childs, A.M., Wiebe, N.: Hamiltonian simulation using linear combinations of unitary operations. Quantum Inf. Comput. 12, 901–924 (2012)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Berry, D.W., Childs, A.M., Cleve, R., Kothari, R., Somma, R.D.: Simulating Hamiltonian dynamics with a truncated Taylor series. Phys. Rev. Lett. 114, 090502 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    Kivlichan, I.D., Wiebe, N., Babbush, R., Aspuru-Guzik, A.: Bounding the costs of quantum simulation of many-body physics in real space. arXiv:1608.05696 (2016)
  27. 27.
    Zalka, C.: Simulating quantum systems on a quantum computer. Proc. R. Soc. Lond. A 454, 313–322 (1998)ADSCrossRefzbMATHGoogle Scholar
  28. 28.
    Kassal, I., Jordan, S.P., Love, P.J., Mohseni, M., Aspuru-Guzik, A.: Polynomial-time quantum algorithms for the simulation of chemical dynamics. Proc. Natl. Acad. Sci. USA 105, 18681–18686 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    Sornborger, A.T.: Quantum simulation of tunneling in small systems. Sci. Rep. 2, 597 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    Feng, G.R., Lu, Y., Hao, L., Zhang, F.H., Long, G.L.: Experimental simulation of quantum tunneling in small systems. Sci. Rep. 3, 2232 (2013)CrossRefGoogle Scholar
  31. 31.
    Benenti, G., Strini, G.: Quantum simulation of the single-particle Schrödinger equation. Am. J. Phys. 76, 657–662 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    Aspuru-Guzik, A., Wasielewski, M.: NSF workshop report: quantum information and computation for chemistry. arXiv:1706.05413 (2017)
  33. 33.
    Geller, M.R., Martinis, J.M., Sornborger, A.T., Stancil, P.C., Pritchett, E.J., You, H., Galiautdinov, A.: Universal quantum simulation with prethreshold superconducting qubits: single-excitation subspace method. Phys. Rev. A 91, 062309 (2015)ADSCrossRefGoogle Scholar
  34. 34.
    Stancil, P.C., You, H., Cook, A., Sornborger, A.T., Geller, M.R.: Towards quantum simulation of chemical dynamics with prethreshold superconducting qubits. arXiv:1602.00063 (2016)
  35. 35.
    Cai, C.Y., Ai, Q., Quan, H.T., Sun, C.P.: Sensitive chemical compass assisted by quantum criticality. Phys. Rev. A 85, 022315 (2012)ADSCrossRefGoogle Scholar
  36. 36.
    Lambert, N., Chen, Y.-N., Cheng, Y.-C., Li, C.-M., Chen, G.-Y., Nori, F.: Quantum biology. Nat. Phys. 9, 10–18 (2013)CrossRefGoogle Scholar
  37. 37.
    Pearson, J., Feng, G.R., Zheng, C., Long, G.L.: Experimental quantum simulation of avian compass in a nuclear magnetic resonance system. Sci. China Phys. Mech. Astron. 59, 120312 (2016)CrossRefGoogle Scholar
  38. 38.
    Child, M.S.: Molecular Collision Theory. Academic Press, London (1984)Google Scholar
  39. 39.
    Minami, T., Pindzola, M.S., Lee, T.-G., Schultz, D.R.: Lattice, time-dependent Schrödinger equation approach for charge transfer in collisions of be\(^{4+}\) with atomic hydrogen. J. Phys. B At. Mol. Opt. Phys. 39, 2877 (2006)ADSCrossRefGoogle Scholar
  40. 40.
    Lin, C.Y., Stancil, P.C., Liebermann, H.-P., Funke, P., Buenker, R.J.: Inelastic processes in collisions of Na(3s,3p) with He at thermal energies. Phys. Rev. A 78, 052706 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    Stancil, P.C., Clarke, N.J., Zygelman, B., Cooper, D.L.: Ab initio study of charge transfer in low-energy Si\(^{3+}\) collisions with helium. J. Phys. B 32, 1523–1534 (1999)ADSCrossRefGoogle Scholar
  42. 42.
    Nolte, J.L., Wu, Y., Stancil, P.C., Liebermann, H.-P., Buenker, R.J., Schultz, D.R., Hui, Y., Draganić, I.N., Havener, C.C., Raković, M.J.: Final-state-resolved charge exchange between O\(^{7+}\) and H (in preparation) (2016)Google Scholar
  43. 43.
    Magnus, W.: On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math. 7, 649–673 (1954)MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Iserles, A., Marthinsen, A., Nørsett, S.P.: On the implementation of the method of Magnus series for linear differential equations. BIT Numer. Math. 39, 281–304 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Wiebe, N., Berry, D., Hoyer, P., Sanders, B.C.: Higher order decompositions of ordered operator exponentials. J. Phys. A. Math. Theor. 43, 065203 (2010)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Sornborger, A.T., Stewart, E.D.: Higher-order methods for simulations on quantum computers. Phys. Rev. A 60, 1956–1965 (1999)ADSCrossRefGoogle Scholar
  47. 47.
    Lloyd, S.: Almost any quantum logic gate is universal. Phys. Rev. Lett. 75, 346–349 (1995)ADSCrossRefGoogle Scholar
  48. 48.
    Barends, R., Shabani, A., Lamata, L., Kelly, J., Mezzacapo A., Las Heras, U., Babbush, R., Fowler, A.G., Campbell, B., Chen Y., Chen Z., Chiaro B., Dunsworth A., Jeffrey E., Lucero E., Megrant A., Mutus, J.Y., Neeley, M., Neill, C., O’Malley, P.J.J., Quintana, C., Roushan, P., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Solano, E., Neven, H., Martinis, J.M.: Digitized adiabatic quantum computing with a superconducting circuit. arXiv:1511.03316 (2015)
  49. 49.
    Suleimanov, YuV, Tscherbul, T.V., Krems, R.V.: Efficient method for quantum calculations of molecule-molecule scattering properties in a magnetic field. J. Chem. Phys. 137, 024103 (2008)ADSCrossRefGoogle Scholar
  50. 50.
    Yang, B., Zhang, P., Wang, X., Stancil, P.C., Bowman, J.M., Balakrishnan, N., Forrey, R.C.: Quantum dynamics of CO-H\(_2\) in full dimensionality. Nat. Commun. 6, 6629 (2015)ADSCrossRefGoogle Scholar
  51. 51.
    Welsch, R., Manthe, U.: Communication: Ro-vibrational control of chemical reactivity in H+CH\(_4 \rightarrow \) H\(_2\)+CH\(_3\): Full-dimensional quantum dynamics calculations and a sudden model. J. Chem. Phys. 141, 051102 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Information Sciences, CCS-3Los Alamos National LaboratoryLos AlamosUSA
  2. 2.Department of Physics and Astronomy and Center for Simulational PhysicsUniversity of GeorgiaAthensUSA

Personalised recommendations