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

Sornborger, Andrew Tyler; Stancil, Phillip; Geller, Michael R.

doi:10.1007/s11128-018-1878-x

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

Journal Article · Thu Mar 22 00:00:00 EDT 2018 · Quantum Information Processing

DOI:https://doi.org/10.1007/s11128-018-1878-x· OSTI ID:1435540

^[1]; Stancil, Phillip ^[2]; Geller, Michael R. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Georgia, Athens, GA (United States)

Here, 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 ≈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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1435540

Report Number(s):: LA-UR-18-21819

Journal Information:: Quantum Information Processing, Vol. 17, Issue 5; ISSN 1570-0755

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 2 works

Citation information provided by
Web of Science

References (58)

Sensitive chemical compass assisted by quantum criticality Cai, C. Y.; Ai, Qing; Quan, H. T. Physical Review A, Vol. 85, Issue 2 https://doi.org/10.1103/PhysRevA.85.022315	journal	February 2012
Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian Using Nuclear Magnetic Resonance Brown, Kenneth R.; Clark, Robert J.; Chuang, Isaac L. Physical Review Letters, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevLett.97.050504	journal	August 2006
Efficient method for quantum calculations of molecule-molecule scattering properties in a magnetic field Suleimanov, Yu. V.; Tscherbul, T. V.; Krems, R. V. The Journal of Chemical Physics, Vol. 137, Issue 2 https://doi.org/10.1063/1.4733288	journal	July 2012
Quantum Simulation of Tunneling in Small Systems Sornborger, Andrew T. Scientific Reports, Vol. 2, Issue 1 https://doi.org/10.1038/srep00597	journal	August 2012
Quantum Simulation of the Klein Paradox with Trapped Ions Gerritsma, R.; Lanyon, B. P.; Kirchmair, G. Physical Review Letters, Vol. 106, Issue 6 https://doi.org/10.1103/PhysRevLett.106.060503	journal	February 2011
On the exponential solution of differential equations for a linear operator Magnus, Wilhelm Communications on Pure and Applied Mathematics, Vol. 7, Issue 4 https://doi.org/10.1002/cpa.3160070404	journal	November 1954
Higher-order methods for simulations on quantum computers Sornborger, A. T.; Stewart, E. D. Physical Review A, Vol. 60, Issue 3 https://doi.org/10.1103/PhysRevA.60.1956	journal	September 1999
Ab initio study of charge transfer in low-energy collisions with helium Stancil, P. C.; Clarke, N. J.; Zygelman, B. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 32, Issue 6 https://doi.org/10.1088/0953-4075/32/6/015	journal	January 1999
Efficient Quantum Algorithms for Simulating Sparse Hamiltonians Berry, Dominic W.; Ahokas, Graeme; Cleve, Richard Communications in Mathematical Physics, Vol. 270, Issue 2 https://doi.org/10.1007/s00220-006-0150-x	journal	December 2006
Simulating a quantum magnet with trapped ions Friedenauer, A.; Schmitz, H.; Glueckert, J. T. Nature Physics, Vol. 4, Issue 10 https://doi.org/10.1038/nphys1032	journal	July 2008
Higher order decompositions of ordered operator exponentials Wiebe, Nathan; Berry, Dominic; Høyer, Peter Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue 6 https://doi.org/10.1088/1751-8113/43/6/065203	journal	January 2010
Inelastic processes in collisions of $Na (3 s, 3 p)$ with He at thermal energies Lin, C. Y.; Stancil, P. C.; Liebermann, H. -P. Physical Review A, Vol. 78, Issue 5 https://doi.org/10.1103/PhysRevA.78.052706	journal	November 2008
Communication: Ro-vibrational control of chemical reactivity in H+CH ₄ → H ₂ +CH ₃ : Full-dimensional quantum dynamics calculations and a sudden model Welsch, Ralph; Manthe, Uwe The Journal of Chemical Physics, Vol. 141, Issue 5 https://doi.org/10.1063/1.4891917	journal	August 2014
Quantum phase transition of ground-state entanglement in a Heisenberg spin chain simulated in an NMR quantum computer Peng, Xinhua; Du, Jiangfeng; Suter, Dieter Physical Review A, Vol. 71, Issue 1 https://doi.org/10.1103/PhysRevA.71.012307	journal	January 2005
Quantum simulation of the Dirac equation Gerritsma, R.; Kirchmair, G.; Zähringer, F. Nature, Vol. 463, Issue 7277 https://doi.org/10.1038/nature08688	journal	January 2010
Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register Wang, Ya; Dolde, Florian; Biamonte, Jacob ACS Nano, Vol. 9, Issue 8 https://doi.org/10.1021/acsnano.5b01651	journal	April 2015
Polynomial-time quantum algorithm for the simulation of chemical dynamics Kassal, I.; Jordan, S. P.; Love, P. J. Proceedings of the National Academy of Sciences, Vol. 105, Issue 48 https://doi.org/10.1073/pnas.0808245105	journal	November 2008
On the Implementation of the Method of Magnus Series for Linear Differential Equations Iserles, A.; Marthinsen, A.; Nørsett, S. P. Bit Numerical Mathematics, Vol. 39, Issue 2, p. 281-304 https://doi.org/10.1023/A:1022393913721	journal	June 1999
NMR simulation of an eight-state quantum system Khitrin, A. K.; Fung, B. M. Physical Review A, Vol. 64, Issue 3 https://doi.org/10.1103/PhysRevA.64.032306	journal	August 2001
Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure Shen, Yangchao; Zhang, Xiang; Zhang, Shuaining Physical Review A, Vol. 95, Issue 2 https://doi.org/10.1103/PhysRevA.95.020501	journal	February 2017
Simulating Hamiltonian Dynamics with a Truncated Taylor Series Berry, Dominic W.; Childs, Andrew M.; Cleve, Richard Physical Review Letters, Vol. 114, Issue 9 https://doi.org/10.1103/PhysRevLett.114.090502	journal	March 2015
Liquid-state NMR simulations of quantum many-body problems Negrevergne, C.; Somma, R.; Ortiz, G. Physical Review A, Vol. 71, Issue 3 https://doi.org/10.1103/PhysRevA.71.032344	journal	March 2005
Lattice, time-dependent Schrödinger equation approach for charge transfer in collisions of Be ⁴⁺ with atomic hydrogen Minami, T.; Pindzola, M. S.; Lee, T-G Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 39, Issue 12 https://doi.org/10.1088/0953-4075/39/12/020	journal	June 2006
Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems Ma, Xiao-song; Dakic, Borivoje; Naylor, William Nature Physics, Vol. 7, Issue 5 https://doi.org/10.1038/nphys1919	journal	February 2011
Almost Any Quantum Logic Gate is Universal Lloyd, Seth Physical Review Letters, Vol. 75, Issue 2 https://doi.org/10.1103/PhysRevLett.75.346	journal	July 1995
Simulating quantum systems on a quantum computer Zalka, Christof Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1969 https://doi.org/10.1098/rspa.1998.0162	journal	January 1998
Simulating Chemistry Using Quantum Computers Kassal, Ivan; Whitfield, James D.; Perdomo-Ortiz, Alejandro Annual Review of Physical Chemistry, Vol. 62, Issue 1 https://doi.org/10.1146/annurev-physchem-032210-103512	journal	May 2011
Quantum simulation and phase diagram of the transverse-field Ising model with three atomic spins Edwards, E. E.; Korenblit, S.; Kim, K. Physical Review B, Vol. 82, Issue 6 https://doi.org/10.1103/PhysRevB.82.060412	journal	August 2010
Quantum dynamics of CO–H2 in full dimensionality Yang, Benhui; Zhang, P.; Wang, X. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms7629	journal	March 2015
NMR Implementation of a Molecular Hydrogen Quantum Simulation with Adiabatic State Preparation Du, Jiangfeng; Xu, Nanyang; Peng, Xinhua Physical Review Letters, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevLett.104.030502	journal	January 2010
Observation of a One-Dimensional Tonks-Girardeau Gas Kinoshita, T. Science, Vol. 305, Issue 5687 https://doi.org/10.1126/science.1100700	journal	August 2004
Towards quantum chemistry on a quantum computer Lanyon, B. P.; Whitfield, J. D.; Gillett, G. G. Nature Chemistry, Vol. 2, Issue 2 https://doi.org/10.1038/nchem.483	journal	January 2010
Quantum simulation of the single-particle Schrödinger equation Benenti, Giuliano; Strini, Giuliano American Journal of Physics, Vol. 76, Issue 7 https://doi.org/10.1119/1.2894532	journal	July 2008
Quantum Simulations on a Quantum Computer Somaroo, S.; Tseng, C. H.; Havel, T. F. Physical Review Letters, Vol. 82, Issue 26 https://doi.org/10.1103/PhysRevLett.82.5381	journal	June 1999
Experimental quantum simulation of Avian Compass in a nuclear magnetic resonance system Pearson, Jason; Feng, GuanRu; Zheng, Chao Science China Physics, Mechanics & Astronomy, Vol. 59, Issue 12 https://doi.org/10.1007/s11433-016-0376-6	journal	October 2016
Experimental simulation of quantum tunneling in small systems Feng, Guan-Ru; Lu, Yao; Hao, Liang Scientific Reports, Vol. 3, Issue 1 https://doi.org/10.1038/srep02232	journal	August 2013
Universal quantum simulation with prethreshold superconducting qubits: Single-excitation subspace method Geller, Michael R.; Martinis, John M.; Sornborger, Andrew T. Physical Review A, Vol. 91, Issue 6 https://doi.org/10.1103/PhysRevA.91.062309	journal	June 2015
Quantum biology Lambert, Neill; Chen, Yueh-Nan; Cheng, Yuan-Chung Nature Physics, Vol. 9, Issue 1 https://doi.org/10.1038/nphys2474	journal	December 2012
Universal Digital Quantum Simulation with Trapped Ions Lanyon, B. P.; Hempel, C.; Nigg, D. Science, Vol. 334, Issue 6052 https://doi.org/10.1126/science.1208001	journal	September 2011
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan Nature, Vol. 549, Issue 7671 https://doi.org/10.1038/nature23879	journal	September 2017
Bounding the costs of quantum simulation of many-body physics in real space Kivlichan, Ian D.; Wiebe, Nathan; Babbush, Ryan Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 30 https://doi.org/10.1088/1751-8121/aa77b8	journal	June 2017
Digitized adiabatic quantum computing with a superconducting circuit Barends, R.; Shabani, A.; Lamata, L. Nature, Vol. 534, Issue 7606 https://doi.org/10.1038/nature17658	journal	June 2016
Quantum phase transition of ground-state entanglement in a Heisenberg spin chain simulated in an NMR quantum computer Suter, Dieter; Peng, Xinhua; Du, Jiangfeng The American Physical Society https://doi.org/10.17877/de290r-10122	text	January 2005
Quantum simulation of the single-particle Schrodinger equation Benenti, Giuliano; Strini, Giuliano arXiv https://doi.org/10.48550/arxiv.0709.1704	text	January 2007
Polynomial-time quantum algorithm for the simulation of chemical dynamics Kassal, Ivan; Jordan, Stephen P.; Love, Peter J. arXiv https://doi.org/10.48550/arxiv.0801.2986	text	January 2008
Quantum simulation of the Dirac equation Gerritsma, R.; Kirchmair, G.; Zähringer, F. arXiv https://doi.org/10.48550/arxiv.0909.0674	text	January 2009
Quantum simulation of the Klein paradox with trapped ions Gerritsma, R.; Lanyon, B.; Kirchmair, G. arXiv https://doi.org/10.48550/arxiv.1007.3683	text	January 2010
Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems Ma, Xiao-song; Dakic, Borivoje; Naylor, William arXiv https://doi.org/10.48550/arxiv.1008.4116	text	January 2010
Sensitive Chemical Compass Assisted by Quantum Criticality Cai, C. Y.; Ai, Qing; Quan, H. T. arXiv https://doi.org/10.48550/arxiv.1105.1511	text	January 2011
Quantum Simulation of Tunneling in Small Systems Sornborger, Andrew T. arXiv https://doi.org/10.48550/arxiv.1202.1536	text	January 2012
Quantum Simulation of Helium Hydride in a Solid-State Spin Register Wang, Ya; Dolde, Florian; Biamonte, Jacob arXiv https://doi.org/10.48550/arxiv.1405.2696	text	January 2014
Simulating Hamiltonian dynamics with a truncated Taylor series Berry, Dominic W.; Childs, Andrew M.; Cleve, Richard arXiv https://doi.org/10.48550/arxiv.1412.4687	text	January 2014
Quantum dynamics of CO-H$_2$ in full dimensionality Yang, Benhui; Zhang, P.; Wang, X. arXiv https://doi.org/10.48550/arxiv.1502.02645	text	January 2015
Bounding the costs of quantum simulation of many-body physics in real space Kivlichan, Ian D.; Wiebe, Nathan; Babbush, Ryan arXiv https://doi.org/10.48550/arxiv.1608.05696	text	January 2016
NMR Simulation of an Eight-State Quantum System Khitrin, A. K.; Fung, B. M. arXiv https://doi.org/10.48550/arxiv.quant-ph/0101029	text	January 2001
Efficient quantum algorithms for simulating sparse Hamiltonians Berry, Dominic W.; Ahokas, Graeme; Cleve, Richard arXiv https://doi.org/10.48550/arxiv.quant-ph/0508139	text	January 2005
Quantum Simulations on a Quantum Computer Somaroo, S. S.; Tseng, C. H.; Havel, T. F. arXiv https://doi.org/10.48550/arxiv.quant-ph/9905045	text	January 1999
Quantum simulation of a three-body interaction Hamiltonian on an NMR quantum computer Tseng, C. H.; Somaroo, S.; Sharf, Y. arXiv https://doi.org/10.48550/arxiv.quant-ph/9908012	text	January 1999

Cited By (1)

Protobiotic Systems Chemistry Analyzed by Molecular Dynamics Kahana, Amit; Lancet, Doron Life, Vol. 9, Issue 2 https://doi.org/10.3390/life9020038	journal	May 2019