Turbulent Mixing Simulation via a Quantum Algorithm
Abstract
Probability density function (PDF) methods have been very useful in describing many physical aspects of turbulent mixing. In applications of these methods, modeled PDF transport equations are commonly simulated via classical Monte Carlo techniques, which provide estimates of moments of the PDF at arbitrary accuracy. In this paper, recently developed techniques in quantum computing and quantum enhanced measurements (quantum metrology) are used to construct a quantum algorithm that accelerates the computation of such estimates. This quantum algorithm provides a quadratic speedup over classical Monte Carlo methods in terms of the number of repetitions needed to achieve the desired precision. This paper illustrates the power of this algorithm by considering a binary scalar mixing process modeled by means of the coalescence/dispersion (C/D) closure. The equation is first simulated using classical Monte Carlo methods, where error estimates for the computation of central moments are provided. Then the quantum algorithm for this problem is simulated by sampling from the same probability distribution as that of the output of a quantum computer, and it is shown that significantly fewer resources are required to achieve the same precision. Finally, the results demonstrate potential applications of future quantum computers for simulation of turbulent mixing, and largemore »
- Authors:
-
- Univ. of Strathclyde, Glasgow, Scotland (United Kingdom). Dept. of Physics. SUPA
- Univ. of Pittsburgh, PA (United States). Mechanical Engineering and Petroleum Engineering
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE; US Air Force Office of Scientific Research (AFOSR); Engineering and Physical Sciences Research Council (EPSRC)
- OSTI Identifier:
- 1458951
- Report Number(s):
- LA-UR-16-25360
Journal ID: ISSN 0001-1452
- Grant/Contract Number:
- AC52-06NA25396; FA9550-12-1-0057; EP/K000586/1
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- AIAA Journal
- Additional Journal Information:
- Journal Volume: 56; Journal Issue: 2; Journal ID: ISSN 0001-1452
- Publisher:
- AIAA
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computer Science; Information Science; Quantum algorithms, turbulent mixing
Citation Formats
Xu, Guanglei, Daley, Andrew J., Givi, Peyman, and Somma, Rolando D. Turbulent Mixing Simulation via a Quantum Algorithm. United States: N. p., 2017.
Web. doi:10.2514/1.J055896.
Xu, Guanglei, Daley, Andrew J., Givi, Peyman, & Somma, Rolando D. Turbulent Mixing Simulation via a Quantum Algorithm. United States. https://doi.org/10.2514/1.J055896
Xu, Guanglei, Daley, Andrew J., Givi, Peyman, and Somma, Rolando D. 2017.
"Turbulent Mixing Simulation via a Quantum Algorithm". United States. https://doi.org/10.2514/1.J055896. https://www.osti.gov/servlets/purl/1458951.
@article{osti_1458951,
title = {Turbulent Mixing Simulation via a Quantum Algorithm},
author = {Xu, Guanglei and Daley, Andrew J. and Givi, Peyman and Somma, Rolando D.},
abstractNote = {Probability density function (PDF) methods have been very useful in describing many physical aspects of turbulent mixing. In applications of these methods, modeled PDF transport equations are commonly simulated via classical Monte Carlo techniques, which provide estimates of moments of the PDF at arbitrary accuracy. In this paper, recently developed techniques in quantum computing and quantum enhanced measurements (quantum metrology) are used to construct a quantum algorithm that accelerates the computation of such estimates. This quantum algorithm provides a quadratic speedup over classical Monte Carlo methods in terms of the number of repetitions needed to achieve the desired precision. This paper illustrates the power of this algorithm by considering a binary scalar mixing process modeled by means of the coalescence/dispersion (C/D) closure. The equation is first simulated using classical Monte Carlo methods, where error estimates for the computation of central moments are provided. Then the quantum algorithm for this problem is simulated by sampling from the same probability distribution as that of the output of a quantum computer, and it is shown that significantly fewer resources are required to achieve the same precision. Finally, the results demonstrate potential applications of future quantum computers for simulation of turbulent mixing, and large classes of related problems.},
doi = {10.2514/1.J055896},
url = {https://www.osti.gov/biblio/1458951},
journal = {AIAA Journal},
issn = {0001-1452},
number = 2,
volume = 56,
place = {United States},
year = {Thu Nov 09 00:00:00 EST 2017},
month = {Thu Nov 09 00:00:00 EST 2017}
}
Web of Science
Works referenced in this record:
Superconducting quantum bits
journal, June 2008
- Clarke, John; Wilhelm, Frank K.
- Nature, Vol. 453, Issue 7198
Probability distribution of a stochastically advected scalar field
journal, December 1989
- Chen, Hudong; Chen, Shiyi; Kraichnan, Robert H.
- Physical Review Letters, Vol. 63, Issue 24
The modeling of turbulent reactive flows based on multiple mapping conditioning
journal, July 2003
- Klimenko, A. Y.; Pope, S. B.
- Physics of Fluids, Vol. 15, Issue 7
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
journal, November 2004
- Giovannetti, V.
- Science, Vol. 306, Issue 5700
A model for turbulent mixing based on shadow-position conditioning
journal, November 2013
- Pope, Stephen B.
- Physics of Fluids, Vol. 25, Issue 11
Mass transfer in dilute turbulent and non-turbulent systems with rapid irreversible reactions and equal diffusivities
journal, March 1962
- Toor, H. L.
- AIChE Journal, Vol. 8, Issue 1
Probability Inequalities for Sums of Bounded Random Variables
journal, March 1963
- Hoeffding, Wassily
- Journal of the American Statistical Association, Vol. 58, Issue 301
Closure of the Transport Equation for the Probability Density Funcfion of Turbulent Scalar Fields
journal, January 1979
- Janicka, J.; Kolbe, W.; Kollmann, W.
- Journal of Non-Equilibrium Thermodynamics, Vol. 4, Issue 1
Simulating Hamiltonian Dynamics with a Truncated Taylor Series
journal, March 2015
- Berry, Dominic W.; Childs, Andrew M.; Cleve, Richard
- Physical Review Letters, Vol. 114, Issue 9
Progress in probability density function methods for turbulent reacting flows
journal, April 2010
- Haworth, D. C.
- Progress in Energy and Combustion Science, Vol. 36, Issue 2
Quantum algorithms: an overview
journal, January 2016
- Montanaro, Ashley
- npj Quantum Information, Vol. 2, Issue 1
Quantum Simulations of Classical Annealing Processes
journal, September 2008
- Somma, R. D.; Boixo, S.; Barnum, H.
- Physical Review Letters, Vol. 101, Issue 13
Quantum Spintronics: Engineering and Manipulating Atom-Like Spins in Semiconductors
journal, March 2013
- Awschalom, D. D.; Bassett, L. C.; Dzurak, A. S.
- Science, Vol. 339, Issue 6124
Semiclassical Fourier Transform for Quantum Computation
journal, April 1996
- Griffiths, Robert B.; Niu, Chi-Sheng
- Physical Review Letters, Vol. 76, Issue 17
State preservation by repetitive error detection in a superconducting quantum circuit
journal, March 2015
- Kelly, J.; Barends, R.; Fowler, A. G.
- Nature, Vol. 519, Issue 7541
A mixing model for turbulent reactive flows based on Euclidean minimum spanning trees
journal, December 1998
- Subramaniam, S.
- Combustion and Flame, Vol. 115, Issue 4
Non-Gaussian scalar statistics in homogeneous turbulence
journal, April 1996
- Jaberi, F. A.; Miller, R. S.; Madnia, C. K.
- Journal of Fluid Mechanics, Vol. 313
Small scales, many species and the manifold challenges of turbulent combustion
journal, January 2013
- Pope, Stephen B.
- Proceedings of the Combustion Institute, Vol. 34, Issue 1
Model-free simulations of turbulent reactive flows
journal, January 1989
- Givi, Peyman
- Progress in Energy and Combustion Science, Vol. 15, Issue 1
Quantum Metrology
journal, January 2006
- Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo
- Physical Review Letters, Vol. 96, Issue 1
PDF methods for turbulent reactive flows
journal, January 1985
- Pope, S. B.
- Progress in Energy and Combustion Science, Vol. 11, Issue 2
Optimal quantum measurements of expectation values of observables
journal, January 2007
- Knill, Emanuel; Ortiz, Gerardo; Somma, Rolando D.
- Physical Review A, Vol. 75, Issue 1
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
journal, June 2016
- Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp
- Nature, Vol. 534, Issue 7608
Modeling of turbulent molecular mixing
journal, October 1987
- Kosály, George; Givi, Peyman
- Combustion and Flame, Vol. 70, Issue 1
Dispersed phase mixing: I. Theory and effects in simple reactors
journal, March 1963
- Curl, R. L.
- AIChE Journal, Vol. 9, Issue 2
Quantum amplitude amplification and estimation
book, January 2002
- Brassard, Gilles; Høyer, Peter; Mosca, Michele
- Quantum Computation and Information
The pdf approach to turbulent flow
journal, January 1990
- Kollmann, W.
- Theoretical and Computational Fluid Dynamics, Vol. 1, Issue 5
Turbulent combustion modelling
journal, January 1988
- Borghi, R.
- Progress in Energy and Combustion Science, Vol. 14, Issue 4
An Improved Turbulent Mixing Model
journal, June 1982
- Pope, S. B.
- Combustion Science and Technology, Vol. 28, Issue 3-4
Mapping closures for turbulent mixing and reaction
journal, August 1991
- Pope, S. B.
- Theoretical and Computational Fluid Dynamics, Vol. 2, Issue 5-6
Monte Carlo solutions of a joint PDF equation for turbulent flows in general orthogonal coordinates
journal, October 1987
- Haworth, D. C.; Pope, S. B.
- Journal of Computational Physics, Vol. 72, Issue 2
Filtered Density Function for Subgrid Scale Modeling of Turbulent Combustion
journal, January 2006
- Givi, Peyman
- AIAA Journal, Vol. 44, Issue 1
Realization of a scalable Shor algorithm
journal, March 2016
- Monz, T.; Nigg, D.; Martinez, E. A.
- Science, Vol. 351, Issue 6277
Optimal frequency measurements with maximally correlated states
journal, December 1996
- Bollinger, J. J. .; Itano, Wayne M.; Wineland, D. J.
- Physical Review A, Vol. 54, Issue 6
Quantum algorithms revisited
journal, January 1998
- Cleve, R.; Ekert, A.; Macchiavello, C.
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1969
Preparing Ground States of Quantum Many-Body Systems on a Quantum Computer
journal, April 2009
- Poulin, David; Wocjan, Pawel
- Physical Review Letters, Vol. 102, Issue 13
The probability approach to the modelling of turbulent reacting flows
journal, August 1976
- Pope, S. B.
- Combustion and Flame, Vol. 27
Demonstration of a small programmable quantum computer with atomic qubits
journal, August 2016
- Debnath, S.; Linke, N. M.; Figgatt, C.
- Nature, Vol. 536, Issue 7614
Johnson-Edgeworth Translation for Probability Modeling of Binary Scalar Mixing in Turbulent Flows
journal, May 1993
- Miller, R. S.; Frankel, S. H.; Madnia, C. K.
- Combustion Science and Technology, Vol. 91, Issue 1-3
A binomial Langevin model for turbulent mixing
journal, December 1991
- Valiño, L.; Dopazo, C.
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 12
Superconducting Circuits for Quantum Information: An Outlook
journal, March 2013
- Devoret, M. H.; Schoelkopf, R. J.
- Science, Vol. 339, Issue 6124
Entangled states of trapped atomic ions
journal, June 2008
- Blatt, Rainer; Wineland, David
- Nature, Vol. 453, Issue 7198
Turbulent Flows
journal, October 2001
- Pope, Stephen B.
- Measurement Science and Technology, Vol. 12, Issue 11
Quantum Simulations of Classical Annealing Processes
text, January 2008
- Somma, R. D.; Boixo, S.; Barnum, H.
- arXiv
Preparing ground states of quantum many-body systems on a quantum computer
text, January 2008
- Poulin, David; Wocjan, Pawel
- arXiv
State preservation by repetitive error detection in a superconducting quantum circuit
text, January 2014
- Kelly, J.; Barends, R.; Fowler, A. G.
- arXiv
Simulating Hamiltonian dynamics with a truncated Taylor series
text, January 2014
- Berry, Dominic W.; Childs, Andrew M.; Cleve, Richard
- arXiv
Realization of a scalable Shor algorithm
text, January 2015
- Monz, Thomas; Nigg, Daniel; Martinez, Esteban A.
- arXiv
Demonstration of a small programmable quantum computer with atomic qubits
text, January 2016
- Debnath, S.; Linke, N. M.; Figgatt, C.
- arXiv
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
text, January 2016
- Martinez, E. A.; Muschik, C. A.; Schindler, P.
- arXiv
Quantum Amplitude Amplification and Estimation
text, January 2000
- Brassard, Gilles; Hoyer, Peter; Mosca, Michele
- arXiv
Quantum-enhanced measurements: beating the standard quantum limit
text, January 2004
- Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo
- arXiv
Optimal Quantum Measurements of Expectation Values of Observables
text, January 2006
- Knill, Emanuel; Ortiz, Gerardo; Somma, Rolando D.
- arXiv
Semiclassical Fourier Transform for Quantum Computation
text, January 1995
- Griffiths, Robert B.; Niu, Chi-Sheng
- arXiv
Quantum Algorithms Revisited
text, January 1997
- Cleve, Richard; Ekert, Artur; Macchiavello, Chiara
- arXiv
Works referencing / citing this record:
Quantum algorithm for the computation of the reactant conversion rate in homogeneous turbulence
journal, June 2019
- Xu, Guanglei; Daley, Andrew J.; Givi, Peyman
- Combustion Theory and Modelling, Vol. 23, Issue 6