skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 » classes of related problems.« less

Authors:
 [1];  [1];  [2];  [3]
  1. Univ. of Strathclyde, Glasgow, Scotland (United Kingdom). Dept. of Physics. SUPA
  2. Univ. of Pittsburgh, PA (United States). Mechanical Engineering and Petroleum Engineering
  3. 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Superconducting quantum bits
journal, June 2008


Probability distribution of a stochastically advected scalar field
journal, December 1989


The modeling of turbulent reactive flows based on multiple mapping conditioning
journal, July 2003


Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
journal, November 2004


A model for turbulent mixing based on shadow-position conditioning
journal, November 2013


Probability Inequalities for Sums of Bounded Random Variables
journal, March 1963


Closure of the Transport Equation for the Probability Density Funcfion of Turbulent Scalar Fields
journal, January 1979


Simulating Hamiltonian Dynamics with a Truncated Taylor Series
journal, March 2015


Progress in probability density function methods for turbulent reacting flows
journal, April 2010


Quantum algorithms: an overview
journal, January 2016


Quantum Simulations of Classical Annealing Processes
journal, September 2008


Quantum Spintronics: Engineering and Manipulating Atom-Like Spins in Semiconductors
journal, March 2013


Turbulent Flows
book, July 2012


Semiclassical Fourier Transform for Quantum Computation
journal, April 1996


State preservation by repetitive error detection in a superconducting quantum circuit
journal, March 2015


Non-Gaussian scalar statistics in homogeneous turbulence
journal, April 1996


Small scales, many species and the manifold challenges of turbulent combustion
journal, January 2013


Model-free simulations of turbulent reactive flows
journal, January 1989


Quantum Metrology
journal, January 2006


PDF methods for turbulent reactive flows
journal, January 1985


Optimal quantum measurements of expectation values of observables
journal, January 2007


Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
journal, June 2016


Modeling of turbulent molecular mixing
journal, October 1987


Quantum amplitude amplification and estimation
book, January 2002


The pdf approach to turbulent flow
journal, January 1990


Turbulent combustion modelling
journal, January 1988


An Improved Turbulent Mixing Model
journal, June 1982


Mapping closures for turbulent mixing and reaction
journal, August 1991


Monte Carlo solutions of a joint PDF equation for turbulent flows in general orthogonal coordinates
journal, October 1987


Realization of a scalable Shor algorithm
journal, March 2016


Optimal frequency measurements with maximally correlated states
journal, December 1996


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
  • https://doi.org/10.1098/rspa.1998.0164

Preparing Ground States of Quantum Many-Body Systems on a Quantum Computer
journal, April 2009


Demonstration of a small programmable quantum computer with atomic qubits
journal, August 2016


Johnson-Edgeworth Translation for Probability Modeling of Binary Scalar Mixing in Turbulent Flows
journal, May 1993


A binomial Langevin model for turbulent mixing
journal, December 1991


Superconducting Circuits for Quantum Information: An Outlook
journal, March 2013


Entangled states of trapped atomic ions
journal, June 2008


Turbulent Flows
journal, October 2001


Quantum Simulations of Classical Annealing Processes
text, January 2008


Simulating Hamiltonian dynamics with a truncated Taylor series
text, January 2014


Realization of a scalable Shor algorithm
text, January 2015


Quantum Amplitude Amplification and Estimation
text, January 2000


Quantum-enhanced measurements: beating the standard quantum limit
text, January 2004


Quantum metrology
text, January 2005


Optimal Quantum Measurements of Expectation Values of Observables
text, January 2006


Quantum Algorithms Revisited
text, January 1997


Works referencing / citing this record:

Quantum algorithm for the computation of the reactant conversion rate in homogeneous turbulence
journal, June 2019