### 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 work, 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. The results demonstrate potential applications of future quantum computers for simulation of turbulent mixing, and large classes of related problems.

Language | English |
---|---|

Pages | 687-699 |

Number of pages | 13 |

Journal | AIAA Journal |

Volume | 56 |

Issue number | 2 |

Early online date | 9 Nov 2017 |

DOIs | |

Publication status | Published - 28 Feb 2018 |

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### Keywords

- probability density function
- Monte Carlo
- quantum algorithm

### Cite this

*AIAA Journal*,

*56*(2), 687-699. https://doi.org/10.2514/1.J055896

}

*AIAA Journal*, vol. 56, no. 2, pp. 687-699. https://doi.org/10.2514/1.J055896

**Turbulent mixing simulation via a quantum algorithm.** / Xu, Guanglei; Daley, Andrew J.; Givi, Peyman; Somma, Rolando D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Turbulent mixing simulation via a quantum algorithm

AU - Xu, Guanglei

AU - Daley, Andrew J.

AU - Givi, Peyman

AU - Somma, Rolando D.

PY - 2018/2/28

Y1 - 2018/2/28

N2 - 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 work, 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. The results demonstrate potential applications of future quantum computers for simulation of turbulent mixing, and large classes of related problems.

AB - 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 work, 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. The results demonstrate potential applications of future quantum computers for simulation of turbulent mixing, and large classes of related problems.

KW - probability density function

KW - Monte Carlo

KW - quantum algorithm

UR - http://www.scopus.com/inward/record.url?scp=85041431583&partnerID=8YFLogxK

U2 - 10.2514/1.J055896

DO - 10.2514/1.J055896

M3 - Article

VL - 56

SP - 687

EP - 699

JO - AIAA Journal

T2 - AIAA Journal

JF - AIAA Journal

SN - 0001-1452

IS - 2

ER -