Riv. Mat. Univ. Parma, Vol. 15, No. 1, 2024

Sauro Succi[a]

Kinetic Theory, Ensemble Simulations and Quantum Computing

Pages: 79-90
Received: 3 March 2023
Accepted: 25 January 2024
Mathematics Subject Classification: 68Q12, 82C40, 76205.
Keywords: Quantum computing, kinetic theory, fluid dynamics.
Authors address:
[a]: Fondazione Istituto Italiano di Tecnologia, Center for Life Nano-Neuroscience at la Sapienza, Viale Regina Elena 291, 00161 Roma, Italy

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Abstract: We discuss a functional kinetic theory approach to perform ensemble simulations on quantum computers. It is argued that the approach requires several hundreds of logical noiseless qubits, hence commanding major technological breakthroughs in noise correction and mitigation practices.

References
[1]
A. P. Bhati, S. Wan, D. Alfè, A. R. Clyde, M. Bode, L. Tan, M. Titov, A. Merzky, et al, Pandemic drugs at pandemic speed: infrastructure for accelerating COVID-19 drug discovery with hybrid machine learning- and physics-based simulations on high-performance computers, Interface focus 11 (2021), no. 6, 20210018. DOI
[2]
L. Budinski, Quantum algorithm for the Navier–Stokes equations by using the streamfunction–vorticity formulation and the lattice Boltzmann method Variational quantum algorithms for nonlinear problems, International Journal of Quantum Information 20 2022, no. 2 , 2150039. DOI
[3]
S. Das Sarma, Quantum computing has a hype problem, MIT Technology Review, March 28, 2022, https://www.technologyreview.com/2022/03/28/1048355/quantum-computing-has-a-hype-problem/.
[4]
J. P. Liu, H. O. Kolden, H. K. Krovi, et al, Efficient quantum algorithm for dissipative nonlinear differential equations, PNAS, 118 (2021), no. 35, e2026805118. DOI
[5]
F. Gaitan, Finding flows of a Navier-Stokes fluid through quantum computing, Npj Quantum Information 6 (2020), 61. DOI
[6]
D. Giannakis, A. Ourmazd, P. Pfeffer, J. Schumacher and J. Slawinska, Embedding classical dynamics in a quantum computer, Phys. Rev. A 105 (2022), no. 5, 052404. DOI
[7]
W. Itani and S. Succi, Analysis of Carleman Linearization of Lattice Boltzmann, Fluids 7 (2022), no.1, 24. DOI
[8]
A.W. Harrow, A. Hassidim and S. Lloyd, Quantum algorithm for linear systems of equations, Phys. Rev. Lett. 103 (2009), no. 15, 150502. DOI
[9]
M. Lubasch, J. Joo, P. Moinier, M. Kiffner and D. Jaksch, Variational quantum algorithms for nonlinear problems, Physical Review A 101 (2021), no. 1, 010301(R). DOI
[10]
A. Mezzacapo, M. Sanz, L. Lamata, I. L. Egusquiza, S. Succi and E. Solano, Quantum simulator for transport phenomena in fluid flows, Scientific reports 5 (2015), no. 1, 13153. DOI
[11]
A. Navarra, J. Tribbia and S. Klus, Estimation of Koopman Transfer Operators for the Equatorial Pacific SST, The Journal of Atmospheric Sciences 78 (2021), no. 4, 1227-1244. DOI
[12]
R. Steijl, Quantum algorithms for fluid simulations, in: F. Bulnes, V. N. Stavrou, O. Morozov and A. V. Bourdine, eds., "Advances in Quantum Communication and Information", IntechOpen, 2020. DOI
[13]
S. Succi, The Lattice Boltzmann Equation for fluid dynamics and beyond, Numer. Math. Sci. Comput., Oxford University Press, Oxford, 2001. Zbmath
[14]
S. Succi, The Lattice Boltzmann Equation for Complex States of Flowing Matter, Oxford University Press, Oxford, 2018. Zbmath
[15]
S. Succi, W. Itani, K. Sreenivasan and R. Steijl, Quantum computing for fluids: Where do we stand?, Europhysics Letters 144 (2023), no. 1, 10001. DOI
[16]
S. Succi, W. Itani, C. Sanavio, K. R. Sreenivasan and R. Steijl, Ensemble fluid simulations on quantum computers, Computers and Fluids 270 (2024), 106148. DOI
[17]
F. Tennie and T. N. Palmer, Quantum Computers for Weather and Climate Prediction: The Good, the Bad and the Noisy, Bullettin of the American Meteorological Society 104 (2023), E488. DOI
[18]
IBM, Technology for the quantum future, https://www.ibm.com/quantum/technology


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