A quantum algorithm for heat conduction with symmetrization

Wei, Shi- Jie1; Wei, Chao2,3,4; Lv, Peng5,6; Shao, Changpeng7; Gao, Pan1,5,6; Zhou, Zengrong1,5,6; Li, Keren8; Xin, Tao2,3,4; Long, Gui-Lu1,5,6,9,10,11

2023-03-15

10.1016/j.scib.2023.02.016

SCIENCE BULLETIN   Impact Factor & Quartile

2095-9273

2095-9281

Heat conduction, driven by thermal non-equilibrium, is the transfer of internal thermal energy through physical contacts, and it exists widely in various engineering problems, such as spacecraft and state-ofthe-art dilution refrigerators. The mathematical equation for heat conduction is a prototypical partial differential equation. Here we report a quantum algorithm for heat conduction (QHC) that significantly outperforms classical algorithms. We represent the original heat conduction system by a symmetric system with an ancilla qubit so that the quantum circuit complexity is polylogarithmic in the number of discretized grid points. Compared with the existing algorithms based on solving linear equations via the Harrow-Hassidim-Lloyd (HHL) algorithm, our method evolves the linear process directly without phase estimation, which involves complex quantum operations and large output error. Therefore, this algorithm is experimental-friendly and without output error after the discretization procedure. We experimentally implemented the algorithm for a one-dimensional thermal conduction process with two-edge constant temperatures and adiabatic conditions on a nuclear spin quantum processor. The spatial and temporal distributions of the temperature are accurately determined from the experimental results. Our work can be naturally applied to any physical processes that can be reduced to the heat equation.@2023 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved.

Quanutm simulation Quantum algorithm Heat conduction Linear combination of unitary operations

SCI

English

Corresponding

National Natural Science Foundation of China["12005015","11974205","11905111","2017YFA0303700","2019B121203002"] ; National Key Research and Development Program of China[12275117] ; Key Research and Development Program of Guangdong Province[11905099] ; Guangdong Basic and Applied Basic Research Foundation["2018B030325002","2022B1515020074"] ; Shenzhen Science and Technology Program[2019A1515011383] ; Guangdong Provincial Key Laboratory[KQTD20200820113010023]

Science & Technology - Other Topics

Multidisciplinary Sciences

WOS:000955939900001

ELSEVIER

Web of Science

1.Beijing Acad Quantum Informat Sci, Beijing 100193, Peoples R China
2.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
3.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
4.Southern Univ Sci & Technol, Guangdong Prov Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China
5.Tsinghua Univ, State Key Lab Low Dimens Quantum Phys, Beijing 100084, Peoples R China
6.Tsinghua Univ, Dept Phys, Beijing 100084, Peoples R China
7.Univ Bristol, Sch Math, Fry Bldg, Bristol BS8 1UG, England
8.Peng Cheng Lab, Shenzhen 518055, Peoples R China
9.Tsinghua Univ, Beijing Natl Res Ctr Informat Sci & Technol, Beijing 100084, Peoples R China
10.Tsinghua Univ, Sch Informat, Beijing 100084, Peoples R China
11.Frontier Sci Ctr Quantum Informat, Beijing 100084, Peoples R China

Wei, Shi- Jie,Wei, Chao,Lv, Peng,et al. A quantum algorithm for heat conduction with symmetrization[J]. SCIENCE BULLETIN,2023,68(5).

Wei, Shi- Jie.,Wei, Chao.,Lv, Peng.,Shao, Changpeng.,Gao, Pan.,...&Long, Gui-Lu.(2023).A quantum algorithm for heat conduction with symmetrization.SCIENCE BULLETIN,68(5).

Wei, Shi- Jie,et al."A quantum algorithm for heat conduction with symmetrization".SCIENCE BULLETIN 68.5(2023).