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A quantum algorithm for heat conduction with symmetrization
Shi-Jie Wei1, Chao Wei2, Peng Lv3
1Beijing Academy of Quantum Information Sciences, Beijing 100193, China.
Science Bulletin
|March 1, 2023
Summary
We developed a novel quantum algorithm for heat conduction (QHC) that efficiently simulates thermal energy transfer. This quantum approach offers significant advantages over classical methods, enabling accurate temperature distribution predictions.
Area of Science:
- Quantum Computing
- Computational Physics
- Thermodynamics
Background:
- Heat conduction is crucial in engineering, governed by partial differential equations.
- Classical algorithms for heat conduction can be computationally intensive and prone to errors.
Purpose of the Study:
- To introduce a novel quantum algorithm for heat conduction (QHC).
- To demonstrate QHC's superior performance compared to classical algorithms.
- To provide an experimental implementation of QHC.
Main Methods:
- Representing the heat conduction system using a symmetric system with an ancilla qubit.
- Directly evolving the linear process without complex phase estimation, unlike HHL algorithms.
- Experimental implementation on a nuclear spin quantum processor for a 1D thermal conduction process.
Main Results:
- The quantum circuit complexity is polylogarithmic in the number of grid points.
- The QHC algorithm is experimental-friendly with no output error post-discretization.
- Accurate determination of spatial and temporal temperature distributions was achieved experimentally.
Conclusions:
- The developed QHC algorithm significantly outperforms classical methods for heat conduction simulations.
- The algorithm's efficiency and accuracy make it suitable for experimental implementation.
- QHC is broadly applicable to physical processes reducible to the heat equation.
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