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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.

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Summary
This summary is machine-generated.

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.

Keywords:
Heat conductionLinear combination of unitary operationsQuantum algorithmQuanutm simulation

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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.