Polynomial-Time Preparation of Low-Temperature Gibbs States for 2D Toric Code

Authors:
  • ZDZhiyan Ding
    Zhiyan Ding
  • ZLZeph Landau
    Zeph Landau
  • BLBowen Li
    Bowen Li
  • LLLin Lin
    Lin Lin
  • RZRuizhe Zhang
    Ruizhe Zhang
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Abstract
We propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial condition, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. Our approach combines the Lindblad dynamics using a local Davies generator with simple global jump operators to enable efficient transitions between logical sectors. Our proof also shows that the Lindblad dynamics with a digitally implemented low-temperature local Davies generator is able to efficiently drive the quantum state towards the ground state manifold.