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

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arxiv 2410.01206 v2 pith:73I6QVY7 submitted 2024-10-02 quant-ph

Zhiyan Ding , Zeph Landau , Bowen Li , Lin Lin , Ruizhe Zhang This is my paper · ORCID
classification quant-ph
keywords statecodedaviesdynamicsgeneratorgibbslindbladlocal
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Viewing protected superconducting qubits through the lens of the cat qubit

    quant-ph 2025-01 conditional novelty 7.0 of 10

    Fluxonium's heavy-limit ground states are squeezed coherent states, producing exponential bit-flip protection in E_j/(k_B T) with constant phase-flip rate, analogous to a squeezed cat code.

  2. Fast mixing of weakly interacting fermionic systems at any temperature

    quant-ph 2024-12 conditional novelty 7.0 of 10

    Weakly interacting fermionic lattice systems have a constant spectral gap in a Gibbs sampler Lindbladian, giving O(n) mixing time and efficient quantum Gibbs state preparation at any fixed temperature.

  3. Convergence monitoring of quantum Gibbs samplers

    quant-ph 2026-08 conditional novelty 6.0 of 10

    A Hamiltonian-agnostic stopping rule for quantum Gibbs samplers based on the equilibrium symmetry of the weak-measurement quasi-frequency record.

  4. Quantum thermodynamics and semi-definite optimization

    quant-ph 2025-05 conditional novelty 5.0 of 10

    Energy minimization with non-commuting charges and semi-definite programs share the same dual, so gradient ascent on chemical potentials solves both with provable convergence.

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