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Efficient quantum Gibbs sampling of stabilizer codes using hybrid computation
Ivan H. C. Shum, Angela Capel·November 13, 2025
Quantum Physics
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Abstract
We present hybrid Gibbs sampling algorithms for the stabilizer code Hamiltonians of the rotated surface code and the toric code with only local quantum algorithms, using $\sim L/2$ quantum circuit depth to prepare the Gibbs state of the rotated surface code Hamiltonian, and $L$ quantum circuit depth to prepare the Gibbs state of the toric code Hamiltonian, being $L$ the side of the side of the square lattice. We further show that if we allow for non-local gates, the Gibbs state of the periodic 1D Ising model can be prepared in logarithmic depth and linearly many simultaneous measurements.