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Peer-reviewedCC BY 4.0New Journal of Physics

Efficient quantum Gibbs sampling of stabilizer codes using hybrid computation

  • Ivan Shum1
  • Ángela Capel1
  1. 1University of Cambridge
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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 ∼ 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.

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Cite

BibTeXRIS
BibTeX
@article{shum2026efficient,
  title = {{Efficient quantum Gibbs sampling of stabilizer codes using hybrid computation}},
  author = {Ivan Shum and Ángela Capel},
  journal = {New Journal of Physics},
  year = {2026},
  month = oct,
  doi = {10.1088/1367-2630/aeb623},
  url = {https://iopscience.iop.org/article/10.1088/1367-2630/aeb623},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Efficient quantum Gibbs sampling of stabilizer codes using hybrid computation
AU  - Ivan Shum
AU  - Ángela Capel
PY  - 2026
DA  - 2026/10/19
JO  - New Journal of Physics
DO  - 10.1088/1367-2630/aeb623
UR  - https://iopscience.iop.org/article/10.1088/1367-2630/aeb623
AB  - 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 ∼ 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.
SN  - 1367-2630
ER  -