Efficient quantum Gibbs sampling of stabilizer codes using hybrid computation

TL;DR

This paper introduces hybrid quantum algorithms for efficiently preparing Gibbs states of stabilizer code Hamiltonians, achieving reduced circuit depths with local gates and further improvements with non-local gates for specific models.

Contribution

It develops novel hybrid quantum Gibbs sampling algorithms for stabilizer codes, optimizing circuit depth and incorporating non-local gates for enhanced efficiency.

Findings

Gibbs state of rotated surface code prepared with ~L/2 depth

Gibbs state of toric code prepared with L depth

Non-local gates enable logarithmic depth for 1D Ising model

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.