We establish a general framework for developing fast sampling and counting algorithms for stoquastic spin systems at high temperature. Our framework is based on a rapidly mixing Markov chain for polymer models and a subcritical percolation process for sampling individual polymers. We apply our framework to obtain fast algorithms for approximating the partition function and sampling from the thermal distribution of (1) general stoquastic spin systems, (2) ferromagnetic Heisenberg models, and (3) antiferromagnetic Heisenberg models on bipartite graphs. For the Heisenberg models, we obtain an improved bound on the inverse temperature by using their respective cycle and loop representations.We establish a general framework for developing fast sampling and counting algorithms for stoquastic spin systems at high temperature. Our framework is based on a rapidly mixing Markov chain for polymer models and a subcritical percolation process for sampling individual polymers. We apply our framework to obtain fast algorithms for approximating the partition function and sampling from the thermal distribution of (1) general stoquastic spin systems, (2) ferromagnetic Heisenberg models, and (3) antiferromagnetic Heisenberg models on bipartite graphs. For the Heisenberg models, we obtain an improved bound on the inverse temperature by using their respective cycle and loop representations.

quant-pharXiv:2608.19489Aug 21, 2026

Pathway to Quantum Thermalization

Anonymous

PhysicsMay 2, 20180 citations

Rapid on-demand generation of thermal states in superconducting quantum circuits

Timm Mörstedt, Wallace S. Teixeira, Arto Viitanen +13 more

We experimentally demonstrate the fast generation of thermal states of a transmon using a single-junction quantum-circuit refrigerator (QCR) as an tunable environment. Through single-shot readout, we monitor the transmon up to its third excited state, assessing population distributions controlled by QCR drive pulses. Whereas cooling can be achieved in the weak-drive regime, high-amplitude pulses can generate Boltzmann-distributed populations from a temperature of 110 mK up to 500 mK within 100 ns. As we propose in our work, this fast and efficient temperature control provides an appealing opportunity to demonstrate a quantum heat engine. Our results also pave the way for efficient dissipative state preparation and for reducing the circuit depth in thermally assisted quantum algorithms and quantum annealing.We experimentally demonstrate the fast generation of thermal states of a transmon using a single-junction quantum-circuit refrigerator (QCR) as an tunable environment. Through single-shot readout, we monitor the transmon up to its third excited state, assessing population distributions controlled by QCR drive pulses. Whereas cooling can be achieved in the weak-drive regime, high-amplitude pulses can generate Boltzmann-distributed populations from a temperature of 110 mK up to 500 mK within 100 ns. As we propose in our work, this fast and efficient temperature control provides an appealing opportunity to demonstrate a quantum heat engine. Our results also pave the way for efficient dissipative state preparation and for reducing the circuit depth in thermally assisted quantum algorithms and quantum annealing.

arXiv:2402.09594Physical Review ResearchAug 13, 20255 citations

Fast algorithm to calculate exact geometrical factors for theq-state Potts model

Chi-Ning Chen, Chin‐Kun Hu

Based on the connection between the q-state Potts model (QPM) and a q-state bond-correlated percolation model, Hu has defined the percolating geometrical factor ${\mathit{N}}_{\mathit{p}}$ and the nonpercolating geometrical factors ${\mathit{N}}_{\mathit{f}}$ . From ${\mathit{N}}_{\mathit{p}}$ nd ${\mathit{N}}_{\mathit{f}}$ , we may obtain the thermal properties of the QPM and construct a percolation renormalization-group method to study the QPM. In this paper we present a fast algorithm to calculate exact ${\mathit{N}}_{\mathit{p}}$ and ${\mathit{N}}_{\mathit{f}}$ for the QPM on finite cells.Based on the connection between the q-state Potts model (QPM) and a q-state bond-correlated percolation model, Hu has defined the percolating geometrical factor ${\mathit{N}}_{\mathit{p}}$ and the nonpercolating geometrical factors ${\mathit{N}}_{\mathit{f}}$. From ${\mathit{N}}_{\mathit{p}}$ nd ${\mathit{N}}_{\mathit{f}}$, we may obtain the thermal properties of the QPM and construct a percolation renormalization-group method to study the QPM. In this paper we present a fast algorithm to calculate exact ${\mathit{N}}_{\mathit{p}}$ and ${\mathit{N}}_{\mathit{f}}$ for the QPM on finite cells.

Physical review. B, Condensed matterMay 1, 19915 citations

Algorithmic Quantum Cooling

Man Hong Yung, Sergio Boixo, Alán Aspuru‐Guzik

Bulletin of the American Physical SocietyFeb 29, 20120 citations

Based on the connection between the q-state Potts model (QPM) and a q-state bond-correlated percolation model, Hu has defined the percolating geometrical factor

{\mathit{N}}_{\mathit{p}}

and the nonpercolating geometrical factors

{\mathit{N}}_{\mathit{f}}

. From

{\mathit{N}}_{\mathit{p}}

{\mathit{N}}_{\mathit{f}}

, we may obtain the thermal properties of the QPM and construct a percolation renormalization-group method to study the QPM. In this paper we present a fast algorithm to calculate exact

{\mathit{N}}_{\mathit{p}}

and

{\mathit{N}}_{\mathit{f}}

for the QPM on finite cells.