Tensor-Network Population Annealing

TL;DR

The paper introduces Tensor-Network Population Annealing (TNPA), a hybrid method combining tensor-network initialization with population annealing for efficient low-temperature sampling in frustrated spin systems.

Contribution

It presents a novel hybrid sampling approach that leverages tensor-network methods for initialization and population annealing for equilibration, addressing limitations of existing techniques.

Findings

TNPA improves low-temperature sampling stability.

The method effectively applies to the 2D Edwards-Anderson Ising spin glass.

Adaptive initialization enhances sampling accuracy.

Abstract

We propose a hybrid sampling method, tensor-network population annealing (TNPA), which combines tensor-network (TN) initialization with population annealing (PA). We apply this method to the two-dimensional Edwards-Anderson Ising spin glass. The approach is motivated by the limitations of existing methods: TN-based samplers can become numerically unstable in frustrated spin systems at low temperatures, whereas conventional PA requires a long annealing schedule when started from the high-temperature limit. In TNPA, TN contractions are used only within a reliable temperature range to generate initial configurations that are close to the equilibrium distribution. The subsequent low-temperature equilibration is then carried out by PA. To stabilize the initialization process, we introduce a diagnostic based on the effective sample size that adaptively selects the initialization temperature. The proposed framework provides a practical and physically motivated route to low-temperature sampling by combining the complementary strengths of TN and PA.