Speaker
Description
Thermal state preparation is a critical subroutine in many quantum algorithms, especially in Quantum Machine Learning (QML) and condensed matter physics. Generative modeling tasks, such as training Quantum Boltzmann Machines (QBMs), rely heavily on drawing samples from thermal distributions or computing expectation values over Gibbs states to evaluate loss functions and gradients. However, thermal state preparation is generally resource-intensive both on quantum computers and with classical methods. To address some of these challenges, we introduce a propagation-based approach to thermal state simulation that adapts Pauli and Majorana propagation to imaginary-time evolution in the Schrödinger picture. Our key observation is that high-temperature states can be sparse in the Pauli or Majorana bases, approaching the identity operator at infinite temperature. By formulating imaginary-time evolution directly in these operator bases and evolving from the maximally mixed state, we can access a continuum of temperatures where the state remains efficiently representable. In this work we analyze complementary truncation strategies: small coefficient truncation and Pauli-weight (or Majorana-length) truncation. We derive upper bounds on the error depending on the truncation threshold and temperature, and deploy our numerical implementation to study the 1D J1-J2 model and the Fermi-Hubbard model on a triangular lattice. Concretely, we study energy estimates across system sizes and temperatures for the former, and demonstrate direct computation of finite-temperature static correlation functions from the propagated thermal state. All our numerical and analytical studies show that simulating high-temperature states is tractable, but low-temperature states remain hard.
| Topic | Hybrid quantum-classical approaches for learning and optimization |
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| Additional Topic | Tensor methods and quantum-inspired machine learning |