Low-temperature thermal state preparation using subspace methods

Estimating finite-temperature observables efficiently poses a significant challenge, as it requires detailed knowledge of a system's eigen-spectrum. While quantum algorithms offer the potential to prepare thermal states for systems beyond classical reach, current quantum hardware limits practical implementations due to high resource costs, particularly at low temperatures. In this work, we introduce a near-term algorithm for estimating low-temperature thermal observables across a range of parameters using subspace-based techniques. For obtaining accurate low-temperature thermal observables, we require a subspace composed of low-energy states, which are prepared using truncated state preparation methods. Our approach constructs these subspaces at selected parameter points through techniques such as Quantum Imaginary Time Evolution (QITE) and the Variational Quantum Eigensolver (VQE) and then applies eigenvector continuation to efficiently compute expectation values throughout the parameter space. We demonstrate this approach for 1D and 2D spin models, including TFXY and XXZ models.