Finite-temperature quantum Krylov method from real-time overlaps

TL;DR

This paper introduces a real-time overlap-based quantum method to evaluate finite-temperature properties of many-body systems without needing thermal state preparation, enabling broad temperature range calculations on quantum hardware.

Contribution

The authors present a novel framework that uses real-time overlaps to compute thermodynamic quantities across temperatures without target temperature specification.

Findings

Accurate specific heat, magnetic susceptibility, and entropy for the 1D Heisenberg model in noiseless simulations.

Magnetic susceptibility computed accurately without symmetry-sector decomposition using pseudorandom vectors.

Method remains robust under finite-shot statistical errors up to approximately 10^{-3}.

Abstract

Accurately evaluating finite-temperature properties of quantum many-body systems remains a central challenge. Many existing quantum approaches typically require thermal-state preparation at each target temperature, making low-temperature calculations especially demanding in terms of circuit depth and accuracy. Here we introduce a distinct framework based only on the real-time overlap sequence $g_n=\langle \phi|e^{-in\tau H}|\phi\rangle$, which enables thermodynamic quantities to be obtained over a broad temperature range, without specifying a target temperature on the quantum device. For the one-dimensional spin-$\frac{1}{2}$ Heisenberg model with periodic boundary conditions, we obtain accurate specific heat, magnetic susceptibility, and entropy in the noiseless case. Magnetic susceptibility is also evaluated accurately without explicit symmetry-sector decomposition by employing pseudorandom vectors compatible with $S_{\mathrm{tot}}^{z}$ conservation. With suitable stabilization, the method further retains the main thermodynamic features under finite-shot statistical errors up to $\sigma\sim10^{-3}$. Our results establish real-time-overlap-based finite-temperature evaluation as a promising framework for finite-temperature computation on near-future quantum hardware.