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arXiv:2604.10543

Finite-temperature quantum Krylov method from real-time overlaps

Hiroto Yamamoto, Katsuhiro Morita

quant-phcond-mat.str-elSubmitted Apr 12, 2026• Announced Apr 14, 2026• 0 citations• Revised Apr 14, 2026 (v2)
v1 · Apr 12, 2026v2 · Apr 14, 2026v3 · Oct 2, 2026
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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 $g_n=\langle φ|e^{-inτH}|φ\rangle$, 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 $σ\sim10^{-3}$. Our results establish real-time-overlap-based finite-temperature evaluation as a promising framework for finite-temperature computation on near-future quantum hardware.

Comments
References slightly revised

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