Finite-temperature quantum Krylov method from real-time overlaps

Abstract:Accurately evaluating finite-temperature properties of quantum many-body systems remains a central challenge. Many existing quantum approaches require thermal-state preparation at each target temperature, making low-temperature calculations especially demanding in terms of circuit depth and accuracy. In this work, we present the finite-temperature quantum Krylov (FTQK) method, which combines stochastic trace estimation with a Hermitian generalized eigenvalue problem based on $\cos(\tilde H)$. The only quantum-side input required is the temperature-independent real-time overlap sequence $g_n=\langle\phi|e^{-in\tau H}|\phi\rangle$. All benchmark results presented in this work were obtained from classical numerical simulations of the quantum-circuit protocol. For periodic spin-$\frac{1}{2}$ Heisenberg chains with $N=14$ and $18$, FTQK accurately reproduces the specific heat, magnetic susceptibility, and entropy in the noiseless case. It also accurately reproduces the specific heat of the $N=14$ honeycomb Kitaev model, demonstrating that FTQK can be applied beyond simple one-dimensional chains to a model on a two-dimensional lattice with bond-dependent interactions. Furthermore, in a proof-of-principle finite-shot study for the $N=14$ Heisenberg chain, the main thermodynamic features remain well preserved even at $\sigma=10^{-3}$. Here, $\sigma=1/\sqrt{N_{\mathrm{shot}}}$, where $N_{\mathrm{shot}}$ is the number of shots used to estimate an overlap. These results demonstrate the potential of FTQK for finite-temperature calculations using reusable, temperature-independent real-time overlap data.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2604.10543 [quant-ph]

(or arXiv:2604.10543v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.10543 Focus to learn more arXiv-issued DOI via DataCite

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