Abstract
We develop an end-to-end framework for estimating canonical thermal properties of particle-number-conserving second-quantized Hamiltonians using quantum simulations. The framework integrates initial state preparation with mixed Dicke states, particle-number-preserving Trotterized simulation, and generalized quantum signal processing to estimate canonical partition functions and observables. Building on this canonical scheme, we introduce a grand-canonical reconstruction scheme in which the same quantum measurement data can be reused for arbitrary chemical potentials through classical reweighting, thereby avoiding repeated quantum circuit executions as the chemical potential is varied. We prove the existence of system-size-independent temperature regimes in which both the canonical and reconstructed grand-canonical schemes have lower asymptotic time complexity than classical Lanczos methods, up to polynomial factors, for physically relevant Hamiltonians. We numerically validate our theoretical results for the two-dimensional Hubbard model in both weak- and intermediate-coupling regimes.
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Publication details
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- Green open access
Cite this article
APA 7
Ko, T., Lim, S., & Choi, S. (2026). Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction. https://omanscience.com/en/articles/particle-number-preserving-quantum-signal-processing-for-thermal-properties-canonical-ensemble-estimation-and-grand-canonical-reconstruction
MLA 9
Ko, Taehee, et al. "Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction." https://omanscience.com/en/articles/particle-number-preserving-quantum-signal-processing-for-thermal-properties-canonical-ensemble-estimation-and-grand-canonical-reconstruction.
Chicago (author–date)
Ko, Taehee, Sungbin Lim, and Sangkook Choi. 2026. "Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction." https://omanscience.com/en/articles/particle-number-preserving-quantum-signal-processing-for-thermal-properties-canonical-ensemble-estimation-and-grand-canonical-reconstruction.
Harvard
Ko, T., Lim, S. and Choi, S. (2026) 'Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction', Available at: https://omanscience.com/en/articles/particle-number-preserving-quantum-signal-processing-for-thermal-properties-canonical-ensemble-estimation-and-grand-canonical-reconstruction.
Vancouver
Ko T, Lim S, Choi S. Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction. https://omanscience.com/en/articles/particle-number-preserving-quantum-signal-processing-for-thermal-properties-canonical-ensemble-estimation-and-grand-canonical-reconstruction
IEEE
T. Ko, S. Lim, and S. Choi, "Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction," https://omanscience.com/en/articles/particle-number-preserving-quantum-signal-processing-for-thermal-properties-canonical-ensemble-estimation-and-grand-canonical-reconstruction.