Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction
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.
Related
- Nonparametric Estimation of Negative Cumulative Extropy for Linear Consecutive Systems: Reliability Properties and Image-Processing Application
- From Common Information to Canonical Correlation Analysis and Beyond: Bridging Information Theory, Signal Processing, and Machine Learning
- LLCT: Learnable Linear Canonical Transform Family with Stability for Visual Feature Processing
- Canonical resolved-transport decomposition and reconstruction of local-unit-aligned ordered semigroups
- Feature-preserving interface reconstruction using piecewise circles and cusps
BibTeX
@misc{ko2026particlenumberpreserving,
title = {{Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction}},
author = {Taehee Ko and Sungbin Lim and Sangkook Choi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09373},
eprint = {2610.09373},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09373},
}
RIS
TY - UNPB
TI - Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction
AU - Taehee Ko
AU - Sungbin Lim
AU - Sangkook Choi
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09373
UR - https://arxiv.org/abs/2610.09373
AB - 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.
ER -