Quantum

Particle-Number-Preserving Quantum Signal Processing for Thermal Properties: Canonical-Ensemble Estimation and Grand-Canonical Reconstruction

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Briefings

A new framework estimates thermal properties of particle-number-conserving quantum systems using quantum simulations, integrating mixed Dicke states and generalized quantum signal processing. The study introduces a grand-canonical reconstruction scheme that reuses measurement data via classical reweighting to avoid repeated quantum executions. Theoretical analysis proves system-size-independent temperature regimes exist where both schemes outperform classical Lanczos methods for the two-dimensional Hubbard model in weak and intermediate coupling regimes.

Key points

• The framework integrates mixed Dicke states, particle-number-preserving Trotterized simulation, and generalized quantum signal processing to estimate canonical partition functions.
• A grand-canonical reconstruction scheme allows arbitrary chemical potentials to be varied using classical reweighting of existing quantum measurement data, eliminating the need for repeated quantum circuit executions.

Context and limitations

Numerical validation is limited to the two-dimensional Hubbard model in weak- and intermediate-coupling regimes. The study presents theoretical existence proofs and numerical validation but does not provide exhaustive coverage of all Hamiltonian types or extreme coupling limits.

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