Canonical Partition Function on a Quantum Computer through Trotter Interpolation

2025/06/11 by Taozhi Guo, Guo, Taozhi, Gumaro Rendon +3 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2506.09318

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we present a Gibbs state observable estimation algorithm based on Trotter interpolation, which reaches a state-of-the-art quantum computational cost of O(βlog1/ε). Our approach saves log(Γ) ancilla qubits compared with the qubitization-based methods for Hamiltonian with Γ stages. To provide a robust assessment of our approach, we benchmark our results against state-of-the-art methodology using the SYK model as a testbed. Our method provides an efficient alternative method for Gibbs-state accessing based on Trotterization in the context of quantum state preparation and estimation of thermal observables.

Citations

• Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians
• An efficient and exact noncommutative quantum Gibbs sampler
• Generalized Quantum Signal Processing
• Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model

Cited by

• On the commutator scaling in Hamiltonian simulation with multi-product formulas

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