2025/05/14 by Yali Du, Du, Yali, Naihuan Jing +6
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.48550/arxiv.2505.09441
openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A fundamental challenge in quantum simulation is approximating the time-evolution operator \(U(t)=e-iHt\) generated by a large sum of typically non-commuting Hamiltonians using resource-efficient circuits compatible with near-term devices. We present a refinement of fixed-depth Lie-theoretic simulation that incorporates second-order Zassenhaus commutator corrections into a Cartan/KAK decomposition template. The resulting approximation retains constant circuit depth while achieving local error \(O(t3)\) in operator norm under standard boundedness assumptions, and it substantially reduces gate counts relative to first-order product formulas when time is large and depth is constrained. The method leverages closure of Pauli commutators inside Pauli-generated Lie algebras, enabling symbolic commutator evaluation and avoiding explicit matrix exponentiation in classical preprocessing. This yields a structured pathway to compile lattice and chemistry-inspired Hamiltonians with locality constraints into fixed-depth circuits suitable for noisy intermediate-scale quantum hardware.