2025/09/11 by Shang, Zhong-Xia, An, Dong, Shao, Changpeng · 2 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2509.09517
We investigate Lindbladian fast-forwarding and its applications to estimating Gibbs state properties. Fast-forwarding refers to the ability to simulate a system of time t using significantly fewer than t queries or circuit depth. While various Hamiltonian systems are known to circumvent the no fast-forwarding theorem, analogous results for dissipative dynamics, governed by Lindbladians, remain largely unexplored. We first present a quantum algorithm for simulating purely dissipative Lindbladians with unitary jump operators, achieving additive query complexity O(t + \fraclog(ε-1)loglog(ε-1)) up to error~ε, improving previous algorithms. When the jump operators have certain structures (i.e., block-diagonal Paulis), the algorithm can be modified to achieve exponential fast-forwarding, attaining circuit depth O(log(t + \fraclog(ε-1)loglog(ε-1))), while preserving query complexity. Using these fast-forwarding techniques, we develop a quantum algorithm for estimating Gibbs state properties of the form ⟨ ψ1 | e-β(H + I) | ψ2 ⟩, up to additive error ε, with H the Hamiltonian and β the inverse temperature. For input states exhibiting certain coherence conditions -- e.g.,~⟨ 0|⊗ n e-β(H + I) |+⟩⊗ n -- our method achieves exponential improvement in complexity (measured by circuit depth), O (2-n/2 ε-1 log β), compared to the quantum singular value transformation-based approach, with complexity O (ε-1 √β ). For general | ψ1 ⟩ and | ψ2 ⟩, we also show how the level of improvement is changed with the coherence resource in | ψ1 ⟩ and | ψ2 ⟩.