Near-optimal simulation of generic lattice Lindbladians

Construct quantum algorithms for generic lattice Lindbladians with finite-range interactions and dissipation whose gate complexity approaches the fundamental lower bound of order \(\Omega(Nt)\).

Background

The paper studies quantum simulation of dissipative many-body dynamics generated by local Lindbladians. Existing methods achieve near-optimal gate complexity only for restricted cases, such as mutually commuting Hermitian jump operators, or for sparsely dissipative systems. For generic finite-range lattice Lindbladians, prior approaches have substantially worse system-size dependence, including approximately $(Nt)^{3/2}$ for observable estimation and $N^2t$ for LCU-based methods.

The paper develops patching and merging techniques that improve the generic one-dimensional observable-estimation cost to approximately $(Nt)^{4/3}$, while achieving approximately $Nt$ for sparsely dissipative systems. Thus, the work leaves unresolved whether generic dissipative lattice systems can attain the near-optimal $\Omega(Nt)$ scaling.