Query-Optimal and Gate-Efficient Lindbladian Simulation

2026-09-16

AI Summary

本文提出了一种量子算法，通过给定哈密顿量和跃迁算子的编码来模拟Lindbladian演化，以最优查询次数和门操作数实现高效模拟。

Abstract

We give a quantum algorithm for Lindbladian simulation given a block encoding of the Hamiltonian $H$ and a projected unitary encoding of the stacked jump operator $B=\sum_{k=1}^m \lvert k\rangle\otimes L_k$, with normalization factors $α_H$ and $α_B$, respectively. For evolution time $t$, set $τ=(α_H+α_B^2)t$. The algorithm approximates the evolution channel to diamond-norm error $\varepsilon$ using $O\!\left(τ+\frac{\log(1/\varepsilon)}{\log\!\left(e+\log(1/\varepsilon)/τ\right)}\right)$ oracle queries, matching the query lower bound for Hamiltonian simulation. The number of additional one- and two-qubit gates is linear in the query complexity up to polylogarithmic factors. The query- and gate-complexity bounds extend to Lipschitz-continuous time-dependent Lindbladians under coherent time-indexed oracle access. Our construction uses a one-query transducer that implements a product of rational approximations to short-time evolution when supplied with a catalyst. We bound the error from omitting the catalyst by exploiting orthogonality between different sequences of Kraus labels. The gate implementation combines a compressed Kraus-label representation, which stores only the positions and values of the nonzero labels, with the rotation factorization of Chen et al.

Problem

• Lindbladian simulation
• Hamiltonian
• query complexity
• gate complexity
• diamond-norm error

Innovation

• Lindbladian Simulation
• Quantum Algorithm
• Query Complexity
• Gate Efficiency
• Catalyst