Query-Optimal and Gate-Efficient Lindbladian Simulation
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=∑k=1m lvert k⟩⊗ Lk, with normalization factors αH and αB, respectively. For evolution time t, set τ=(αH+αB2)t. The algorithm approximates the evolution channel to diamond-norm error ε using O (τ+log(1/ε)/(log (e+log(1/ε)/τ))) 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.
Related
- Gate-Efficient Implementation of the Query-Optimal Time-Dependent Hamiltonian Simulation
- Near-optimal quantum simulation of lattice Lindbladian dynamics
- Query-optimal quantum simulation of Lindblad evolution
- Efficient Simulation of Gate Leakage Currents in Ultra-scaled Transistors from First Principles
- Causal Query Compression for Lindblad Dynamics: Optimal Queries and Nearly Linear Local Simulation
BibTeX
@misc{chen2026queryoptimal,
title = {{Query-Optimal and Gate-Efficient Lindbladian Simulation}},
author = {Boyang Chen and Minbo Gao and Xinzhao Wang and Shuo Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18757},
eprint = {2609.18757},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18757},
}
RIS
TY - UNPB
TI - Query-Optimal and Gate-Efficient Lindbladian Simulation
AU - Boyang Chen
AU - Minbo Gao
AU - Xinzhao Wang
AU - Shuo Zhou
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18757
UR - https://arxiv.org/abs/2609.18757
AB - 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=∑_k=1^m lvert k⟩⊗ 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 ε using O (τ+log(1/ε)/(log (e+log(1/ε)/τ))) 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.
ER -