Causal Query Compression for Lindblad Dynamics: Optimal Queries and Nearly Linear Local Simulation
Abstract
We construct a causal query compiler for time-dependent Lindblad dynamics and establish query and gate bounds under distinct input models. With coherent block encodings of the Hamiltonian and individual jump operators, a Lipschitz generator can be simulated to diamond-norm error ε using O(1+τ+log(1/ε)/log(e+log(1/ε)/τ)) controlled queries, where τ=T(αH+∑μαμ2). This bound is independent of the time-grid size and is worst-case optimal for τ≥1. Weak active entry and clean return yield a factorial history tail; combining two reuse lengths removes the auxiliary input. A three-call polar correction supplies the Lindblad cells. The compiler also characterizes the minimum oracle action of bounded adaptive Markovian protocols by quantum query complexity and the general adversary bound, up to constant factors. For finite-range dynamics on n lattice sites, efficient coherent evaluation of the local matrices and fixed local parameters give O(n(T+1)polylogX) elementary gates, where X=max{e,n(T+1)(1+Kt+B)/ε}, for piecewise Hölder generators with fixed exponent, local variation bound Kt, and at most B breakpoints per term. The jumps need not commute. This gate bound includes evaluation, arithmetic, selection, routing, and environment storage. Its proof combines a spatial decomposition on a common bath, compilation on occupied inputs, and routing on compressed records. Reusing bath storage between short segments gives depth (T+1)polylogX and space npolylogX.
Related
- Query-optimal quantum simulation of Lindblad evolution
- Optimal low-rank compression of quantum dynamics
- Near-optimal quantum simulation of lattice Lindbladian dynamics
- Optimal Linear Combination of Hamiltonian Simulation for Dissipative Dynamics
- Fault-tolerant resource estimation for ground-state preparation via Lindblad simulation
BibTeX
@misc{kitchen2026causal,
title = {{Causal Query Compression for Lindblad Dynamics: Optimal Queries and Nearly Linear Local Simulation}},
author = {Jacob Kitchen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31312},
eprint = {2609.31312},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31312},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Causal Query Compression for Lindblad Dynamics: Optimal Queries and Nearly Linear Local Simulation
AU - Jacob Kitchen
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31312
UR - https://arxiv.org/abs/2609.31312
AB - We construct a causal query compiler for time-dependent Lindblad dynamics and establish query and gate bounds under distinct input models. With coherent block encodings of the Hamiltonian and individual jump operators, a Lipschitz generator can be simulated to diamond-norm error ε using O(1+τ+log(1/ε)/log(e+log(1/ε)/τ)) controlled queries, where τ=T(α_H+∑_μα_μ^2). This bound is independent of the time-grid size and is worst-case optimal for τ≥1. Weak active entry and clean return yield a factorial history tail; combining two reuse lengths removes the auxiliary input. A three-call polar correction supplies the Lindblad cells. The compiler also characterizes the minimum oracle action of bounded adaptive Markovian protocols by quantum query complexity and the general adversary bound, up to constant factors. For finite-range dynamics on n lattice sites, efficient coherent evaluation of the local matrices and fixed local parameters give O(n(T+1)polylogX) elementary gates, where X=max{e,n(T+1)(1+K_t+B)/ε}, for piecewise Hölder generators with fixed exponent, local variation bound K_t, and at most B breakpoints per term. The jumps need not commute. This gate bound includes evaluation, arithmetic, selection, routing, and environment storage. Its proof combines a spatial decomposition on a common bath, compilation on occupied inputs, and routing on compressed records. Reusing bath storage between short segments gives depth (T+1)polylogX and space npolylogX.
ER -