For strictly dissipative linear ODEs, quantum solvers based on time-marching or LCHS achieve query complexity O(polylog(1/ε)) that is independent of the evolution time T.
Variable time amplitude amplification and quantum algorithms for linear algebra problems
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Quantum Differential Equation Solvers with Low State Preparation Cost: Eliminating the Time Dependence in Dissipative Equations
For strictly dissipative linear ODEs, quantum solvers based on time-marching or LCHS achieve query complexity O(polylog(1/ε)) that is independent of the evolution time T.