Quantum Simulation of Dissipative Non-Markovian Coupled Classical Oscillators — E8 Intelligence Research

We present a quantum algorithm for simulating classical oscillator networks characterized by non-Markovian dissipation and time-varying material properties, extending recent speedups for undamped harmonic systems to viscoacoustic and viscoelastic media. We embed the history-dependent dynamics into a Markovian state space governed by a non-Hermitian operator by approximating memory kernels through a Prony series. We then use linear combination of Hamiltonian simulation to estimate the instantaneous kinetic and potential energy for a subset of oscillators at time $t$ within error $ε$ using a number of queries to the oscillator system that scales as $\widetilde{\mathcal{O}}(α_{\rm tot} t/ε)$, where $α_{\rm tot}$ is polynomial in the strength of the dissipation, spring constants, inverse masses, and sparsity of the connections in the network. We further show that this energy estimation task is in the worst-case classically hard (i.e., a corresponding decision problem is $\mathsf{BQP}$-comp Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com