End-to-end quantum algorithm for the response function of coupled oscillators

The computation of the response function of coupled oscillators can be reformulated as solving an eigenvalue problem, making it applicable to various fields. In this talk, we present an end-to-end quantum algorithm for computing the response function of coupled oscillators. The algorithm makes use of quantum phase estimation in combination with Hamiltonian simulation based on quantum walks. This enables us to prepare the full Hamiltonian, which describes the coupled oscillators, with just two queries to a matrix oracle. We provide an explicit compilation of the oracles for some basic examples. By focusing solely on the response of a single oscillator, the input-output bottleneck in quantum phase estimation can be mitigated. Standard classical methods require O(N³) operations for N oscillators. Our algorithm has the possibility of polylog(N) complexity, but only under certain assumptions, that we analyze in details. Recently, Babbush et al [1] analyzed a similar problem, but focusing on simulating the time-evolution of coupled oscillators.

[1] R. Babbush, D. Berry, R. Kothari, R. Somma, N. Wiebe, “Exponential quantum speed-up in

simulating coupled classical oscillators”, arXiv:2303.13012 (2023).