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@ARTICLE{Danz:1038554,
      author       = {Danz, Sven and Berta, Mario and Schröder, Stefan and
                      Kienast, Pascal and Wilhelm-Mauch, Frank and Ciani,
                      Alessandro},
      title        = {{C}alculating response functions of coupled oscillators
                      using quantum phase estimation},
      journal      = {Quantum Physics},
      publisher    = {arXiv},
      reportid     = {FZJ-2025-01537},
      year         = {2024},
      abstract     = {We study the problem of estimating frequency response
                      functions of systems of coupled, classical harmonic
                      oscillators using a quantum computer. The functional form of
                      these response functions can be mapped to a corresponding
                      eigenproblem of a Hermitian matrix $H$, thus suggesting the
                      use of quantum phase estimation. Our proposed quantum
                      algorithm operates in the standard $s$-sparse, oracle-based
                      query access model. For a network of $N$ oscillators with
                      maximum norm $\lVert H \rVert_{\mathrm{max}}$, and when the
                      eigenvalue tolerance $\varepsilon$ is much smaller than the
                      minimum eigenvalue gap, we use $\mathcal{O}(\log(N s \lVert
                      H \rVert_{\mathrm{max}}/\varepsilon)$ algorithmic qubits and
                      obtain a rigorous worst-case query complexity upper bound
                      $\mathcal{O}(s \lVert H \rVert_{\mathrm{max}}/(δ^2
                      \varepsilon) )$ up to logarithmic factors, where $δ$
                      denotes the desired precision on the coefficients appearing
                      in the response functions. Crucially, our proposal does not
                      suffer from the infamous state preparation bottleneck and
                      can as such potentially achieve large quantum speedups
                      compared to relevant classical methods. As a
                      proof-of-principle of exponential quantum speedup, we show
                      that a simple adaptation of our algorithm solves the random
                      glued-trees problem in polynomial time. We discuss practical
                      limitations as well as potential improvements for
                      quantifying finite size, end-to-end complexities for
                      application to relevant instances.},
      keywords     = {Quantum Physics (quant-ph) (Other) / FOS: Physical sciences
                      (Other)},
      cin          = {PGI-12},
      cid          = {I:(DE-Juel1)PGI-12-20200716},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522) / ML4Q - Machine Learning for Quantum (101120240)
                      / Verbundprojekt, Quantum Artificial Intelligence for the
                      Automotive Industry (Q(AI)2) - Teilvorhaben:
                      Implementierung, Benchmarking, und Management (13N15584)},
      pid          = {G:(DE-HGF)POF4-5221 / G:(EU-Grant)101120240 /
                      G:(BMBF)13N15584},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2405.08694},
      url          = {https://juser.fz-juelich.de/record/1038554},
}