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001038554 0247_ $$2doi$$a10.48550/ARXIV.2405.08694
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001038554 041__ $$aEnglish
001038554 1001_ $$0P:(DE-Juel1)192152$$aDanz, Sven$$b0$$eCorresponding author$$ufzj
001038554 245__ $$aCalculating response functions of coupled oscillators using quantum phase estimation
001038554 260__ $$barXiv$$c2024
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001038554 520__ $$aWe 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.
001038554 536__ $$0G:(DE-HGF)POF4-5221$$a5221 - Advanced Solid-State Qubits and Qubit Systems (POF4-522)$$cPOF4-522$$fPOF IV$$x0
001038554 536__ $$0G:(EU-Grant)101120240$$aML4Q - Machine Learning for Quantum (101120240)$$c101120240$$fHORIZON-MSCA-2022-DN-01$$x1
001038554 536__ $$0G:(BMBF)13N15584$$aVerbundprojekt, Quantum Artificial Intelligence for the Automotive Industry (Q(AI)2) - Teilvorhaben: Implementierung, Benchmarking, und Management (13N15584)$$c13N15584$$x2
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001038554 650_7 $$2Other$$aQuantum Physics (quant-ph)
001038554 650_7 $$2Other$$aFOS: Physical sciences
001038554 7001_ $$0P:(DE-HGF)0$$aBerta, Mario$$b1
001038554 7001_ $$0P:(DE-Juel1)176448$$aSchröder, Stefan$$b2$$ufzj
001038554 7001_ $$0P:(DE-HGF)0$$aKienast, Pascal$$b3
001038554 7001_ $$0P:(DE-Juel1)184630$$aWilhelm-Mauch, Frank$$b4$$ufzj
001038554 7001_ $$0P:(DE-Juel1)187048$$aCiani, Alessandro$$b5$$ufzj
001038554 773__ $$a10.48550/ARXIV.2405.08694$$tQuantum Physics$$y2024
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