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• W2001450478 abstract "The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting phenomena such as fractal spectra, mixed phase space, dynamical localization, anomalous diffusion, or partial delocalization, and can describe electrons in a magnetic field. Three different quantum algorithms are presented and analyzed, enabling us to simulate efficiently the evolution operator of this system with different precision using different resources. Depending on the parameters chosen, the system is near integrable, localized, or partially delocalized. In each case we identify transport or spectral quantities which can be obtained more efficiently on a quantum computer than on a classical one. In most cases, a polynomial gain compared to classical algorithms is obtained, which can be quadratic or less depending on the parameter regime. We also present the effects of static imperfections on the quantities selected and show that depending on the regime of parameters, very different behaviors are observed. Some quantities can be obtained reliably with moderate levels of imperfection even for large number of qubits, whereas others are exponentially sensitive to the number of qubits. In particular, the imperfection threshold for delocalization becomes exponentially small in the partially delocalized regime. Our results show that interesting behavior can be observed with as little as $7--8phantom{rule{0.3em}{0ex}}mathrm{qubits}$ and can be reliably measured in presence of moderate levels of internal imperfections." @default.
• W2001450478 created "2016-06-24" @default.
• W2001450478 creator A5029107105 @default.
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• W2001450478 date "2004-11-22" @default.
• W2001450478 modified "2023-10-03" @default.
• W2001450478 title "Quantum computation of a complex system: The kicked Harper model" @default.
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• W2001450478 doi "https://doi.org/10.1103/physreve.70.056218" @default.
• W2001450478 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/15600739" @default.
• W2001450478 hasPublicationYear "2004" @default.
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