dorsal/arxiv
View SchemaQuantum Computation of a Complex System : the Kicked Harper Model
| Authors | Benjamin Levi, Bertrand Georgeot |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409028 |
| URL | https://arxiv.org/abs/quant-ph/0409028 |
| DOI | 10.1103/PhysRevE.70.056218 |
| Journal | Physical Review E 70 (2004) 056218 |
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 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, whereas others are exponentially sensitive to imperfection strength. 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 7-8 qubits, and can be reliably measured in presence of moderate levels of internal imperfections.
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"abstract": "The simulation of complex quantum systems on a quantum computer is studied,\ntaking the kicked Harper model as an example. This well-studied system has a\nrich variety of dynamical behavior depending on parameters, displays\ninteresting phenomena such as fractal spectra, mixed phase space, dynamical\nlocalization, anomalous diffusion, or partial delocalization, and can describe\nelectrons in a magnetic field. Three different quantum algorithms are presented\nand analyzed, enabling to simulate efficiently the evolution operator of this\nsystem with different precision using different resources. Depending on the\nparameters chosen, the system is near-integrable, localized, or partially\ndelocalized. In each case we identify transport or spectral quantities which\ncan be obtained more efficiently on a quantum computer than on a classical one.\nIn most cases, a polynomial gain compared to classical algorithms is obtained,\nwhich can be quadratic or less depending on the parameter regime. We also\npresent the effects of static imperfections on the quantities selected, and\nshow that depending on the regime of parameters, very different behaviors are\nobserved. Some quantities can be obtained reliably with moderate levels of\nimperfection, whereas others are exponentially sensitive to imperfection\nstrength. In particular, the imperfection threshold for delocalization becomes\nexponentially small in the partially delocalized regime. Our results show that\ninteresting behavior can be observed with as little as 7-8 qubits, and can be\nreliably measured in presence of moderate levels of internal imperfections.",
"arxiv_id": "quant-ph/0409028",
"authors": [
"Benjamin Levi",
"Bertrand Georgeot"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"nlin.CD"
],
"doi": "10.1103/PhysRevE.70.056218",
"journal_ref": "Physical Review E 70 (2004) 056218",
"title": "Quantum Computation of a Complex System : the Kicked Harper Model",
"url": "https://arxiv.org/abs/quant-ph/0409028"
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