dorsal/arxiv
View SchemaDelocalization border and onset of chaos in a model of quantum computation
| Authors | G. P. Berman, F. Borgonovi, F. M. Izrailev, V. I. Tsifrinovich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0104086 |
| URL | https://arxiv.org/abs/quant-ph/0104086 |
| DOI | 10.1103/PhysRevE.64.056226 |
| Journal | Phys. Rev. E 64, 056226 (2001) |
Abstract
We study the properties of spectra and eigenfunctions for a chain of $1/2- $spins (qubits) in an external time-dependent magnetic field, and under the conditions of non-selective excitation (when the amplitude of the magnetic field is large). This model is known as a possible candidate for experimental realization of quantum computation. We present the theory for finding delocalization transition and show that for the interaction between nearest qubits, the transition is very different from that to quantum chaos. We explain this phenomena by showing that in the considered region of parameters our model is close to an integrable one. According to a general opinion, the threshold for the onset of quantum chaos due to the interqubit interaction decreases with an increase of the number of qubits. Contrary to this expectation, for a magnetic field with constant gradient we have found that chaos border does not depend on the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting our analysis. Random models with long-range interactions are studied as well. In particular, we show that in this case the delocalization and quantum chaos borders coincide.
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"abstract": "We study the properties of spectra and eigenfunctions for a chain of $1/2-\n$spins (qubits) in an external time-dependent magnetic field, and under the\nconditions of non-selective excitation (when the amplitude of the magnetic\nfield is large). This model is known as a possible candidate for experimental\nrealization of quantum computation. We present the theory for finding\ndelocalization transition and show that for the interaction between nearest\nqubits, the transition is very different from that to quantum chaos. We explain\nthis phenomena by showing that in the considered region of parameters our model\nis close to an integrable one. According to a general opinion, the threshold\nfor the onset of quantum chaos due to the interqubit interaction decreases with\nan increase of the number of qubits. Contrary to this expectation, for a\nmagnetic field with constant gradient we have found that chaos border does not\ndepend on the number of qubits. We give analytical estimates which explain this\neffect, together with numerical data supporting our analysis. Random models\nwith long-range interactions are studied as well. In particular, we show that\nin this case the delocalization and quantum chaos borders coincide.",
"arxiv_id": "quant-ph/0104086",
"authors": [
"G. P. Berman",
"F. Borgonovi",
"F. M. Izrailev",
"V. I. Tsifrinovich"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"nlin.CD"
],
"doi": "10.1103/PhysRevE.64.056226",
"journal_ref": "Phys. Rev. E 64, 056226 (2001)",
"title": "Delocalization border and onset of chaos in a model of quantum computation",
"url": "https://arxiv.org/abs/quant-ph/0104086"
},
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