dorsal/arxiv
View SchemaEfficient Decoupling Schemes Based on Hamilton Cycles
| Authors | Martin Roetteler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408078 |
| URL | https://arxiv.org/abs/quant-ph/0408078 |
| Journal | Journal of Mathematical Physics, 49:042106, 2008 |
Abstract
Decoupling the interactions in a spin network governed by a pair-interaction Hamiltonian is a well-studied problem. Combinatorial schemes for decoupling and for manipulating the couplings of Hamiltonians have been developed which use selective pulses. In this paper we consider an additional requirement on these pulse sequences: as few {\em different} control operations as possible should be used. This requirement is motivated by the fact that optimizing each individual selective pulse will be expensive, i. e., it is desirable to use as few different selective pulses as possible. For an arbitrary $d$-dimensional system we show that the ability to implement only two control operations is sufficient to turn off the time evolution. In case of a bipartite system with local control we show that four different control operations are sufficient. Turning to networks consisting of several $d$-dimensional nodes which are governed by a pair-interaction Hamiltonian, we show that decoupling can be achieved if one is able to control a number of different control operations which is logarithmic in the number of nodes.
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"abstract": "Decoupling the interactions in a spin network governed by a pair-interaction\nHamiltonian is a well-studied problem. Combinatorial schemes for decoupling and\nfor manipulating the couplings of Hamiltonians have been developed which use\nselective pulses. In this paper we consider an additional requirement on these\npulse sequences: as few {\\em different} control operations as possible should\nbe used. This requirement is motivated by the fact that optimizing each\nindividual selective pulse will be expensive, i. e., it is desirable to use as\nfew different selective pulses as possible. For an arbitrary $d$-dimensional\nsystem we show that the ability to implement only two control operations is\nsufficient to turn off the time evolution. In case of a bipartite system with\nlocal control we show that four different control operations are sufficient.\nTurning to networks consisting of several $d$-dimensional nodes which are\ngoverned by a pair-interaction Hamiltonian, we show that decoupling can be\nachieved if one is able to control a number of different control operations\nwhich is logarithmic in the number of nodes.",
"arxiv_id": "quant-ph/0408078",
"authors": [
"Martin Roetteler"
],
"categories": [
"quant-ph",
"cs.ET"
],
"journal_ref": "Journal of Mathematical Physics, 49:042106, 2008",
"title": "Efficient Decoupling Schemes Based on Hamilton Cycles",
"url": "https://arxiv.org/abs/quant-ph/0408078"
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