dorsal/arxiv
View SchemaEncoding a qubit into multilevel subspaces
| Authors | Matthew Grace, Constantin Brif, Herschel Rabitz, Ian Walmsley, Robert Kosut, Daniel Lidar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412059 |
| URL | https://arxiv.org/abs/quant-ph/0412059 |
| DOI | 10.1088/1367-2630/8/3/035 |
| Journal | New J. Phys. 8, 35 (2006) |
Abstract
We present a formalism for encoding the logical basis of a qubit into subspaces of multiple physical levels. The need for this multilevel encoding arises naturally in situations where the speed of quantum operations exceeds the limits imposed by the addressability of individual energy levels of the qubit physical system. A basic feature of the multilevel encoding formalism is the logical equivalence of different physical states and correspondingly, of different physical transformations. This logical equivalence is a source of a significant flexibility in designing logical operations, while the multilevel structure inherently accommodates fast and intense broadband controls thereby facilitating faster quantum operations. Another important practical advantage of multilevel encoding is the ability to maintain full quantum-computational fidelity in the presence of mixing and decoherence within encoding subspaces. The formalism is developed in detail for single-qubit operations and generalized for multiple qubits. As an illustrative example, we perform a simulation of closed-loop optimal control of single-qubit operations for a model multilevel system, and subsequently apply these operations at finite temperatures to investigate the effect of decoherence on operational fidelity.
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"abstract": "We present a formalism for encoding the logical basis of a qubit into\nsubspaces of multiple physical levels. The need for this multilevel encoding\narises naturally in situations where the speed of quantum operations exceeds\nthe limits imposed by the addressability of individual energy levels of the\nqubit physical system. A basic feature of the multilevel encoding formalism is\nthe logical equivalence of different physical states and correspondingly, of\ndifferent physical transformations. This logical equivalence is a source of a\nsignificant flexibility in designing logical operations, while the multilevel\nstructure inherently accommodates fast and intense broadband controls thereby\nfacilitating faster quantum operations. Another important practical advantage\nof multilevel encoding is the ability to maintain full quantum-computational\nfidelity in the presence of mixing and decoherence within encoding subspaces.\nThe formalism is developed in detail for single-qubit operations and\ngeneralized for multiple qubits. As an illustrative example, we perform a\nsimulation of closed-loop optimal control of single-qubit operations for a\nmodel multilevel system, and subsequently apply these operations at finite\ntemperatures to investigate the effect of decoherence on operational fidelity.",
"arxiv_id": "quant-ph/0412059",
"authors": [
"Matthew Grace",
"Constantin Brif",
"Herschel Rabitz",
"Ian Walmsley",
"Robert Kosut",
"Daniel Lidar"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1367-2630/8/3/035",
"journal_ref": "New J. Phys. 8, 35 (2006)",
"title": "Encoding a qubit into multilevel subspaces",
"url": "https://arxiv.org/abs/quant-ph/0412059"
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