dorsal/arxiv
View SchemaQuantum Codes for Controlling Coherent Evolution
| Authors | Yehuda Sharf, Timothy F. Havel, David G. Cory |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0004029 |
| URL | https://arxiv.org/abs/quant-ph/0004029 |
| DOI | 10.1063/1.1326071 |
Abstract
Control over spin dynamics has been obtained in NMR via coherent averaging, which is implemented through a sequence of RF pulses, and via quantum codes which can protect against incoherent evolution. Here, we discuss the design and implementation of quantum codes to protect against coherent evolution. A detailed example is given of a quantum code for protecting two data qubits from evolution under a weak coupling (Ising) term in the Hamiltonian, using an ``isolated'' ancilla which does not evolve on the experimental time scale. The code is realized in a three-spin system by liquid-state NMR spectroscopy on 13C-labelled alanine, and tested for two initial states. It is also shown that for coherent evolution and isolated ancillae, codes exist that do not require the ancillae to initially be in a (pseudo-)pure state. Finally, it is shown that even with non-isolated ancillae quantum codes exist which can protect against evolution under weak coupling. An example is presented for a six qubit code that protects two data spins to first order.
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"abstract": "Control over spin dynamics has been obtained in NMR via coherent averaging,\nwhich is implemented through a sequence of RF pulses, and via quantum codes\nwhich can protect against incoherent evolution. Here, we discuss the design and\nimplementation of quantum codes to protect against coherent evolution. A\ndetailed example is given of a quantum code for protecting two data qubits from\nevolution under a weak coupling (Ising) term in the Hamiltonian, using an\n``isolated\u0027\u0027 ancilla which does not evolve on the experimental time scale. The\ncode is realized in a three-spin system by liquid-state NMR spectroscopy on\n13C-labelled alanine, and tested for two initial states. It is also shown that\nfor coherent evolution and isolated ancillae, codes exist that do not require\nthe ancillae to initially be in a (pseudo-)pure state. Finally, it is shown\nthat even with non-isolated ancillae quantum codes exist which can protect\nagainst evolution under weak coupling. An example is presented for a six qubit\ncode that protects two data spins to first order.",
"arxiv_id": "quant-ph/0004029",
"authors": [
"Yehuda Sharf",
"Timothy F. Havel",
"David G. Cory"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1326071",
"title": "Quantum Codes for Controlling Coherent Evolution",
"url": "https://arxiv.org/abs/quant-ph/0004029"
},
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