dorsal/arxiv
View SchemaQuantum Process Tomography of the Quantum Fourier Transform
| Authors | Yaakov S. Weinstein, Timothy F. Havel, Joseph Emerson, Nicolas Boulant, Marcos Saraceno, Seth Lloyd, David G. Cory |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406239 |
| URL | https://arxiv.org/abs/quant-ph/0406239 |
| DOI | 10.1063/1.1785151 |
| Journal | J. Chem. Phys. 121(13), 6117-6133 (2004) |
Abstract
The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently-developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive - although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors during the quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cummulative effect of small errors in the single qubit gates.
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"abstract": "The results of quantum process tomography on a three-qubit nuclear magnetic\nresonance quantum information processor are presented, and shown to be\nconsistent with a detailed model of the system-plus-apparatus used for the\nexperiments. The quantum operation studied was the quantum Fourier transform,\nwhich is important in several quantum algorithms and poses a rigorous test for\nthe precision of our recently-developed strongly modulating control fields. The\nresults were analyzed in an attempt to decompose the implementation errors into\ncoherent (overall systematic), incoherent (microscopically deterministic), and\ndecoherent (microscopically random) components. This analysis yielded a\nsuperoperator consisting of a unitary part that was strongly correlated with\nthe theoretically expected unitary superoperator of the quantum Fourier\ntransform, an overall attenuation consistent with decoherence, and a residual\nportion that was not completely positive - although complete positivity is\nrequired for any quantum operation. By comparison with the results of computer\nsimulations, the lack of complete positivity was shown to be largely a\nconsequence of the incoherent errors during the quantum process tomography\nprocedure. These simulations further showed that coherent, incoherent, and\ndecoherent errors can often be identified by their distinctive effects on the\nspectrum of the overall superoperator. The gate fidelity of the experimentally\ndetermined superoperator was 0.64, while the correlation coefficient between\nexperimentally determined superoperator and the simulated superoperator was\n0.79; most of the discrepancies with the simulations could be explained by the\ncummulative effect of small errors in the single qubit gates.",
"arxiv_id": "quant-ph/0406239",
"authors": [
"Yaakov S. Weinstein",
"Timothy F. Havel",
"Joseph Emerson",
"Nicolas Boulant",
"Marcos Saraceno",
"Seth Lloyd",
"David G. Cory"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1785151",
"journal_ref": "J. Chem. Phys. 121(13), 6117-6133 (2004)",
"title": "Quantum Process Tomography of the Quantum Fourier Transform",
"url": "https://arxiv.org/abs/quant-ph/0406239"
},
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