Interpretation of tomography and spectroscopy as dual forms of quantum computation
It is important to be able to determine the state of a quantum system and to measure properties of its evolution. State determination can be achieved using tomography, in which the system is subjected to a series of experiments, whereas spectroscopy can be used to probe the energy spectrum associate...
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2002
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paper:paper_00280836_v418_n6893_p59_Miquel2023-06-08T14:54:43Z Interpretation of tomography and spectroscopy as dual forms of quantum computation Miquel, César Paz, Juan Pablo Saraceno, Marcos Algorithms Computer simulation Nuclear magnetic resonance Numerical methods Spectroscopy Spectrum analysis Tomography Quantum computation Quantum theory physics spectroscopy tomography algorithm article computer system evolution integrated circuit mathematical analysis mathematical model nuclear magnetic resonance priority journal probability quantum mechanics quantum theory radiation scattering spectroscopy statistics tomography It is important to be able to determine the state of a quantum system and to measure properties of its evolution. State determination can be achieved using tomography, in which the system is subjected to a series of experiments, whereas spectroscopy can be used to probe the energy spectrum associated with the system's evolution. Here we show that, for a quantum system whose state or evolution can be modelled on a quantum computer, tomography and spectroscopy can be interpreted as dual forms of quantum computation. Specifically, we find that the phase estimation algorithm (which underlies a quantum computer's ability to perform efficient simulations and to factorize large numbers) can be adapted for tomography or spectroscopy. This is analogous to the situation encountered in scattering experiments, in which it is possible to obtain information about both the state of the scatterer and its interactions. We provide an experimental demonstration of the tomographic application by performing a measurement of the Wigner function (a phase space distribution) of a quantum system. For this purpose, we use three qubits formed from spin-1/2 nuclei in a quantum computation involving liquid-state nuclear magnetic resonance. Fil:Miquel, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Paz, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Saraceno, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2002 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00280836_v418_n6893_p59_Miquel http://hdl.handle.net/20.500.12110/paper_00280836_v418_n6893_p59_Miquel |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Algorithms Computer simulation Nuclear magnetic resonance Numerical methods Spectroscopy Spectrum analysis Tomography Quantum computation Quantum theory physics spectroscopy tomography algorithm article computer system evolution integrated circuit mathematical analysis mathematical model nuclear magnetic resonance priority journal probability quantum mechanics quantum theory radiation scattering spectroscopy statistics tomography |
| spellingShingle |
Algorithms Computer simulation Nuclear magnetic resonance Numerical methods Spectroscopy Spectrum analysis Tomography Quantum computation Quantum theory physics spectroscopy tomography algorithm article computer system evolution integrated circuit mathematical analysis mathematical model nuclear magnetic resonance priority journal probability quantum mechanics quantum theory radiation scattering spectroscopy statistics tomography Miquel, César Paz, Juan Pablo Saraceno, Marcos Interpretation of tomography and spectroscopy as dual forms of quantum computation |
| topic_facet |
Algorithms Computer simulation Nuclear magnetic resonance Numerical methods Spectroscopy Spectrum analysis Tomography Quantum computation Quantum theory physics spectroscopy tomography algorithm article computer system evolution integrated circuit mathematical analysis mathematical model nuclear magnetic resonance priority journal probability quantum mechanics quantum theory radiation scattering spectroscopy statistics tomography |
| description |
It is important to be able to determine the state of a quantum system and to measure properties of its evolution. State determination can be achieved using tomography, in which the system is subjected to a series of experiments, whereas spectroscopy can be used to probe the energy spectrum associated with the system's evolution. Here we show that, for a quantum system whose state or evolution can be modelled on a quantum computer, tomography and spectroscopy can be interpreted as dual forms of quantum computation. Specifically, we find that the phase estimation algorithm (which underlies a quantum computer's ability to perform efficient simulations and to factorize large numbers) can be adapted for tomography or spectroscopy. This is analogous to the situation encountered in scattering experiments, in which it is possible to obtain information about both the state of the scatterer and its interactions. We provide an experimental demonstration of the tomographic application by performing a measurement of the Wigner function (a phase space distribution) of a quantum system. For this purpose, we use three qubits formed from spin-1/2 nuclei in a quantum computation involving liquid-state nuclear magnetic resonance. |
| author |
Miquel, César Paz, Juan Pablo Saraceno, Marcos |
| author_facet |
Miquel, César Paz, Juan Pablo Saraceno, Marcos |
| author_sort |
Miquel, César |
| title |
Interpretation of tomography and spectroscopy as dual forms of quantum computation |
| title_short |
Interpretation of tomography and spectroscopy as dual forms of quantum computation |
| title_full |
Interpretation of tomography and spectroscopy as dual forms of quantum computation |
| title_fullStr |
Interpretation of tomography and spectroscopy as dual forms of quantum computation |
| title_full_unstemmed |
Interpretation of tomography and spectroscopy as dual forms of quantum computation |
| title_sort |
interpretation of tomography and spectroscopy as dual forms of quantum computation |
| publishDate |
2002 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00280836_v418_n6893_p59_Miquel http://hdl.handle.net/20.500.12110/paper_00280836_v418_n6893_p59_Miquel |
| work_keys_str_mv |
AT miquelcesar interpretationoftomographyandspectroscopyasdualformsofquantumcomputation AT pazjuanpablo interpretationoftomographyandspectroscopyasdualformsofquantumcomputation AT saracenomarcos interpretationoftomographyandspectroscopyasdualformsofquantumcomputation |
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