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Interpretation of tomography and spectroscopy as dual forms of quantum computation

Nature volume 418, pages 59–62 (2002)Cite this article

Abstract

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 tomography1, 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 computation2. Specifically, we find that the phase estimation algorithm3 (which underlies a quantum computer's ability to perform efficient simulations4 and to factorize large numbers5) 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.

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Figure 1: The scattering circuit.
Figure 2: Circuit for evaluating the spectral density of a hamiltonian h modulated by the energy populations of the state ρ.
Figure 3: Measured Wigner functions for the four computational states of a two-qubit system.

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Acknowledgements

This work was supported by UBACYT, ANPCYT, Fundación Autorchas (J.P.P., C.M. and M.S.) and NSA (E.K., R.L. and C.N.).

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Authors and Affiliations

  1. Departamento de Física, FCEN, UBA, Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina

    César Miquel & Juan Pablo Paz

  2. Unidad de Actividad Física, Tandar, CNEA, Buenos Aires, Argentina

    Marcos Saraceno

  3. Los Alamos National Laboratory, MS B265, Los Alamos, 87545, New Mexico, USA

    Emanuel Knill & Camille Negrevergne

  4. Department of Physics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Raymond Laflamme

  5. Perimeter Institute for Theoretical Physics, Waterloo, 35 King Street N, Ontario, N2J 2W9, Canada

    Raymond Laflamme

Authors
  1. César Miquel
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  2. Juan Pablo Paz
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  3. Marcos Saraceno
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  4. Emanuel Knill
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  5. Raymond Laflamme
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  6. Camille Negrevergne
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Correspondence to Juan Pablo Paz.

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Miquel, C., Paz, J., Saraceno, M. et al. Interpretation of tomography and spectroscopy as dual forms of quantum computation. Nature 418, 59–62 (2002). https://doi.org/10.1038/nature00801

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