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Abstract:

We present in a unified manner the existing methods for scalable partial quantum process tomography. We focus on two main approaches: the one presented in Bendersky [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.100.190403 100, 190403 (2008)] and the ones described, respectively, in Emerson [ScienceSCIEAS0036-807510.1126/science.1145699 317, 1893 (2007)] and López [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.79.042328 79, 042328 (2009)], which can be combined together. The methods share an essential feature: They are based on the idea that the tomography of a quantum map can be efficiently performed by studying certain properties of a twirling of such a map. From this perspective, in this paper we present extensions, improvements, and comparative analyses of the scalable methods for partial quantum process tomography. We also clarify the significance of the extracted information, and we introduce interesting and useful properties of the χ-matrix representation of quantum maps that can be used to establish a clearer path toward achieving full tomography of quantum processes in a scalable way. © 2010 The American Physical Society.

Registro:

Documento: Artículo
Título:Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies
Autor:López, C.C.; Bendersky, A.; Paz, J.P.; Cory, D.G.
Filiación:Department of Nuclear Science and Engineering, MIT, Cambridge, MA 02139, United States
Theoretische Physik, Universität des Saarlandes, D-66041 Saarbrücken, Germany
Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
Departamento de Física, FCEyN, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Perimeter Institute for Theoretical Physics, Waterloo, ON N2J 2W9, Canada
Palabras clave:Comparative analysis; Emerson; Existing method; Matrix representation; Quantum maps; Quantum process; Quantum process tomography; Scalable methods; Useful properties; Scalability; Tomography
Año:2010
Volumen:81
Número:6
DOI: http://dx.doi.org/10.1103/PhysRevA.81.062113
Título revista:Physical Review A - Atomic, Molecular, and Optical Physics
Título revista abreviado:Phys Rev A
ISSN:10502947
CODEN:PLRAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10502947_v81_n6_p_Lopez

Referencias:

  • Nielsen M, A., Chuang, I.L., (2000) Quantum Computation and Quantum Information, , Cambridge University Press, Cambridge, UK
  • Mohseni, M., Rezakhani, A.T., Lidar, D.A., Quantum-process tomography: Resource analysis of different strategies (2008) Physical Review A - Atomic, Molecular, and Optical Physics, 77 (3), p. 032322. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevA.77.032322&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevA.77.032322
  • Emerson, J., Alicki, R., Zyczkowski, K., Scalable noise estimation with random unitary operators (2005) Journal of Optics B: Quantum and Semiclassical Optics, 7 (10), pp. S347-S352. , DOI 10.1088/1464-4266/7/10/021, PII S1464426605972595
  • Lévi, B., López, C.C., Emerson, J., Cory, D.G., (2007) Phys. Rev. A, 75, p. 022314. , PLRAAN 1050-2947 10.1103/PhysRevA.75.022314
  • Dankert, C., Cleve, R., Emerson, J., Livine, E., (2009) Phys. Rev. A, 80, p. 012304. , PLRAAN 1050-2947 10.1103/PhysRevA.80.012304
  • e-print arXiv: quant-ph/0606161v1 (2006); Emerson, J., Silva, M., Moussa, O., Ryan, C., Laforest, M., Baugh, J., Cory, D.G., Laflamme, R., Symmetrized characterization of noisy quantum processes (2007) Science, 317 (5846), pp. 1893-1896. , DOI 10.1126/science.1145699
  • Silva, M., Magesan, E., Kribs, D.W., Emerson, J., (2008) Phys. Rev. A, 78, p. 012347. , PLRAAN 1050-2947 10.1103/PhysRevA.78.012347
  • Bendersky, A., Pastawski, F., Paz, J.P., Selective and efficient estimation of parameters for quantum process tomography (2008) Physical Review Letters, 100 (19), p. 190403. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevLett.100.190403&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevLett.100.190403
  • López, C.C., Lévi, B., Cory, D.G., (2009) Phys. Rev. A, 79, p. 042328. , PLRAAN 1050-2947 10.1103/PhysRevA.79.042328
  • Bendersky, A., Pastawski, F., Paz, J.P., (2009) Phys. Rev. A, 80, p. 032116. , PLRAAN 1050-2947 10.1103/PhysRevA.80.032116
  • Bennett, C.H., Divincenzo, D.P., Smolin, J.A., Wootters, W.K., (1996) Phys. Rev. A, 54, p. 3824. , PLRAAN 1050-2947 10.1103/PhysRevA.54.3824
  • An example of such kind of basis is the one formed by the generalized Pauli operators. However, until Sec. IV we refrain from using a particular basis so our results remain general; Shabani, A., Lidar, D.A., (2009) Phys. Rev. Lett., 102, p. 100402. , PRLTAO 0031-9007 10.1103/PhysRevLett.102.100402
  • Samuel, S., (1980) J. Math. Phys., 21, p. 2695. , JMAPAQ 0022-2488 10.1063/1.524386
  • Mello, P.A., (1990) J. Phys. A, 23, p. 4061. , JPHAC5 0305-4470 10.1088/0305-4470/23/18/013
  • Brouwer, P.W., Beenakker, C.W.J., (1996) J. Math. Phys., 37, p. 4904. , JMAPAQ 0022-2488 10.1063/1.531667
  • Renes, J.M., Blume-Kohout, R., Scott, A.J., Caves, C.M., Symmetric informationally complete quantum measurements (2004) Journal of Mathematical Physics, 45 (6), pp. 2171-2180. , DOI 10.1063/1.1737053
  • Pechukas, P., (1994) Phys. Rev. Lett., 73, p. 1060. , PRLTAO 0031-9007 10.1103/PhysRevLett.73.1060
  • Alicki, R., (1995) Phys. Rev. Lett., 75, p. 3020. , PRLTAO 0031-9007 10.1103/PhysRevLett.75.3020
  • Pechukas, P., (1995) Phys. Rev. Lett., 75, p. 3021. , PRLTAO 0031-9007 10.1103/PhysRevLett.75.3021
  • Carteret, H.A., Terno, D.R., Zyczkowski, K., Dynamics beyond completely positive maps: Some properties and applications (2008) Physical Review A - Atomic, Molecular, and Optical Physics, 77 (4), p. 042113. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevA.77.042113&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevA.77.042113
  • Gross, D., Audenaert, K., Eisert, J., (2007) J. Math. Phys., 48, p. 052104. , JMAPAQ 0022-2488 10.1063/1.2716992
  • López, C.C., (2009), http://hdl.handle.net/1721.1/51777, Ph.D. thesis Massachusetts Institute of Technology; Schmiegelow, C.T., Larotonda, M.A., Paz, J.P., (2010) Phys. Rev. Lett., 104, p. 123601. , PRLTAO 0031-9007 10.1103/PhysRevLett.104.123601
  • Nielsen, M.A., (2002) Phys. Lett. A, 303, p. 249. , PYLAAG 0375-9601 10.1016/S0375-9601(02)01272-0
  • Klappenecker, A., Roetteler, M., (2005) Proceedings of the IEEE International Symposium on Information Theory, pp. 1740-1744. , in IEEE, Adelaide, SA
  • Gottesman, D., (1997), Ph.D. thesis, California Institute of Techonology; e-print arXiv: quant-ph/9705052v1; Gottesman, D., (1996) Phys. Rev. A, 54, p. 1862. , PLRAAN 1050-2947 10.1103/PhysRevA.54.1862
  • Dankert, C., (2005), Master's thesis, University of Waterloo; e-print arXiv: quant-ph/0512217v2; Mitchell, M.W., Ellenor, C.W., Schneider, S., Steinberg, A.M., (2003) Phys. Rev. Lett., 91, p. 120402. , Examples of process tomography using the largest systems in different setups are as follows: (a) with photons, PRLTAO 0031-9007 10.1103/PhysRevLett. 91.120402
  • O'Brien, J.L., Pryde, G.J., Gilchrist, A., James, D.F.V., Langford, N.K., Ralph, T.C., White, A.G., (2004) Phys. Rev. Lett., 93, p. 080502. , PRLTAO 0031-9007 10.1103/PhysRevLett.93.080502
  • Weinstein, Y.S., Havel, T.F., Emerson, J., Boulant, N., Saraceno, M., Lloyd, S., (2004) J. Chem. Phys., 121, p. 6117. , JCPSA6 0021-9606 10.1063/1.1785151
  • Myrskog, S.H., Fox, J.K., Mitchell, M.W., Steinberg, A.M., Quantum process tomography on vibrational states of atoms in an optical lattice (2005) Physical Review A - Atomic, Molecular, and Optical Physics, 72 (1), p. 5. , http://oai.aps.org/oai/?verb=ListRecords&metadataPrefix= oai_apsmeta_2&set=journal:PRA:72, DOI 10.1103/PhysRevA.72.013615, 013615
  • Howard, M., Twamley, J., Wittmann, C., Gaebel, T., Jelezko, F., Wrachtrup, J., (2006) New J. Phys., 8, p. 33. , NJOPFM 1367-2630 10.1088/1367-2630/8/3/033
  • Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Katz, N., Lucero, E., O'Connell, A., Martinis, J.M., (2008) Nature Phys., 4, p. 523. , NJOPFM 1745-2473 10.1038/nphys972
  • Chow, J.M., Gambetta, J.M., Tornberg, L., Koch, J., Bishop, L.S., Houck, A.A., Johnson, B.R., Schoelkopf, R.J., (2009) Phys. Rev. Lett., 102, p. 090502. , PRLTAO 0031-9007 10.1103/PhysRevLett.102.090502
  • Monz, T., Kim, K., Hänsel, W., Riebe, M., Villar, A.S., Schindler, P., Chwalla, M., Blatt, R., (2009) Phys. Rev. Lett., 102, p. 040501. , PRLTAO 0031-9007 10.1103/PhysRevLett.102.040501
  • Hanneke, D., Home, J.P., Jost, J.D., Amini, J.M., Leibfried, D., Wineland, D.J., (2009) Nature Phys., 6, p. 13. , PRLTAO 1745-2473 10.1038/nphys1453
  • The set {e-iπσq/4,e -iπσq/4σp} with p,q=x,y,z generates only half of the Clifford group for one qubit (up to a global phase). Nevertheless, this set of 12 operators is enough to implement the Clifford twirl we need; http://digbib.ubka.uni-karlsruhe.de/volltexte/181894, For example, for wco<n/2, it is trivial to prove that Mco≤(wco+1)(ne/wco)wco. In T. Worsch, Universität Karlsruhe, Fakultät für Informatik, Technical Report No. 31/94, 1994; Branderhorst, M.P.A., Nunn, J., Walmsley, I.A., Kosut, R.L., (2009) New J. Phys., 11, p. 115010. , NJOPFM 1367-2630 10.1088/1367-2630/11/11/115010

Citas:

---------- APA ----------
López, C.C., Bendersky, A., Paz, J.P. & Cory, D.G. (2010) . Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies. Physical Review A - Atomic, Molecular, and Optical Physics, 81(6).
http://dx.doi.org/10.1103/PhysRevA.81.062113
---------- CHICAGO ----------
López, C.C., Bendersky, A., Paz, J.P., Cory, D.G. "Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies" . Physical Review A - Atomic, Molecular, and Optical Physics 81, no. 6 (2010).
http://dx.doi.org/10.1103/PhysRevA.81.062113
---------- MLA ----------
López, C.C., Bendersky, A., Paz, J.P., Cory, D.G. "Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies" . Physical Review A - Atomic, Molecular, and Optical Physics, vol. 81, no. 6, 2010.
http://dx.doi.org/10.1103/PhysRevA.81.062113
---------- VANCOUVER ----------
López, C.C., Bendersky, A., Paz, J.P., Cory, D.G. Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies. Phys Rev A. 2010;81(6).
http://dx.doi.org/10.1103/PhysRevA.81.062113