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Quantum Information Processing
Erschienen in: Quantum Information Processing 1/2021

01.01.2021

True experimental reconstruction of quantum states and processes via convex optimization

verfasst von: Akshay Gaikwad, Arvind, Kavita Dorai

Erschienen in: Quantum Information Processing | Ausgabe 1/2021

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Abstract

We use a constrained convex optimization (CCO) method to experimentally characterize arbitrary quantum states and unknown quantum processes on a two-qubit NMR quantum information processor. Standard protocols for quantum state and quantum process tomography are based on linear inversion, which often result in an unphysical density matrix and hence an invalid process matrix. The CCO method, on the other hand, produces physically valid density matrices and process matrices, with significantly improved fidelity as compared to the standard methods. We use the CCO method to estimate the Kraus operators and characterize gates in the presence of errors due to decoherence. We then assume Markovian system dynamics and use a Lindblad master equation in conjunction with the CCO method, to completely characterize the noise processes present in the NMR system.
Vorheriger Artikel Locally distinguishable maximally entangled states by two-way LOCC
Nächster Artikel Tripartite quantum discord dynamics in qubits driven by the joint influence of distinct classical noises

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Literatur
1.
Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Quantum computers. Nature 464, 45 (2010)ADS
2.
James, D.F.V., Kwiat, P.G., William J, M., White, A.G.: Measurement of qubits. Phys. Rev. A 64, 052312 (2001)ADS
3.
Long, G.L., Yan, H.Y., Sun, Y.: Analysis of density matrix reconstruction in NMR quantum computing. J. Opt. B. Quantum Semiclass. Opt. 3, 376 (2001)ADS
4.
O’Brien, J.L., Pryde, G.J., Gilchrist, A., James, D.F.V., Langford, N.K., Ralph, T.C., White, A.G.: Quantum process tomography of a controlled-NOT gate. Phys. Rev. Lett. 93, 080502 (2004)ADS
5.
Chuang, I.L., Nielsen, M.A.: Prescription for experimental determination of the dynamics of a quantum black box. J. Mod. Opt. 44, 2455–2467 (1997)ADS
6.
Bartkiewicz, K., Černoch, A., Lemr, K., Miranowicz, A.: Priority choice experimental two-qubit tomography: measuring one by one all elements of density matrices. Sci. Rep. 6, 19610 (2016)ADS
7.
Miranowicz, A., Bartkiewicz, K., Peřina, J., Koashi, M., Imoto, N., Nori, F.: Optimal two-qubit tomography based on local and global measurements: maximal robustness against errors as described by condition numbers. Phys. Rev. A 90, 062123 (2014)ADS
8.
Wölk, S., Sriarunothai, T., Giri, G.S., Wunderlich, C.: Distinguishing between statistical and systematic errors in quantum process tomography. New J. Phys. 21, 013015 (2019)ADS
9.
Xin, T., Dawei, L., Klassen, J., Nengkun, Y., Ji, Z., Chen, J., Ma, X., Long, G., Zeng, B., Laflamme, R.: Quantum state tomography via reduced density matrices. Phys. Rev. Lett. 118, 020401 (2017)ADSMathSciNet
10.
Li, J., Huang, S., Luo, Z., Li, K., Dawei, L., Zeng, B.: Optimal design of measurement settings for quantum-state-tomography experiments. Phys. Rev. A 96, 032307 (2017)ADS
11.
Miranowicz, A.,   Özdemir, K., Bajer, J., Yusa, G., Imoto, N., Hirayama, Y., Nori, F.: Quantum state tomography of large nuclear spins in a semiconductor quantum well: optimal robustness against errors as quantified by condition numbers. Phys. Rev. B 92, 075312 (2015)ADS
12.
Vind, F.A., Souza, A.M., Sarthour, R.S., Oliveira, I.S.: Quantum state tomography for strongly coupled nuclear spin systems. Phys. Rev. A 90, 062339 (2014)ADS
13.
Qi, B., Hou, Z., Wang, Y., Dong, D., Zhong, H.-S., Li, L., Xiang, G.-Y., Wiseman, H.M., Li, C.-F., Guo, G.-C.: Adaptive quantum state tomography via linear regression estimation: theory and two-qubit experiment. Quantum Inf. Process. 3, 19 (2017)ADS
14.
Schwemmer, C., Knips, L., Richart, D., Weinfurter, H., Moroder, T., Kleinmann, M., Gühne, O.: Systematic errors in current quantum state tomography tools. Phys. Rev. Lett. 114, 080403 (2015)ADS
15.
Shang, J., Zhang, Z., Ng, H.K.: Superfast maximum-likelihood reconstruction for quantum tomography. Phys. Rev. A 95, 062336 (2017)ADSMathSciNet
16.
17.
Ferrie, C.: Self-guided quantum tomography. Phys. Rev. Lett. 113, 190404 (2014b)ADS
18.
Yang, J., Cong, S., Liu, X., Li, Z., Li, K.: Effective quantum state reconstruction using compressed sensing in NMR quantum computing. Phys. Rev. A 96, 052101 (2017)ADS
19.
Altepeter, J.B., Branning, D., Jeffrey, E., Wei, T.C., Kwiat, P.G., Thew, R.T., O’Brien, J.L., Nielsen, M.A., White, A.G.: Ancilla-assisted quantum process tomography. Phys. Rev. Lett. 90, 193601 (2003)ADS
20.
Branderhorst, M.P.A., Nunn, J., Walmsley, I.A., Kosut, R.L.: Simplified quantum process tomography. New J. Phys. 11, 115010 (2009)ADS
21.
Perito, I., Roncaglia, A.J., Bendersky, A.: Selective and efficient quantum process tomography in arbitrary finite dimension. Phys. Rev. A 98, 062303 (2018)ADS
22.
Merkel, S.T., Gambetta, J.M., Smolin, J.A., Poletto, S., Córcoles, A.D., Johnson, B.R., Ryan, C.A., Steffen, M.: Self-consistent quantum process tomography. Phys. Rev. A 87, 062119 (2013)ADS
23.
Rodionov, A.V., Veitia, A., Barends, R., Kelly, J., Sank, D., Wenner, J., Martinis, J.M., Kosut, R.L., Korotkov, A.N.: Compressed sensing quantum process tomography for superconducting quantum gates. Phys. Rev. B 90, 144504 (2014)ADS
24.
Struchalin, G.I., Pogorelov, I.A., Straupe, S.S., Kravtsov, K.S., Radchenko, I.V., Kulik, S.P.: Experimental adaptive quantum tomography of two-qubit states. Phys. Rev. A 93, 012103 (2016)ADS
25.
Pogorelov, I.A., Struchalin, G.I., Straupe, S.S., Radchenko, I.V., Kravtsov, K.S., Kulik, S.P.: Experimental adaptive process tomography. Phys. Rev. A 95, 012302 (2017)ADS
26.
Maciel, T.O., Vianna, R.O., Sarthour, R.S., Oliveira, I.S.: Quantum process tomography with informational incomplete data of two J-coupled heterogeneous spins relaxation in a time window much greater than T1. New J. Phys. 17, 113012 (2015)ADS
27.
Singh, H., Arvind: Constructing valid density matrices on an NMR quantum information processor via maximum likelihood estimation. Phys. Lett. A 380, 3051–3056 (2016a)
28.
Gaikwad, A., Rehal, D., Singh, A., Arvind: Experimental demonstration of selective quantum process tomography on an NMR quantum information processor. Phys. Rev. A 97, 022311 (2018)
29.
Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Katz, N., Lucero, E., O’Connell, A., Wang, H., Cleland, A.N., Martinis, J.M.: Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state. Nature 4, 523–526 (2008)
30.
Howard, M., Twamley, J., Wittmann, C., Gaebel, T., Jelezko, F., Wrachtrup, J.: Quantum process tomography and Linblad estimation of a solid-state qubit. New J. Phys. 8, 33–33 (2006)ADS
31.
Zhang, J., Souza, A.M., Brandao, F.D., Suter, D.: Protected quantum computing: interleaving gate operations with dynamical decoupling sequences. Phys. Rev. Lett. 112, 050502 (2014)ADS
32.
Schmiegelow, C.T., Larotonda, M.A., Paz, J.P.: Selective and efficient quantum process tomography with single photons. Phys. Rev. Lett. 104, 123601 (2010)ADS
33.
Robert, J., Chapman, C.F., Peruzzo, A.: Experimental demonstration of self-guided quantum tomography. Phys. Rev. Lett. 117, 040402 (2016)
34.
Wu, Z., Li, S., Zheng, W., Peng, X., Feng, M.: Experimental demonstration of simplified quantum process tomography. J. Chem. Phys. 138, 024318 (2013)ADS
35.
Schmiegelow, C.T., Bendersky, A., Larotonda, M.A., Paz, J.P.: Selective and efficient quantum process tomography without ancilla. Phys. Rev. Lett. 107, 100502 (2011)ADS
36.
Kim, Y., Kim, Y.-S., Lee, S.-Y., Han, S.-W., Moon, S., Kim, Y.-H., Cho, Y.-W.: Direct quantum process tomography via measuring sequential weak values of incompatible observables. Nat. Commun. 9, 192 (2018)ADS
37.
Myrskog, S.H., Fox, J.K., Mitchell, M.W., Steinberg, A.M.: Quantum process tomography on vibrational states of atoms in an optical lattice. Phys. Rev. A 72, 013615 (2005)ADS
38.
Riebe, M., Kim, K., Schindler, P., Monz, T., Schmidt, P.O., Körber, T.K., Hänsel, W., Häffner, H., Roos, C.F., Blatt, R.: Process tomography of ion trap quantum gates. Phys. Rev. Lett. 97, 220407 (2006)ADS
39.
Bialczak, R.C., Ansmann, M., Hofheinz, M., Lucero, E., Neeley, M., O’ Connell, A.D., Sank, D., Wang, H., Wenner, J., Steffen, M., Cleland, A.N., Martinis, J.M.: Quantum process tomography of a universal entangling gate implemented with Josephson phase qubits. Nat. Phys. 6, 409 (2010)
40.
Mohseni, M., Rezakhani, A.T., Lidar, D.A.: Quantum-process tomography: resource analysis of different strategies. Phys. Rev. A 77, 032322 (2008)ADS
41.
Branderhorst, M.P.A., Walmsley, I.A., Kosut, R.L., Rabitz, H.: Optimal experiment design for quantum state tomography of a molecular vibrational mode. J. Phys. B At. Mol. Opt. Phys. 41, 074004 (2008)ADS
42.
43.
Vandersypen, L.M.K., Chuang, I.L.: NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037–1069 (2005)ADS
44.
Singh, A., Arvind: Entanglement detection on an NMR quantum-information processor using random local measurements. Phys. Rev. A 94, 062309 (2016b)
45.
Lofberg, J.: YALMIP: a toolbox for modeling and optimization in MATLAB. In: 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508) pp. 284–289 (2004)
46.
47.
Weinstein, Y.S., Pravia, M.A., Fortunato, E.M., Lloyd, S., Cory, D.G.: Implementation of the quantum Fourier transform. Phys. Rev. Lett. 86, 1889–1891 (2001)ADS
48.
Oliveira, I. S., Bonagamba, T. J., Sarthour, R. S., Freitas, J. C. C., deAzevedo, E. R.: NMR Quantum Information Processing. (Elsevier, Linacre House, Jordan Hill, Oxford OX2 8DP, UK, 2007)
49.
Gavini-Viana, A., Souza, A.M., Soares-Pinto, D.O., Teles, J., Sarthour, R.S., deAzevedo, E.R., Bonagamba, T.J., Oliveira, I.S.: Normalization procedure for relaxation studies in NMR quantum information processing. Quantum Inf. Process. 9, 575–589 (2010)MATH
50.
Kraus, K., Bohm, A., Dollard, J.D., Wootters, W.H.: States, Effects, and Operations: Fundamental Notions of Quantum Theory. Springer, Berlin (1983)
51.
Childs, A.M., Chuang, I.L., Leung, D.W.: Realization of quantum process tomography in NMR. Phys. Rev. A 64, 012314 (2001)ADS
52.
Kofman, A.G., Korotkov, A.N.: Two-qubit decoherence mechanisms revealed via quantum process tomography. Phys. Rev. A 80, 042103 (2009)ADSMathSciNet
53.
Singh, H., Arvind: Experimentally freezing quantum discord in a dephasing environment using dynamical decoupling. EPL Europhys. Lett. 118, 50001 (2017)
Metadaten
Titel
True experimental reconstruction of quantum states and processes via convex optimization
verfasst von
Akshay Gaikwad
Arvind
Kavita Dorai
Publikationsdatum
01.01.2021
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 1/2021
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02930-z

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