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Quantum Information Processing
Erschienen in: Quantum Information Processing 10/2021

01.10.2021

Quantum tomography benchmarking

verfasst von: B. I. Bantysh, A. Yu. Chernyavskiy, Yu. I. Bogdanov

Erschienen in: Quantum Information Processing | Ausgabe 10/2021

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Abstract

Recent advances in quantum computers and simulators are steadily leading us toward full-scale quantum computing devices. Due to the fact that debugging is necessary to create any computing device, quantum tomography (QT) is a critical milestone on this path. In practice, the choice between different QT methods faces the lack of comparison methodology. Modern research provides a wide range of QT methods, which differ in their application areas, as well as experimental and computational complexity. Testing such methods is also being made under different conditions, and various efficiency measures are being applied. Moreover, many methods have complex programming implementations; thus, comparison becomes extremely difficult. In this study, we have developed a general methodology for comparing quantum-state tomography methods. The methodology is based on an estimate of the resources needed to achieve the required accuracy. We have developed a software library (in MATLAB and Python) that makes it easy to analyze any QT method implementation through a series of numerical experiments. The conditions for such a simulation are set by the number of tests corresponding to real physical experiments. As a validation of the proposed methodology and software, we analyzed and compared a set of QT methods. The analysis revealed some method-specific features and provided estimates of the relative efficiency of the methods.
Vorheriger Artikel Comment on “controlled quantum secure direct communication with authentication protocol based on five-particle cluster state and classical XOR operation"
Nächster Artikel Perfect controlled joint remote state preparation of arbitrary multi-qubit states independent of entanglement degree of the quantum channel

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Fußnoten
1
Some measurements protocols could consider only a part of the measurement events and do not form complete POVM measurements. In this case, assuming N to be the total number of observed events could result in \(\eta > 1\) according to Eq. (3).
 
Literatur
1.
Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., Brandao, F.G., Buell, D.A., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505 (2019)ADSCrossRef
2.
Bernien, H., Schwartz, S., Keesling, A., Levine, H., Omran, A., Pichler, H., Choi, S., Zibrov, A.S., Endres, M., Greiner, M., et al.: Probing many-body dynamics on a 51-atom quantum simulator. Nature 551(7682), 579 (2017)ADSCrossRef
3.
Banaszek, K., Cramer, M., Gross, D.: Focus on quantum tomography. New J. Phys. (2013)
4.
Paris, M., Rehacek, J.: Quantum state estimation. In: Lecture Notes in Physics, p. 649. Springer, Heidelberg (2004)
5.
D’Ariano, G., Paris, M., Sacchi, M.: Quantum tomography (2003)
6.
Lvovsky, A., Raymer, M.: Continuous-variable optical quantum-state tomography (2009)
7.
Bogdanov, Yu.I., Gavrichenko, A.K., Kravtsov, K.S., Kulik, S.P., Moreva, E.V., Soloviev, A.A.: Statistical reconstruction of mixed states of polarization qubits (2011)
8.
Pogorelov, I.A., Struchalin, G.I., Straupe, S.S., Radchenko, I.V., Kravtsov, K.S., Kulik. S.P.: Experimental adaptive process tomography (2017)
9.
Huszár, F., Houlsby, N.M.: Adaptive Bayesian quantum tomography (2012)
10.
Bagan, E., Ballester, M.A., Gill, R.D., Muñoz-Tapia, R., Romero-Isart, O.: Separable measurement estimation of density matrices and its fidelity gap with collective protocols. Phys. Rev. Lett. 97(13), 130501 (2006)
11.
12.
Smolin, J.A., Gambetta, J.M., Smith, G.: Efficient method for computing the maximum-likelihood quantum state from measurements with additive gaussian noise. Phys. Rev. Lett. 108(7), 070502 (2012)
13.
De Burgh, M.D., Langford, N.K., Doherty, A.C., Gilchrist, A.: Choice of measurement sets in qubit tomography. Phys. Rev. A 78(5), 052122 (2008)
14.
Banaszek, K., D’ariano, G.M., Paris, M.G.A., Sacchi, M.F.: Maximum-likelihood estimation of the density matrix. Phys. Rev. A 61(1), 010304 (1999)
15.
Bolduc, E., Knee, G.C., Gauger, E.M., Leach, J.: Projected gradient descent algorithms for quantum state tomography. npj Quantum Inf. 3(1), 1 (2017)CrossRef
16.
Shang, J., Zhang, Z., Ng, H.K.: Superfast maximum-likelihood reconstruction for quantum tomography. Phys. Rev. A 95(6), 062336 (2017)
17.
Gill, R.D., Massar, S.: In state estimation for large ensembles. In: Asymptotic Theory of Quantum Statistical Inference: Selected Papers, pp. 178–214. World Scientific (2005)
18.
Bogdanov, Yu.I.: Unified statistical method for reconstructing quantum states by purification. J. Exp. Theor. Phys. 108(6), 928 (2009)ADSCrossRef
19.
Bogdanov, Yu.I., Brida, G., Bukeev, I.D., Genovese, M., Kravtsov, K.S., Kulik, S.P., Moreva, E.V., Soloviev, A.A., Shurupov, A.P.: Statistical estimation of the quality of quantum-tomography protocols. Phys. Rev. A 84(4), 042108 (2011)
20.
Bantysh, B.I., Chernyavskiy, AYu., Bogdanov, Yu.I.: Comparison of tomography methods for pure and almost pure quantum states. JETP Lett. 111(9), 512 (2020)ADSCrossRef
21.
Flammia, S.T., Gross, D., Liu, Y.K., Eisert, J.: Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators. New J. Phys. 14(9), 095022 (2012)
22.
Struchalin, G.I., Kovlakov, E.V., Straupe, S.S., Kulik, S.P.: Adaptive quantum tomography of high-dimensional bipartite systems. Phys. Rev. A 98(3), 032330 (2018)
23.
24.
Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800-22, NIST (2001)
25.
Uhlmann, A.: Fidelity and concurrence of conjugated states. Phys. Rev. A 62(3), 032307 (2000)
26.
27.
Liang, Y.C., Yeh, Y.H., Mendonça, P.E., Teh, R.Y., Reid, M.D., Drummond, P.D.: Quantum fidelity measures for mixed states. Rep. Prog. Phys. 82(7), 076001 (2019)
28.
Bogdanov, Yu.I., Brida, G., Genovese, M., Kulik, S.P., Moreva, E.V., Shurupov, A.P.: Statistical estimation of the efficiency of quantum state tomography protocols. Phys. Rev. Lett. 105(1), 010404 (2010)
29.
Hubert, M., Vandervieren, E.: An adjusted boxplot for skewed distributions. Comput. Stat. Data Anal. 52(12), 5186 (2008)MathSciNetCrossRef
30.
Brys, G., Hubert, M., Struyf, A.: A comparison of some new measures of skewness. In: Developments in Robust Statistics, pp. 98–113. Physica, Heidelberg (2003)
31.
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH
32.
Zyczkowski, K., Sommers, H.J.: Induced measures in the space of mixed quantum states. J. Phys. A Math. Gen. 34(35), 7111 (2001)ADSMathSciNetCrossRef
33.
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(1), 012103 (2016)
34.
Palmieri, A.M., Kovlakov, E., Bianchi, F., Yudin, D., Straupe, S., Biamonte, J.D., Kulik, S.: Experimental neural network enhanced quantum tomography. npj Quantum Inf. 6(1), 1 (2020)
35.
Dür, W., Hein, M., Cirac, J.I., Briegel, H.J.: Standard forms of noisy quantum operations via depolarization. Phys. Rev. A 72(5), 052326 (2005)
36.
Watson, T.F., Philips, S.G.J., Kawakami, E., Ward, D.R., Scarlino, P., Veldhorst, M., Savage, D.E., Lagally, M.G., Friesen, M., Coppersmith, S.N., et al.: A programmable two-qubit quantum processor in silicon. Nature 555(7698), 633 (2018)
37.
Tosi, G., Mohiyaddin, F.A., Schmitt, V., Tenberg, S., Rahman, R., Klimeck, G., Morello, A.: Silicon quantum processor with robust long-distance qubit couplings. Nat. Commun. 8(1), 1 (2017)CrossRef
38.
Wu, Y., Wang, Y., Qin, X., Rong, X., Du, J.: A programmable two-qubit solid-state quantum processor under ambient conditions. npj Quantum Inf. 5(1), 1 (2019)
39.
Wright, K., Beck, K.M., Debnath, S., Amini, J.M., Nam, Y., Grzesiak, N., et al.: Benchmarking an 11-qubit quantum computer. Nat. Commun. 10, 5464 (2019)ADSCrossRef
40.
41.
42.
Ahn, D., Teo, Y.S., Jeong, H., Bouchard, F., Hufnagel, F., Karimi, E., Koutnỳ, D., Řeháček, J., Hradil, Z., Leuchs, G., et al.: Adaptive compressive tomography with no a priori information. Physical Review Letters 122(10), 100404 (2019)ADSCrossRef
43.
Goyeneche, D., Cañas, G., Etcheverry, S., Gómez, E., Xavier, G., Lima, G., Delgado, A.: Five measurement bases determine pure quantum states on any dimension. Phys. Rev. Lett. 115(9), 090401 (2015)
44.
Torlai, G., Mazzola, G., Carrasquilla, J., Troyer, M., Melko, R., Carleo, G.: Neural-network quantum state tomography. Nat. Phys. 14(5), 447 (2018)CrossRef
45.
Fastovets, D.V., Bogdanov, Yu.I., Bantysh, B.I., Lukichev, V.F.: Machine learning methods in quantum computing theory 11022, 110222S (2019)
46.
Bogdanov, Yu.I., Avosopyants, G.V., Belinskii, L.V., Katamadze, K.G., Kulik, S.P., Lukichev, V.F.: Statistical reconstruction of optical quantum states based on mutually complementary quadrature quantum measurements. JETP 123(2), 212 (2016)ADSCrossRef
47.
Bengtsson, I.: Three ways to look at mutually unbiased bases. In: AIP Conference Proceedings, vol. 889, pp. 40–51. AIP (2007)
48.
Adamson, R.B.A., Steinberg, A.M.: Improving quantum state estimation with mutually unbiased bases. Phys. Rev. Lett. 105(3), 030406 (2010)
49.
Chen, Y., Ye, X.: Projection onto a simplex (2011)
50.
51.
Kosut, R., Walmsley, I.A., Rabitz, H.: Optimal experiment design for quantum state and process tomography and Hamiltonian parameter estimation (2004)
52.
53.
Nielsen, M., Chuang, I.: The Advanced Theory of Statistics, Vol. 2: Inference and Relationship. Charles Griffin & Company Ltd. (1961)
54.
55.
56.
Fazel, M., Hindi, H., Boyd, S.: Rank minimization and applications in system theory. In: Proceedings of the 2004 American Control Conference, pp. 3273–3278. IEEE (2004)
57.
Steffens, A., Riofrío, C., McCutcheon, W., Roth, I., Bell, B.A., McMillan, A., Tame, M., Rarity, J., Eisert, J.: Experimentally exploring compressed sensing quantum tomography. Quantum Sci. Technol. 2(2), 025005 (2017)
58.
Ferrie, C.: Self-guided quantum tomography. Phys. Rev. Lett. 113(19), 190404 (2014)
59.
Chapman, R.J., Ferrie, C., Peruzzo, A.: Experimental demonstration of self-guided quantum tomography. Phys. Rev. Lett. 117(4), 040402 (2016)
60.
61.
Knee, G.C., Bolduc, E., Leach, J., Gauger, E.M.: Quantum process tomography via completely positive and trace-preserving projection. Phys. Rev. A 98(6), 062336 (2018)
62.
Bantysh, B.I., Fastovets, D.V., Bogdanov, Yu.I.: MATLAB library for the root approach quantum tomography 11022, 110222N (2019)
63.
Huang, W., Yang, C.H., Chan, K.W., Tanttu, T., Hensen, B., Leon, R.C.C., Fogarty, M.A., Hwang, J.C.C., Hudson, F.E., Itoh, K.M., et al.: Fidelity benchmarks for two-qubit gates in silicon. Nature 569(7757), 532 (2019)ADSCrossRef
Metadaten
Titel
Quantum tomography benchmarking
verfasst von
B. I. Bantysh
A. Yu. Chernyavskiy
Yu. I. Bogdanov
Publikationsdatum
01.10.2021
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 10/2021
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-021-03285-9

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