Built on

R. Harper, I. Hincks, C. Ferrie, S. T. Flammia, and J. J. Wallman, Phys. Rev. A (2019a), arXiv:1901.00535
Original
1901
Earlier work this paper cites.
A. Erhard, J. J. Wallman, L. Postler, M. Meth, R. Stricker, E. A. Martinez, P. Schindler, T. Monz, J. Emerson, and R. Blatt, arXiv e-prints , arXiv:1902.08543 (2019), arXiv:1902.08543 [quant-ph]
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1907
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R. Harper, S. T. Flammia, and J. J. Wallman, (2019b), arXiv:1907.13022
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D. Gottesman, Stabilizer codes and quantum error correction , Ph.D. thesis , Caltech, Pasadena, California (1997), quant-ph/9705052
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F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, Phys. Rev. Lett. 93
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M. Zwolak and G. Vidal, Phys. Rev. Lett. 93
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J. Emerson, R. Alicki, and K. Życzkowski, J. Opt. B 7
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C. Dankert, Efficient Simulation of Random Quantum States and Operators , Ph.D. thesis, University of Waterloo (2005), quant-ph/0512217
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P. Abbeel, D. Koller, and A. Y. Ng, Journal of Machine Learning Research 7
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E. J. Candès and T. Tao, IEEE Trans. Info. Theory 52
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E. Candès, J. Romberg, and T. Tao, IEEE Trans. Inform. Theory 52
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J. Emerson, M. Silva, O. Moussa, C. Ryan, M. Laforest, J. Baugh, D. G. Cory, and R. Laflamme, Science 317
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2007
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P. Aliferis and J. Preskill, Phys. Rev. A 78
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E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Phys. Rev. A 77
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2008
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C. Dankert, R. Cleve, J. Emerson, and E. Livine, Phys. Rev. A 80
2009
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C. A. Ryan, M. Laforest, and R. Laflamme, New J. Phys. 11
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2009
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2019

Efficient estimation of Pauli channels

Flammia, Steven T., Wallman, Joel J.

Understand

Pauli channels are ubiquitous in quantum information, both as a dominant noise source in many computing architectures and as a practical model for analyzing error correction and fault tolerance.

Here we prove several results on efficiently learning Pauli channels, and more generally the Pauli projection of a quantum channel.
We first derive a procedure for learning a Pauli channel on $n$ qubits with high probability to a relative precision $\epsilon$ using $O\bigl(\epsilon^{-2} n 2^n\bigr)$ measurements, which is efficient in the Hilbert space dimension.
The estimate is robust to state preparation and measurement errors which, together with the relative precision, makes it especially appropriate for applications involving characterization of high-accuracy quantum gates.

Built on

R. Harper, I. Hincks, C. Ferrie, S. T. Flammia, and J. J. Wallman, Phys. Rev. A (2019a), arXiv:1901.00535
Original
1901
Earlier work this paper cites.
A. Erhard, J. J. Wallman, L. Postler, M. Meth, R. Stricker, E. A. Martinez, P. Schindler, T. Monz, J. Emerson, and R. Blatt, arXiv e-prints , arXiv:1902.08543 (2019), arXiv:1902.08543 [quant-ph]
Original
1902
Earlier work this paper cites.
D. K. Tuckett, S. D. Bartlett, S. T. Flammia, and B. J. Brown, Physical Review Letters 124
Original
1907
Earlier work this paper cites.
R. Harper, S. T. Flammia, and J. J. Wallman, (2019b), arXiv:1907.13022
Original
1907
Earlier work this paper cites.
W. Hoeffding, Journal of the American Statistical Association 58
1963
Earlier work this paper cites.
M. Pinsker, Information and information stability of random variables and processes (Holden-Day, 1964)
1964
Earlier work this paper cites.
C. Chow and C. Liu, IEEE Transactions on Information Theory 14
1968
Earlier work this paper cites.
J. M. Hammersley and P. Clifford, “Markov fields on finite graphs and lattices,” (1971), available at http://www.statslab.cam.ac.uk/˜grg/books/hammfest/hamm-cliff.pdf
1971
Earlier work this paper cites.
R. J. Serfling, The Annals of Statistics 2
1974
Earlier work this paper cites.
J. Besag, Journal of the Royal Statistical Society. Series B (Methodological) 36
1974
Earlier work this paper cites.
F. Barahona, Journal of Physics A: Mathematical and General 15
1982
Earlier work this paper cites.
W. K. Wootters and B. D. Fields, Annals of Physics 191
1989
Earlier work this paper cites.
T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991)
1991
Earlier work this paper cites.
M. Jerrum and A. Sinclair, SIAM Journal on Computing 22
1993
Earlier work this paper cites.
I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44
1997
Earlier work this paper cites.
D. Gottesman, Stabilizer codes and quantum error correction , Ph.D. thesis , Caltech, Pasadena, California (1997), quant-ph/9705052
1997
Earlier work this paper cites.
F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
M. Zwolak and G. Vidal, Phys. Rev. Lett. 93
Original
2004
Earlier work this paper cites.
J. Emerson, R. Alicki, and K. Życzkowski, J. Opt. B 7
2005
Earlier work this paper cites.
C. Dankert, Efficient Simulation of Random Quantum States and Operators , Ph.D. thesis, University of Waterloo (2005), quant-ph/0512217
2005
Earlier work this paper cites.
P. Abbeel, D. Koller, and A. Y. Ng, Journal of Machine Learning Research 7
Original
2006
Earlier work this paper cites.
E. J. Candès and T. Tao, IEEE Trans. Info. Theory 52
2006
Earlier work this paper cites.
E. Candès, J. Romberg, and T. Tao, IEEE Trans. Inform. Theory 52
2006
Earlier work this paper cites.
D. Donoho, IEEE Trans. Info. Theory 52
2006
Earlier work this paper cites.
J. Emerson, M. Silva, O. Moussa, C. Ryan, M. Laforest, J. Baugh, D. G. Cory, and R. Laflamme, Science 317
Original
2007
Earlier work this paper cites.
P. Aliferis and J. Preskill, Phys. Rev. A 78
Original
2008
Earlier work this paper cites.
E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Phys. Rev. A 77
Original
2008
Earlier work this paper cites.
C. Dankert, R. Cleve, J. Emerson, and E. Livine, Phys. Rev. A 80
2009
Earlier work this paper cites.
C. A. Ryan, M. Laforest, and R. Laflamme, New J. Phys. 11
Original
2009
Earlier work this paper cites.

Similar

D. Koller and N. Friedman, Probabilistic graphical models: principles and techniques (MIT Press, Cambridge, MA, 2009)
2009
Cited alongside, same era.
D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, Phys. Rev. Lett. 105
Original
2010
Cited alongside, same era.
M. Cramer, M. B. Plenio, S. T. Flammia, R. Somma, D. Gross, S. D. Bartlett, O. Landon-Cardinal, D. Poulin, and Y.-K. Liu, Nat Commun 1
Original
2010
Cited alongside, same era.
A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, Phys. Rev. Lett. 106
Original
2011
Cited alongside, same era.
H. Bombin, R. S. Andrist, M. Ohzeki, H. G. Katzgraber, and M. A. Martin-Delgado, Physical Review X 2
Original

Then

R. O’Donnell and J. Wright, in Proceedings of the Forty-eighth Annual ACM Symposium on Theory of Computing , STOC ’16 (ACM, New York, NY, USA, 2016) pp. 899–912
2016
Later among the works it cites.
R. Blume-Kohout, J. K. Gamble, E. Nielsen, K. Rudinger, J. Mizrahi, K. Fortier, and P. Maunz, Nature Communications 8
Original
2016
Later among the works it cites.
A. S. Darmawan and D. Poulin, Phys. Rev. Lett. 119
Original
2017
Later among the works it cites.
A. Robertson, C. Granade, S. D. Bartlett, and S. T. Flammia, Phys. Rev. Applied 8
Original
2017
Later among the works it cites.
T. Proctor, K. Rudinger, K. Young, M. Sarovar, and R. Blume-Kohout, Phys. Rev. Lett. 119
Original

Beyond the bibliography

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Cited alongside, same era.

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Cited alongside, same era.

2017