Fetching the paper…
Reading the bibliography…
With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems.
C. Eckart and G. Young, “The approximation of one matrix by another of lower rank,” Psychometrika
1936
Earlier work this paper cites.
J. Nelder and R. Mead, “A simplex method for function minimization,” The computer journal
1965
Earlier work this paper cites.
L. Mirsky, “A trace inequality of John von Neumann,” Monatshefte für mathematik
1975
Earlier work this paper cites.
J. Cullum, R. Willoughby, and M. Lake, “A Lanczos algorithm for computing singular values and vectors of large matrices,” SIAM Journal on Scientific and Statistical Computing
1983
Earlier work this paper cites.
Y. Nesterov, “A method of solving a convex programming problem with convergence rate O
1983
Earlier work this paper cites.
C. Michelot, “A finite algorithm for finding the projection of a point onto the canonical simplex of
1986
Earlier work this paper cites.
G. Stewart, “On the early history of the singular value decomposition,” SIAM review
1993
Earlier work this paper cites.
K. Banaszek, G. D’Ariano, M. Paris, and M. Sacchi, “Maximum-likelihood estimation of the density matrix,” Physical Review A
1999
Earlier work this paper cites.
J. Sturm, “Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,” Optimization methods and software
1999
Earlier work this paper cites.
M. Hochstenbach, “A Jacobi–Davidson type SVD method,” SIAM Journal on Scientific Computing
2001
Earlier work this paper cites.
M. Paris, G. D’Ariano, and M. Sacchi, “Maximum-likelihood method in quantum estimation,” in
2001
Earlier work this paper cites.
Samuel Burer and Renato D. C. Monteiro, “A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization,” Mathematical Programming
2003
Earlier work this paper cites.
R. Tütüncü, K.-C. Toh, and M. Todd, “Solving semidefinite-quadratic-linear programs using SDPT3,” Mathematical programming
2003
Earlier work this paper cites.
E. Kokiopoulou, C. Bekas, and E. Gallopoulos, “Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization,” Applied numerical mathematics
2004
Earlier work this paper cites.
J. Altepeter, E. Jeffrey, and P. Kwiat, “Photonic state tomography,” Advances in Atomic, Molecular, and Optical Physics
2005
Earlier work this paper cites.
S. Flammia, A. Silberfarb, and C. Caves, “Minimal informationally complete measurements for pure states,” Foundations of Physics
2005
Earlier work this paper cites.
J. Baglama and L. Reichel, “Augmented implicitly restarted Lanczos bidiagonalization methods,” SIAM Journal on Scientific Computing
2005
Earlier work this paper cites.
Samuel Burer and Renato D. C. Monteiro, “Local minima and convergence in low-rank semidefinite programming,” Mathematical Programming
2005
Earlier work this paper cites.
D. Donoho, “Compressed sensing,” IEEE Transactions on information theory
2006
Earlier work this paper cites.
J. Baglama and L. Reichel, “Restarted block Lanczos bidiagonalization methods,” Numerical Algorithms
2006
Earlier work this paper cites.
H. Haffner, M. Riebe, C. Becher, C. Roos, P. Schmidt, J. Benhelm, T. Korber, R. Blatt, D. Chek-Al-kar, and W. Dur, “Scalable multi-particle entanglement of trapped ions,” Nature
2006
Earlier work this paper cites.
R. Baraniuk, “Compressive sensing,” IEEE signal processing magazine
2007
Earlier work this paper cites.
J. Řeháček, Z. Hradil, E. Knill, and A. I. Lvovsky, “Diluted maximum-likelihood algorithm for quantum tomography,”
2007
Earlier work this paper cites.
J. Duchi, S. Shalev-Shwartz, Y. Singer, and T. Chandra, “Efficient projections onto the
2008
Cited alongside, same era.
E. Hazan, “Sparse approximate solutions to semidefinite programs,” Lecture Notes in Computer Science
2008
Cited alongside, same era.
E. Candès and B. Recht, “Exact matrix completion via convex optimization,” Foundations of Computational mathematics
2009
Cited alongside, same era.
D. Gross, Y.-K. Liu, S. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Physical review letters
2010
Cited alongside, same era.
B. Recht, M. Fazel, and P. Parrilo, “Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization,” SIAM review
2010
Cited alongside, same era.
T. Zhao, Z. Wang, and H. Liu, “A nonconvex optimization framework for low rank matrix estimation,” in
2015
Later among the works it cites.
2015
Later among the works it cites.
2015
Later among the works it cites.
Qinqing Zheng and John Lafferty, “A convergent gradient descent algorithm for rank minimization and semidefinite programming from random linear measurements,” in
2015
Later among the works it cites.
A. Yurtsever, Quoc T. Dinh, and V. Cevher, “A universal primal-dual convex optimization framework,” in
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. Agarwal, S. Negahban, and M. Wainwright, “Fast global convergence rates of gradient methods for high-dimensional statistical recovery,” in
2010
Cited alongside, same era.
Y. Chen and S. Sanghavi, “A general framework for high-dimensional estimation in the presence of incoherence,” in
2010
Cited alongside, same era.
E. Candès and Y. Plan, “Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements,” IEEE Transactions on Information Theory
2011
Cited alongside, same era.
S. Flammia and Y.-K. Liu, “Direct fidelity estimation from few Pauli measurements,” Physical Review Letters
2011
Cited alongside, same era.
Y.-K. Liu, “Universal low-rank matrix recovery from Pauli measurements,” in
2011
Cited alongside, same era.
J. Smolin, J. Gambetta, and G. Smith, “Efficient method for computing the maximum-likelihood quantum state from measurements with additive Gaussian noise,” Physical review letters
2012
Cited alongside, same era.
Inc. CVX Research, “CVX: Matlab software for disciplined convex programming, version 2.0,”
2012
Cited alongside, same era.
2015
Later among the works it cites.
S. Bubeck, “Convex optimization: Algorithms and complexity,” Foundations and Trends® in Machine Learning
2015
Later among the works it cites.
C. Baldwin, I. Deutsch, and A. Kalev, “Strictly-complete measurements for bounded-rank quantum-state tomography,” Physical Review A
2016
Later among the works it cites.
S. Tu, R. Boczar, M. Simchowitz, M. Soltanolkotabi, and B. Recht, “Low-rank solutions of linear matrix equations via Procrustes flow,” in
2016
Later among the works it cites.
S. Bhojanapalli, A. Kyrillidis, and S. Sanghavi, “Dropping convexity for faster semi-definite optimization,” in
2016
Later among the works it cites.
R. Ge, J. Lee, and T. Ma, “Matrix completion has no spurious local minimum,” in
2016
Later among the works it cites.
Y. Li, Y. Liang, and A. Risteski, “Recovery guarantee of non-negative matrix factorization via alternating updates,” in
2016
Later among the works it cites.
2016
Later among the works it cites.
D. Gonçalves, M. Gomes-Ruggiero, and C. Lavor, “A projected gradient method for optimization over density matrices,” Optimization Methods and Software
2016
Later among the works it cites.
Z. Hou, H.-S. Zhong, Y. Tian, D. Dong, B. Qi, L. Li, Y. Wang, F. Nori, G.-Y. Xiang, and C.-F. Li, “Full reconstruction of a 14-qubit state within four hours,” New Journal of Physics
2016
Later among the works it cites.
2017
Closest in time.
A. Stathopoulos, E. Romero, and L. Wu, “Extended functionality and interfaces of the PRIMME eigensolver,” SIAM News Blog (2017)
2017
Closest in time.
D. Park, A. Kyrillidis, C. Carmanis, and S. Sanghavi, “Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach,” in
2017
Closest in time.
2017
Closest in time.
2017
Closest in time.
Jiangwei Shang, Zhengyun Zhang, and Hui Khoon Ng, “Superfast maximum-likelihood reconstruction for quantum tomography,”
2017
Closest in time.
E. Bolduc, G. Knee, E. Gauger, and J. Leach, “Projected gradient descent algorithms for quantum state tomography,” npj Quantum Information
2017
Closest in time.
C. Riofrío, D. Gross, S.T. Flammia, T. Monz, D. Nigg, R. Blatt, and J. Eisert, “Experimental quantum compressed sensing for a seven-qubit system,” Nature Communications
2017
Closest in time.