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We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.
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A. Shabani, M. Mohseni, S. Lloyd, R. L. Kosut, and H. Rabitz, arXiv:1002.1330 (2010)
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W. van Dam and S. Hallgren, Efficient quantum algorithms for shifted quadratic character problems , eprint arXiv:quant-ph/0011067v2
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D. Aharonov, Z. Landau, and J. Makowsky, eprint quant-ph/0611156
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The result in [ 10 ] incorrectly cites the results of Theorem 2 of [ 22 ] leading to the conclusion that the cost of linear inversion scales with the sparseness as 𝒪 ~ ( s 2 ) \tilde{\cal O}(s^{2}) rather than 𝒪 ~ ( s 4 ) \tilde{\cal O}(s^{4})
Cited in the paper.
D. W. Berry and A. M. Childs, Quantum Information and Computation 12
2012
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