Fast quantum algorithm for numerical gradient estimation.

@article{Jordan2005FastQA,
  title={Fast quantum algorithm for numerical gradient estimation.},
  author={Stephen P. Jordan},
  journal={Physical review letters},
  year={2005},
  volume={95 5},
  pages={
          050501
        }
}
  • S. Jordan
  • Published 25 May 2004
  • Computer Science
  • Physical review letters
Given a black box for f, a smooth real scalar function of d real variables, one wants to estimate [symbol: see text]f at a given point with n bits of precision. On a classical computer this requires a minimum of d + 1 black box queries, whereas on a quantum computer it requires only one query regardless of d. The number of bits of precision to which f must be evaluated matches the classical requirement in the limit of large n. 
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References

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TLDR
This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.