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Although quantum computers are capable of solving problems like factoring exponentially faster than the best-known classical algorithms, determining the resources responsible for their computational power remains unclear.
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See Appendix D. Also see Abrams and Lloyd 1999 for another algorithm on eigenvector retrieval
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The F ( s 0 ) F(s_{0}) overhead is analogous to the case in DQC1 when using a slightly mixed state probe state instead of the pure state | + ⟩ ⟨ + | \delimiter 2532108+\delimiter 86414091\delimiter 69632778+\delimiter 2532108 Datta 2008 . The degree of mixedness does not affect the result that the computation is efficient. The amount of squeezing in our model thus corresponds to the degree of mixedness in the input state of DQC1. Higher squeezing corresponds to greater purity
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Mile Gu, Christian Weedbrook, Nicolas C Menicucci, Timothy C Ralph, and Peter van Loock, “Quantum computing with continuous-variable clusters,” Phys. Rev. A 79
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This ensures that m / r m/r is recovered exactly by using the continued fractions algorithm. See Nielsen and Chuang 2010 for an explicit demonstration
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2015
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