Foundations of Computational Mathematics

, Volume 2, Issue 2, pp 145–154 | Cite as

Poly-Locality in Quantum Computing

  • Michael H. Freedman
Article

Abstract

A polynomial depth quantum circuit affects, by definition, a poly-local unitary transformation of a tensor product state space. It is a reasonable belief [Fe], [L], [FKW] that, at a fine scale, these are precisely the transformations which will be available from physics to solve computational problems. The poly-locality of a discrete Fourier transform on cyclic groups is at the heart of Shor's factoring algorithm. We describe a class of poly-local transformations, which include the discrete orthogonal wavelet transforms, in the hope that these may be helpful in constructing new quantum algorithms. We also observe that even a rather mild violation of poly-locality leads to a model without one-way functions, giving further evidence that poly-locality is an essential concept.

Key words

Quantum computing Wavelet One-way function 

AMS Classification

81P68 65T60 

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Copyright information

© SFoCM 2001

Authors and Affiliations

  • Michael H. Freedman
    • 1
  1. 1.Theory Group Microsoft Research One Microsoft Way Redmond, WA 98052-6399, USA michaelf@microsoft.comUSA

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