Poly-locality in quantum computing

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.

• Type: Journal
• Year: 2000
• Where: CORR
• Authors: Michael H. Freedman
• Keywords: CORR 2000, Education, Poly-local Unitary Transformation, Polynomial Depth Quantum, Tensor Product State