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arXiv · 0909.4673

Computational depth complexity of measurement-based quantum computation

Dan E. Browne·Elham Kashefi·Simon Perdrix
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Abstract

We prove that one-way quantum computations have the same computational power as quantum circuits with unbounded fan-out. It demonstrates that the one-way model is not only one of the most promising models of physical realisation, but also a very powerful model of quantum computation. It confirms and completes previous results which have pointed out, for some specific problems, a depth separation between the one-way model and the quantum circuit model. Since one-way model has the same computational power as unbounded quantum fan-out circuits, the quantum Fourier transform can be approximated in constant depth in the one-way model, and thus the factorisation can be done by a polytime probabilistic classical algorithm which has access to a constant-depth one-way quantum computer. The extra power of the one-way model, comparing with the quantum circuit model, comes from its classical-quantum hybrid nature. We show that this extra power is reduced to the capability to perform unbounded classical parity gates in constant depth.

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Dan E. Browne, Elham Kashefi, Simon Perdrix. 2009-09-25. Computational depth complexity of measurement-based quantum computation. https://arxiv.org/abs/0909.4673

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