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 fanout 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.
We also note that recent results by Browne, Kashefi, and Perdrix (BKP) connect the power of measurement-based quantum computing to the quantum circuit model augmented with unbounded fanout REF .
Computational depth complexity of measurement-based quantum computation
In Proceeding of the Fifth Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2010), Leeds 2010
Mathematics Physics Computer Science