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Abstract: We prove that one-way quantum computations have the same computational poweras quantum circuits with unbounded fan-out. It demonstrates that the one-waymodel is not only one of the most promising models of physical realisation, butalso a very powerful model of quantum computation. It confirms and completesprevious results which have pointed out, for some specific problems, a depthseparation between the one-way model and the quantum circuit model. Sinceone-way model has the same computational power as unbounded quantum fan-outcircuits, the quantum Fourier transform can be approximated in constant depthin the one-way model, and thus the factorisation can be done by a polytimeprobabilistic classical algorithm which has access to a constant-depth one-wayquantum computer. The extra power of the one-way model, comparing with thequantum circuit model, comes from its classical-quantum hybrid nature. We showthat this extra power is reduced to the capability to perform unboundedclassical parity gates in constant depth.

Author: Dan E. Browne, Elham Kashefi, Simon Perdrix


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