Parallelizing with Limited Number of Ancillae
In this paper, parallelization methods on a condition are proposed for three types of quantum circuits, where the condition is that the number of available ancillae is limited and parallelization means that a given quantum circuit is reconstructed as one with smaller depth. As a by-product, for the three types of n-input quantum circuits, upper bounds on the number of ancillae for parallelizing to logarithmic depth are reduced to 1/ log n of the previous upper bounds.
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