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Strictly speaking, AA only prove that the (Equation presented) matrix which encodes the Gaussian permanent estimation problem can be embedded into a random (Equation presented) unitary, if (Equation presented). AA state that they believe that the complexity arguments will still hold when (Equation presented), which we follow here. The arguments concerning the complexity of the randomized boson-sampling problem follow equally well if the (Equation presented) scaling is insisted upon
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Strictly speaking, AA only prove that the (Equation presented) matrix which encodes the Gaussian permanent estimation problem can be embedded into a random (Equation presented) unitary, if (Equation presented). AA state that they believe that the complexity arguments will still hold when (Equation presented), which we follow here. The arguments concerning the complexity of the randomized boson-sampling problem follow equally well if the (Equation presented) scaling is insisted upon.
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See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.113.100502, which includes Ref. [3].
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AA indicate they are aware of this exact sampling result for squeezed states but do not discuss it further
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AA indicate they are aware of this exact sampling result for squeezed states but do not discuss it further.
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