296 research outputs found
How to efficiently select an arbitrary Clifford group element
We give an algorithm which produces a unique element of the Clifford group
C_n on n qubits from an integer 0\le i < |C_n| (the number of elements in the
group). The algorithm involves O(n^3) operations. It is a variant of the
subgroup algorithm by Diaconis and Shahshahani which is commonly applied to
compact Lie groups. We provide an adaption for the symplectic group Sp(2n,F_2)
which provides, in addition to a canonical mapping from the integers to group
elements g, a factorization of g into a sequence of at most 4n symplectic
transvections. The algorithm can be used to efficiently select randomelements
of C_n which is often useful in quantum information theory and quantum
computation. We also give an algorithm for the inverse map, indexing a group
element in time O(n^3).Comment: 7 pages plus 4 1/2 pages of python cod
Additive Extensions of a Quantum Channel
We study extensions of a quantum channel whose one-way capacities are
described by a single-letter formula. This provides a simple technique for
generating powerful upper bounds on the capacities of a general quantum
channel. We apply this technique to two qubit channels of particular
interest--the depolarizing channel and the channel with independent phase and
amplitude noise. Our study of the latter demonstrates that the key rate of BB84
with one-way post-processing and quantum bit error rate q cannot exceed
H(1/2-2q(1-q)) - H(2q(1-q)).Comment: 6 pages, one figur
Classical signature of quantum annealing
A pair of recent articles concluded that the D-Wave One machine actually
operates in the quantum regime, rather than performing some classical
evolution. Here we give a classical model that leads to the same behaviors used
in those works to infer quantum effects. Thus, the evidence presented does not
demonstrate the presence of quantum effects.Comment: 8 pages, 3 pdf figure
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