Weblinearly independent subset of Clifford group operations [29]. We generalise this result by noting that the Clifford group can be replaced by an arbitrary unitary 2-design and also explicitly provide an analytic form of the reconstruction. Our main result is a practical reconstruction procedure for quantum channels that are close to being unitary.

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WebOct 9, 2015 · We prove that the Clifford group is a 3-design, showing that it is a better approximation to Haar random unitaries than previously expected. Our proof strategy … WebThe uniform distribution over the Clifford group on n qubits is a unitary 2-design with D=2n. As is known, the Clifford group C n on n qubits can be implemented by quantum circuits of size O n2 2,15 . This general result allows us to immediately deduce that, for ex-ample, the Clifford group gives a more efficient solution to chords going back the byrds

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WebNov 1, 2016 · We prove that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected. Our proof strategy … http://cliffordandclifford.com/ WebWe prove that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected. Our proof strategy works for any distribution of unitaries satisfying a property we call Pauli 2-mixing and proceeds without the use of heavy mathematical machinery. chords god whispered your name