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$\mathrm{QAC}^0$ is the family of constant-depth polynomial-size quantum circuits consisting of arbitrary single qubit unitaries and multi-qubit Toffoli gates. It was introduced by Moore [arXiv: 9903046] as a quantum counterpart of $\mathrm{AC}^0$, a
Externí odkaz:
http://arxiv.org/abs/2410.06499
We prove an almost optimal hypercontractive inequality for quantum erasure channels, generalizing the hypercontractivity for classical binary erasure channels [NW16]. To our knowledge, this is the first hypercontractivity bound for non-unital quantum
Externí odkaz:
http://arxiv.org/abs/2311.14321