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Lower Bounds on Stabilizer Rank
[article]

2021

The stabilizer rank of a quantum state $ψ$ is the minimal $r$ such that $\left| ψ\right \rangle = \sum_{j=1}^r c_j \left|φ_j \right\rangle$ for $c_j \in \mathbb{C}$ and stabilizer states $φ_j$. The running time of several classical simulation methods for quantum circuits is determined by the stabilizer rank of the $n$-th tensor power of single-qubit magic states. We prove a lower bound of $Ω(n)$ on the stabilizer rank of such states, improving a previous lower bound of $Ω(\sqrt{n})$ of Bravyi,

doi:10.48550/arxiv.2106.03214
fatcat:ppy3ppuytfbqrhfisriwbphera