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The best classical simulators run in time set by a number called the stabilizer rank, and no one has proven that it must grow exponentially.","posed_since":"2016","precise":"The stabilizer rank $\\chi(\\psi)$ is the least number of stabilizer states whose linear combination equals $\\psi$. Prove chi(|T>^(tensor n)) >= 2^(c n) for some constant $c > 0$, where |T> = (|0> + e^(i pi/4) |1>)/sqrt(2). Known upper bounds are of order $2^{0.4 n}$ (approximate exponent) and known lower bounds are only polynomial in n.","problem_ref":null,"references":"","settled_by":"A proof of an exponential lower bound, or a construction with subexponential rank.","status_note":"","title":"Exponential lower bound on the stabilizer rank of magic 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