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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 $\\chi(\\left|T\\right>^{\\otimes n}) \\ge 2^{c n}$ for some constant $c > 0$, where $\\left|T\\right> = (\\left|0\\right> + e^{i \\pi/4} \\left|1\\right>)/\\sqrt{2}$. Known upper bounds are of order $2^{0.4 n}$ (approximate exponent) and known lower bounds are only polynomial in n.","problem_ref":"d5c69c47dcdea08ce8133a347ee03bb57ac1f35aed63c34c474676c55f410806","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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