{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"6f9a71bec2453ea2e41d5154564bd0ce536973ecb3fa779cf501334e09b5ec5c","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","d5c69c47dcdea08ce8133a347ee03bb57ac1f35aed63c34c474676c55f410806"],"salt":"f15e46c44dd621bc4854d605ae415f847025b2d10b05f7c5a5730833b83fce1f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":["ai:gpt-5.5"],"external_id":"qi.classical-simulability.t-state-stabilizer-rank","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Circuits built from one special gate family can be simulated fast classically; adding extra 'magic' states makes them universal. 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 states","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"c8bd3a032f41f51f698076465a7ecc2bbc67b6cd0a23fa82e3890dcacbe3dfd1","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"0032866e287f40a3ca42bd04f5d525e69e14e4cfe86318976e92c2288a0b4730","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"lmat3dbDSrEwGZS_QwdFc8MZaL8nCdJU-qB1OvFDkGfqTix8wJUzaFulPTe3NGwTkezfCi1q2rbLP58KXZs0BA"},"schema":"pubphys.envelope/1"},"record_hash":"c8bd3a032f41f51f698076465a7ecc2bbc67b6cd0a23fa82e3890dcacbe3dfd1","leaf_index":3696}