Improved Upper Bounds on the Stabilizer Rank of Magic States

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" summary

Proves a smaller exponential upper bound on the exact stabilizer rank of M magic states by building large code states from small ones rather than blocking magic states directly claims an asymptotic exponent alpha ≈ 0.3962 versus prior best ≈ 0.4629 and shows the six‑qubit magic cat state has stabilizer rank 3 which yields ≤6 for six magic states thereby falsifying the earlier χ=7 heuristic bound uses gadgetization, Clifford contractions and long chain contractions and leaves a large gap to approximate rank α≈0.228 and no strong lower bounds

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" chapters (8)

1. 0:00Classical simulation of quantum circuits
2. 7:09Stabilizer-rank simulators
3. 12:34Stabilizer rank role
4. 21:05Upper bounds on approximate rank
5. 26:07Exact rank and prior bounds
6. 31:14Magic cat states and improved bounds
7. 41:00Open problems and future work
8. 44:40Q&A