On constant T-depth circuits
summary
Claims that many basic quantum subroutines admit constant T-depth constructions: single-qubit rotations (including programmable rotation) and the quantum part of Shor’s algorithm require a catalyst state of size N for N-bit precision, while reversible encoded addition needs no catalyst. Key tools are a GF(2^n) encoding (multiplication becomes a Clifford/CNOT), Chudnovsky-style bilinear decompositions giving R = O(n) so out-of-place multiplication runs at Toffoli depth 2 with linear ancilla, and experiments showing magic-state fidelities improved (physical 2-qubit error ~1.1×10^-3, encoded magic ~5.5×10^-4).
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chapters (7)
- 0:00Constant T-depth circuits
- 7:57Optimizing T-depth in compilation
- 10:24Low T-depth subroutines
- 27:51Constant T-depth rotation
- 34:51Programmable rotations in T-depth
- 46:20Open problems in T-depth circuits
- 48:04Conclusion
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