Optimal Two-Qubit Circuits for Universal Fault-Tolerant Quantum Computation
summary
Provides an exact, efficient synthesis procedure for two-qubit unitaries over a Clifford+CS (super Clifford+T) gate set, producing a unique optimal normal form and a linear-time rewrite algorithm on input circuits. Reduces 92,160 conjugates to 15 canonical RPQ operators, uses a spin-6 isomorphism and residue maps to lower the denominator exponent one step at a time, and proves any synthesis needs at least k CS gates for exponent k and ≥5 log(1/ε) CS gates to ε-approximate; code is released.
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chapters (10)
- 0:00Intro
- 0:56Problem Statement
- 5:10The Problem
- 8:09Rewriting a Circuit
- 9:24Exceptional Isomorphism
- 10:51Spin 6 Generators
- 12:03Group G Operators
- 13:41Synthesis
- 15:24Example
- 16:24Conclusion
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