Constructing approximately diagonal quantum gates

We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are conjectured to converge to diagonal gates doubly exponentially fast and are verified for small integers. We systemically study this conjecture and prove several important partial results. Some techniques are developed to pave the way for a final resolution of the conjecture. The sequences provided here have applications in quantum search algorithms, quantum circuit compilation, generation of leakage-free entangled gates in topological quantum computing, etc.

Automated summary

We study a method for generating approximately diagonal 1-qubit gates and verify its effectiveness for small integers. Through systematic investigation, we prove important partial results and develop techniques to further resolve the conjecture. The sequences generated by this method have applications in quantum search algorithms, quantum circuit compilation, and generation of leakage-free entangled gates in topological quantum computing.