Constructing Approximately Diagonal Unitary Gates
Abstract
We study a method of producing approximately diagonal 1qubit 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 leakagefree entangled gates in topological quantum computing, etc.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.05138
 Bibcode:
 2021arXiv210905138G
 Keywords:

 Quantum Physics;
 Mathematical Physics;
 Mathematics  Quantum Algebra
 EPrint:
 21 pages