We discuss our p-adic version of the best known quantum compiling algorithm on a single qubit that is developed by Ross and Selinger. Two main applications of our algorithm are computing optimally the discrete log of diagonal matrices of PGL2(ℤ/qℤ) with respect to Lubotzky, Phillips and Sarnak generators and navigation problem for diagonal vertices of LPS Ramanujan graphs. My algorithm and Ross and Selinger's algorithm are conditional on assuming one can factor quickly, and a natural conjecture on the distribution of integers representable as a sum of two squares.
You must be logged in to post a comment.