



01389nas a2200157   4500008004100000245005900041210005700100260001400157300001000171490000800181520094200189100002501131700001901156700001901175856003701194       2019                        eng d00aCanonical forms for single-qutrit Clifford+T operators0 aCanonical forms for singlequtrit CliffordT operators  c8/19/2019  a54-700 v4063 a<p><span style="color: rgb(51, 51, 51); font-family: &quot;Open Sans&quot;, &quot;Lucida Grande&quot;, &quot;Helvetica Neue&quot;, Helvetica, Arial, sans-serif; font-size: 14px;">We introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the single-qutrit Clifford+T circuits implementing a given operator our canonical form uses the least number of T gates. Finally, we provide an algorithm which inputs the description of an operator (as a matrix or a circuit) and constructs the canonical form for this operator. The algorithm runs in time linear in the number of T gates. Our results provide a higher-dimensional generalization of prior work by Matsumoto and Amano who introduced similar canonical forms for single-qubit Clifford+T circuits.&nbsp;</span></p>1 aGlaudell, Andrew, N.1 aRoss, Neil, J.1 aTaylor, J., M.  uhttps://arxiv.org/abs/1803.05047