Optimal Quantum Circuits for General Multi‐Qutrit Quantum Computation

Abstract

Abstract Quantum circuits of a general quantum gate acting on multiple ‐level quantum systems play a prominent role in multi‐valued quantum computation. A recursive Cartan decomposition of semi‐simple unitary Lie group (arbitrary ‐qutrit gate) is first proposed with a rigorous proof, which completely decomposes an ‐qutrit gate into local and non‐local operations. On this basis, an explicit quantum circuit is designed for implementing arbitrary two‐qutrit gates, and the cost of the construction is 21 generalized controlled (GCX) and controlled increment (CINC) gates less than the earlier best result of 26 GGXs. Furthermore, the program is extended to the ‐qutrit system, and the quantum circuit of generic ‐qutrit gates contained GGXs and CINCs is presented. Such asymptotically optimal structure is the best known result so far and its strength becomes more remarkable as increases, for example, when , the program saves 7146 GCXs compared to the previous best result. In addition, concrete recursive decomposition expressions is given for each non‐local operation instead of only quantum circuit diagrams.