Quantum circuit optimization for arbitrary high-dimensional bipartite quantum computation
Gui‐Long Jiang, Hai‐Rui Wei · New Journal of Physics · 2026
Abstract Implementation of high-dimensional (HD) quantum gates shows very promising perspectives for HD quantum computation. A bipartite quantum system with arbitrary dimensions n and m is termed a quNit–quMit. Here we propose a synthesis scheme to construct the quantum circuit for general quNit–quMit gates with controlled increment (CINC) gates and local gates. This shows that CINC gates combined with local gates form a universal gate set for HD quantum computation. An upper bound of O ( n 2 ) CINC gates is achieved for arbitrary quNit–quMit gate implementation in the proposed scheme, which is the best known result. Especially for the controlled quNit–quMit gates, our scheme requires only 2 CINC gates, whereas the previous scheme required 2 n .