A new synthesis method constructs general quNit-quMit gates with O(n²) CINC gates and controlled quNit-quMit gates with only 2 CINC gates, improving on prior 2n requirement.
Ifn 1 = 1 andn 2 >1 (i.e.,n 2 = 2), it is only necessary to decomposeU 2, in whichW 1 =U 1 andW ′ 1 =V 1 =I m in equation (31)
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Quantum circuit optimization for arbitrary high-dimensional bipartite quantum computation
A new synthesis method constructs general quNit-quMit gates with O(n²) CINC gates and controlled quNit-quMit gates with only 2 CINC gates, improving on prior 2n requirement.