Radix-independent, efficient arrays for multi-level n-qudit quantum and reversible computation

Multiple-valued quantum logic allows the designers to reduce the number of cells while obtaining more functionality in the quantum circuits. Large r-valued reversible or quantum gates (r stands for radix and is more than 2) cannot be directly realized in the current quantum technology. Therefore, we are interested in designing the large reversible and quantum controlled gates using the arrays of one-quantum digit (qudit) or two-qudit gates. In our previous work, we proposed quantum arrays to implement the r-valued quantum circuits. In this paper, we propose novel efficient structures and arrays, for r-valued quantum logic gates. The quantum costs of the developed quantum arrays are independent of the radix of calculations in the quantum circuit.