Quantum Inf Process DOI 10.1007/s11128-015-1011-3 Radix-independent, efficient arrays for multi-level n-qudit quantum and reversible computation Majid Mohammadi 1 Received: 5 November 2014 / Accepted: 22 April 2015 © Springer Science+Business Media New York 2015 Abstract 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. Keywords Quantum computing · Reversible logic · Multiple-valued logic · Controlled gate · Quantum cost · Optimization 1 Introduction Multiple-valued quantum and reversible logic (MVQRL) circuits are important in the emerging quantum technologies. Using r -valued quantum circuits, designers can reduce the number of quantum cells to obtain a desired functionality for the quan- tum circuit [1]. A large amount of work has been done in the field of synthesis and optimization of binary quantum circuits. Methods for automated synthesis of binary and r -valued quantum circuits, based on genetic algorithms (GA) and evolutionary algorithms (EA), have also been developed [2–8]. An important group of r -valued B Majid Mohammadi M_mohamadi@sbu.ac.ir 1 Faculty of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran 123