Efficient realization of quantum balanced ternary reversible multiplier building blocks: A great step towards sustainable computing

Nowadays, quantum computing plays a significant role in reducing the execution time in complicated computations. There are different reversible algorithms for quantum computation and many quantum circuits theoretically designed until now. These designs are only built from reversible gates because reversibility is a necessary logic in quantum circuits. Additionally, ternary representation can allow designing a circuit with fewer inputs and outputs, leading to a considerable decline in size or number of qutrits. Although other papers in quantum ternary reversible logic are in unbalanced representation, this paper, for the first time, considers balanced ternary advantages to achieve a more efficient design for quantum multipliers as the main component in arithmetic blocks. Six criteria are introduced to show how balanced representation increases the overall performance. In this work, two general balanced ternary adder blocks (full-adder and half-adder) and two balanced ternary partial product generators (BTPPGs) are proposed, and also a 2 × 2 and a 3 × 3 balanced ternary multipliers built from these components. The quantum costs of proposed balanced ternary multipliers enhanced 17% for a 2 × 2 multiplier and 34% for a 3 × 3 multiplier.