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Quantum computing is one of the most significant anticipation towards the accomplishment of interminable consumer demands of small, high speed, and low-power operable electronics devices. As reversible logic circuits have direct applicability to quantum circuits, design and synthesis of these circuits are finding grounds for emerging nano-technologies of quantum computing. Multiple Controlled Toffoli (MCT) and Multiple Controlled Fredkin (MCF) are the fundamental reversible gates that playing key role in this phase of development. A number of special reversible gates have also been presented so far, which were claimed superior for providing certain purposes like logic development and testing. This paper critically analyses a range of these gates to procure an optimal solution for design, synthesis and testing of reversible circuits. The experimentation is facilitated at three subsequent levels, i.e. gates properties, quantum cost and design & testability. MCT and MCF gates are found up to 50% more cost-effective than special gates at design level and 34.4% at testability level. Maximum reversibility depth (MRD) is included as a new measurement parameter for comparison. Special gates exhibit MRD up to 7 which ideally should be 1 for a system to be physically reversible as that of MCT and MCF gates. [ABSTRACT FROM AUTHOR]

In this paper, we present a systematic method for designing single error correcting (SEC) and double error detecting finite field (Galois field) multipliers over GF(2m). The detection and correction are done on-line. We use multiple Parity Predictions to detect and correct errors. Specifically, a structural approach is first presented. The predicted parity bits are derived from the primitive polynomials for generating the fields. Further, a hybrid approach is presented where the multipliers and PP circuits are synthesised, and the decoding and correction circuits are structurally combined to form the complete error correcting designs. Although the article considers only a finite field multiplier, without loss of generality, the technique could be applied to any combinational logic circuit. Our technique, when compared with existing techniques, gives better performance. We show that our SEC multipliers over GF(2m) require about 100% extra hardware, whereas with the traditional SEC techniques, such as the triple-modular redundancy (TMR), this figure is more than 200%. Moreover, the multiple bit error detection and correction using multiple Hamming code were also introduced. [ABSTRACT FROM AUTHOR]