Quantum computers base their operations on optimized circuit designs. These quantum circuits, unlike classic circuits, follow the set of rules determined by quantum mechanics. Currently, one of the main problems to solve in Quantum Computation is Shor's algorithm, which consists in factoring large numbers. It is based on arithmetic operations, therefore to optimize such operations is hence relevant. In this work, a novel half subtractor circuit is presented; it is referred to as F GE * and it has demonstrated to be a 25% faster than the state-of-the-arts reversible circuits. It is based on reversible quantum gates and it does not have any garbage output. Moreover, a robust metric is considered for comparing, in terms of resources and speed, the proposed circuit with other circuits in the literature.
Adders are one of the most interesting circuits in quantum computing due to their use in major algorithms that benefit from the special characteristics of this type of computation. Among these algorithms, Shor’s algorithm stands out, which allows decomposing numbers in a time exponentially lower than the time needed to do it with classical computation. In this work, we propose three fault-tolerant carry lookahead adders that improve the cost in terms of quantum gates and qubits with respect to the rest of quantum circuits available in the literature. Their optimal implementation in a real quantum computer is also presented. Finally, the work ends with a rigorous comparison where the advantages and disadvantages of the proposed circuits against the rest of the circuits of the state of the art are exposed. Moreover, the information obtained from such a comparison is summarized in tables that allow a quick consultation to interested researchers.
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