A review on reversible quantum adders

Orts, Francisco; Ortega, Gloria; Combarro, Elías F.

doi:10.1016/j.jnca.2020.102810

Cited by 28 publications

(14 citation statements)

References 41 publications

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“…Although the methodology described above is the most widely used for constructing carry lookahead adders, other alternatives have been proposed in the literature [37,38]. Some of these alternatives have been used in the construction of adders for quantum computing, as we discussed in [13]. Particularly interesting is the work presented by Bahadori et al [38], where the authors use a hybrid methodology for the calculation of the sum, whereby modules called carry lookahead sub-tree (CLST) are constructed to allow a quick calculation of the carries.…”

Section: Methodology To Design Carry Look-ahead Addersmentioning

confidence: 99%

“…In order to compare the proposed circuits with those available in the literature, we have mainly relied on two sources. The first source is an exhaustive review of quantum adders [13], which makes different comparisons between the various types of adders. One of these comparisons is devoted precisely to carry lookahead adders.…”

Section: (A) (B)mentioning

confidence: 99%

“…Achieving more optimized adders will allow the acceleration of this part of Shor's algorithm, as well as scaling its applicability to larger number sizes. With the implications that this algorithm has on such matters as cryptographic protocols [12], the interest in achieving such optimization is real and tangible [13]. However, it would be a mistake to limit the interest of adders to Shor's algorithm, as there is a plethora of algorithms that use addition as part of their computational process [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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Implementation of three efficient 4-digit fault-tolerant quantum carry lookahead adders

et al. 2022

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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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Section: Methodology To Design Carry Look-ahead Addersmentioning

confidence: 99%

Section: (A) (B)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Implementation of three efficient 4-digit fault-tolerant quantum carry lookahead adders

et al. 2022

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“…An example already mentioned is Shor's algorithm, which requires adders for its implementation. It is precisely because of this algorithm that addition is the arithmetic operation that receives more interest from the scientific community [20]. As a consequence, there are a huge amount of adders for quantum computing published in the literature [5,20,21].…”

Section: State-of-the-art In Quantum Circuit Design For Arithmetic Op...mentioning

confidence: 99%

“…Subtraction is also represented in the literature [36][37][38]. However, it is often performed using adders and two's complement representation (as in classical digital electronics) [20]. Given the aforementioned high interest that adders receive in quantum computing, which implies a high availability of this type of circuits, it is not surprising that the second option (using adders and two's complement representation to perform the subtraction) is the most widespread one [20].…”

Section: State-of-the-art In Quantum Circuit Design For Arithmetic Op...mentioning

confidence: 99%

Efficient design of a quantum absolute-value circuit using Clifford+T gates

Orts

Ortega

Combarro

et al. 2022

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Current quantum computers have a limited number of resources and are heavily affected by internal and external noise. Therefore, small, noise-tolerant circuits are of great interest. With regard to circuit size, it is especially important to reduce the number of required qubits. Concerning to fault-tolerance, circuits entirely built with Clifford+T gates allow the use of error correction codes. However, the T-gate has an excessive cost, so circuits with a high number of T-gates should be avoided. This work focuses on optimising in such terms an operation that is widely used in larger circuits and algorithms: the calculation of the absolute-value of two's complement encoded integers. The proposed circuit reduces by more than half the number of required T gates with respect to the best circuit currently available in the literature. Moreover, our proposal is the circuit that requires the fewest qubits for such an operation.

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