Efficient Realization of Toffoli and NCV Circuits for IBM QX Architectures

Almeida, Alexandre A. A. de; Dueck, Gerhard W.; Silva, Alexandre César Rodrigues da

doi:10.1007/978-3-030-21500-2_8

Cited by 11 publications

(6 citation statements)

References 16 publications

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“…Moreover, we could use some other approaches such as permutation group theory and Reed-Muller spectra [Maslov et al, 2007, Zakablukov, 2016 in order to find better gate sequences. We could also apply similar techniques to the synthesis of quantum circuits [de Almeida et al, 2019], taking into account that moving to the level of quantum circuits requires a more fine-grained gate set than considered here and optimizations that align with error-correction needs.…”

Section: Discussionmentioning

confidence: 99%

A reversible circuit synthesis algorithm with progressive increase of controls in generalized Toffoli gates

Dalcumune¹,

Kowada²,

Ribeiro³

et al. 2021

jucs

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We present a new algorithm for synthesis of reversible circuits for arbitrary n-bit bijective functions. This algorithm uses generalized Toffoli gates, which include positive and negative controls. Our algorithm is divided into two parts. First, we use partially controlled gen- eralized Toffoli gates, progressively increasing the number of controls. Second, exploring the properties of the representation of permutations in disjoint cycles, we apply generalized Toffoli gates with controls on all lines except for the target line. Therefore, new in the method is the fact that the obtained circuits use first low cost gates and consider increasing costs towards the end of the synthesis. In addition, we employ two bidirectional synthesis strategies to improve the gate count, which is the metric used to compare the results obtained by our algorithm with the results presented in the literature. Accordingly, our experimental results consider all 3-bit bijective functions and twenty widely used benchmark functions. The results obtained by our synthesis algorithm are competitive when compared with the best results known in the literature, considering as a complexity metric just the number of gates, as done by alternative best heuristics found in the literature. For example, for all 3-bit bijective functions using generalized Toffoli gates library, we obtained the best so far average count of 5.23.

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Section: Discussionmentioning

confidence: 99%

A reversible circuit synthesis algorithm with progressive increase of controls in generalized Toffoli gates

Dalcumune¹,

Kowada²,

Ribeiro³

et al. 2021

jucs

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“…The Clifford+T library consists of the gates NOT, CNOT, H (Hadamard), S, S †, T, and T †. Figure 2 shows the gates of Clifford+T libraries [13,14].…”

Section: Quantum Circuitsmentioning

confidence: 99%

“…13 The single-bit fault model Fig. 14 The multiple bit fault model multiple-bit fault. Figures 13 and 14 show the single-bit fault model and the multiple bit fault model in circuit, respectively.…”

Section: Bit Fault Modelmentioning

confidence: 99%

Efficient techniques for fault detection and location of multiple controlled Toffoli-based reversible circuit

Kheirandish

Haghparast

Reshadi

et al. 2021

Quantum Inf Process

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It is very important to detect and correct faults for ensuring the validity and reliability of these circuits. In this regard, a comparative study with related existing techniques is undertaken. Two techniques to achieve the testability of reversible circuits are introduced that have been improved in terms of quantum cost and fault coverage rate. Considering this aspect, the main focus of these techniques is on the efficient detection and location of faults with 100% accuracy. These techniques for fault detection in reversible circuit design, in addition to being able to produce the correct outputs, can also provide information for fault location that has already been done at a higher cost. Proposed approaches have been successfully tested for all types of SMGF, MMGF, PMGF, RGF, and SBF. In order to verify the functional correctness of the proposed scheme, it also has executed the testing over a reversible full adder circuit, and findings are checked. In the following, the proposed approach of reversible sequential circuits is presented for the first time so far. The cost metrics are evaluated for all the proposed designs and compared the estimated results against some existing design approaches of reversible circuits for better understanding.

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“…The next step will be the study of dual gates at the level of their Clifford-T model and evaluate their performance in the context of the IBM-QX quantum computers [1], [3]. Fig.…”

Section: Rule 14mentioning

confidence: 99%

“…This reversible gate has intensively been used ever since and has received several "extensions", like multi-controlled Toffoli gates and their decomposition as V-shaped cascades of elementary Toffoli gates and ancillary bits [5], a quantum realization model [5]. mixed polarity controlled Toffoli gates [14], [26], and, in recent times, Clifford-T realizations [1] and mappings to the IBM QX quantum computers [1], [3]. Together with the Toffoli gate, the NOT gate and CNOT, the controlled NOT gate, are the basic components of reversible circuits.…”

Section: Imintroductionmentioning

confidence: 99%

OR-Toffoli and OR-Peres Reversible Gates

Moraga

2021

Reversible Computation

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The paper introduces dual Toffoli and Peres reversible gates, which operate under disjunctive control, and shows their functionality based on the Barenco et al. quantum model. Both uniform and mixed polarity are considered for the controls. Rewriting rules are presented, which provide a possible reduction of the number of gates and quantum cost of reversible (sub)circuits using standard Toffoli or Peres gates. Finally, a Clifford+T realization of a dual Toffoli and a dual Peres gate is shown, which may be used when mapping reversible circuits to the IBM quantum computers.

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Efficient Realization of Toffoli and NCV Circuits for IBM QX Architectures

Cited by 11 publications

References 16 publications

A reversible circuit synthesis algorithm with progressive increase of controls in generalized Toffoli gates

A reversible circuit synthesis algorithm with progressive increase of controls in generalized Toffoli gates

Efficient techniques for fault detection and location of multiple controlled Toffoli-based reversible circuit

OR-Toffoli and OR-Peres Reversible Gates

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