An Ultra-Energy-Efficient Reversible Quantum-Dot Cellular Automata 8:1 Multiplexer Circuit

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

I have carefully reviewed the authors' response and the paper.  My comments related to authors' repsonse follow:

 

> Section 3 now includes a discussion related […] in this study.

 

The inserted lines lack clarity in explaining the problem. As highlighted in the cited reference, it's crucial to note that the single-branch inverter should be exclusively employed in neutral QCA technologies, and circuits designed using single-branch inverters are compatible solely with neutral QCA cells. This distinction must be explicitly stated for the benefit of future designers trying to implement this technology. It's important to emphasize that the proposed circuit is compatible with a few QCA technologies, but not all. Therefore, I strongly recommend that the authors consider explicitly specifying the limitations of their architecture.

 

> The multiplexer circuit has garnered […] near-zero energy dissipation

 

This point was addressed well by the authors.

 

> The reversible majority gate, as demonstrated […] '1' input value.

 

The authors claim that the QCA majority gate becomes reversible through recycling two input bits, citing references [15,23]. However, neither of these references explicitly mentions the reversibility of the majority voter achieved by replicating two inputs out of three. Reference 15 specifically discusses the reversibility of the majority voter when duplicating two inputs, but confines this claim to OR and AND logic gates, not the majority voter itself. Additionally, Reference 15 proposes a reversible majority voter by replicating all inputs, not solely two out of three. This unresolved discrepancy implies that the main scope of this work, ensuring or demonstrating the reversibility of the majority gate, remains unaddressed in the reviewer's opinion. 

 

> Yes, both in the present research and the […] provided in Table 2.

 

This point was addressed well by the authors.

 

>  The technology characteristics used in this […] of the QCA system.

 

The authors inserted Section 2 to introduce some background about QCA technology. However, in the reviewer's perspective, there is a background regarding the modelling of QCA paradigm, but no discussion regarding technology is presented (e.g. Magnetic, molecular, solid-state, heterojunctions,…).

 

In general, it appears that there may be an inclination in presenting the findings in a more optimistic light than their actual substantiation allows. While the paper certainly holds value and contributes to the field, it might benefit from a reconsideration of the language used to avoid overestimating the significance of the results. A balanced and accurate portrayal of the research findings will further strengthen the credibility and impact of their work within the scientific community.

Comments on the Quality of English Language

The Quality of English in the article is clear and coherent.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

All my comments have been done in this valuable paper so I strongly recommend it to publish.

Author Response

We appreciate your decision to accept the paper. It's our pleasure that you find the paper valuable.

Reviewer 3 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

The authors made appropriate corrections to the text. The paper can be published.

Comments on the Quality of English Language

English is good, small corrections are required. 

Author Response

We appreciate your decision to accept the paper.

The English language of the manuscript has been thoroughly reviewed and polished.

 

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

The authors study energy efficiency and power dissipation in digital circuits. They propose multilayer reversible quantum-dot cellular automata multiplexer circuits. They present numerical results using a special software program. A significant part of the text has a  yellow background, denoting obviously that this is an addition to the text following the reviewer's comments. Two pages 3 and 4, describing the system's physics, raise many questions. Starting with "the expectation value of the Pauli matrices" (what is this?), introducing parameter $\tau$ and the inverse of the product of Boltzmann constant and the temperature $(2k_BT)^{-1}$ after Eq. (8) (which do not appear in Eq. (8)) and finishing with an incredible Eq. (9) where an energy $E_{env}$ equals to itself three times and then equals to zero, the authors succeed in the total confusing of the reader. The authors introduce three new circuits that dissipate significantly different amounts of energy; therefore, I believe they need to discuss the differences between these circuits in detail.

It is somewhat unusual for the referee to comment on the manuscript's language presented by researchers from UK universities, but the text (especially in the "yellow" regions) must be revised. Line 102 on page 3: "$-\lambda_z$ corresponds to it is polarization." The text after Eq. (1), "The $\gamma$ corresponds" is wrong. I am sure it must be "The parameter $\gamma$ corresponds."

The manuscript can be accepted only after major revision.

Comments on the Quality of English Language

It is somewhat unusual for the referee to comment on the manuscript's language presented by researchers from UK universities, but the text (especially in the "yellow" regions) must be revised.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The authors did a great work in addressing the reviewer comments for their manuscript "Ultra-Energy-Efficient Reversible Quantum-Dot Cellular Automata 8:1 Multiplexer Circuit". Their meticulous attention to detail and comprehensive revisions have significantly strengthened the quality and rigor of the research. I am confident that their dedication and the improvements made will contribute substantially to the scientific community.

 

I have recommended your manuscript for publication, acknowledging the significant effort and thoughtfulness you have invested in addressing the reviewer comments. I sincerely hope that your research receives the recognition it deserves and makes a valuable contribution to the academic discourse.

 

Once again, congratulations on a job well done.

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

The authors revised manuscript according to my comments. Now I can recommend its acceptance.

Comments on the Quality of English Language

Fine.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper entitled "Ultra-Energy-Efficient Reversible Quantum-Dot Cellular Automata 8:1 Multiplexer Circuit" proposes a reversible majority voter and uses it to design a 8-bit reversible multiplexer in QCA paradigm. In general, the paper currently lacks important information and is lacking in terms of novelty. In the reviewer's perspective, the manuscript requires improvement in several aspects:

 

Major points:

• The proposed design seems to base the inversion on the single-diagonal QCA operation and analyse the device with QCADesigner. This approach has some limits, as demonstrated in 10.3390/electronics11020276, indeed, the QCA inversion made with single-diagonal interaction is available only on a few technologies, and QCADesigner results are not always reliable. The authors should discuss this point and motivate the use of single-branch inverter, eventually limitating the design to specific QCA technologies.
• The design of multiplexers is not particularly novel, e.g. 10.1002/dac.4254 designed multiplexer in 2019, even though they did not evaluated the power dissipation. Other works evaluated the power dissipation in multiplexers, e.g. 10.1016/j.dib.2017.03.001. Also reversible majority voter exist in the literature, and generally rely on more complex techniques, rather than replicating inputs, and eventually improving the robustness of the device.
• It is not clear to the reviewer how the single multiplexer can be reversible. To be reversible, one should be able to understand the inputs from the outputs. The authors copy inputs A,B to the output to provide reversibility. However, the combinations A=B=C=1 and A=B=1, C=0 both provide the same outputs, thus A=B=1, M(A,B,C)=1. And there is no way to understand the inputs from the output. How can be the proposed device logically reversible?
• The authors compare the energy dissipation of their proposed MUX with literature results. Yet, there is no information regarding the consistency of the comparison. Do the other work use similar methodologies and QCADesigner parameters? This point is crucial since the shown energy values are really small compared to present literature.
• The Authors do not address a specific technology. On the contrary, it is completely general. A technological-dependent analysis of the energy dissipation would permit the work to be more useful for the scientific literature. 

Minor points:

• I would not say QCA is "nascent", it was born in 1993, 30 years ago.
• Pay attention to capitalization of acronyms, e.g. page 1, line 42, Very Large Scale Integration, with capital first letters

The reviewer encourages the authors to enhance the manuscript. Best wishes to the authors in their endeavors to improve the paper.

Comments on the Quality of English Language

English must be improved, there are a lot of typos and sentences difficult to understand.

Author Response

Referee 1

Major points:

1. The proposed design seems to base the inversion on the single-diagonal QCA operation and analyse the device with QCADesigner. This approach has some limits, as demonstrated in 10.3390/electronics11020276, indeed, the QCA inversion made with single-diagonal interaction is available only on a few technologies, and QCADesigner results are not always reliable. The authors should discuss this point and motivate the use of single-branch inverter, eventually limiting the design to specific QCA technologies.

Section 3 now includes a discussion related to the QCA inversion approaches (lines 185-195), along with a clear explanation for the reason behind utilising the single-branch inverter in this study.

2. The design of multiplexers is not particularly novel, e.g., 1002/dac.4254 designed multiplexer in 2019, even though they did not evaluate the power dissipation. Other works evaluated the power dissipation in multiplexers, e.g., 10.1016/j.dib.2017.03.001. Also, reversible majority voter exists in the literature, and generally rely on more complex techniques, rather than replicating inputs, and eventually improving the robustness of the device.

The multiplexer circuit has garnered significant attention in past research due to its essential role in constructing digital circuits for computing systems. Energy efficiency is a fundamental consideration in the development of computer circuits. Several previous studies have proposed different configurations for reversible QCA multiplexer circuit, in order to reduce energy dissipation. These studies addressed reversibility only at the synthesis level and neglected reversibility at the layout level, i.e., the physical ‘instantiation’ of the circuit. However, maintaining reversibility at a physical level is the only way to achieve significant further energy reductions, in reversible computing [1]. Therefore, in this study, we present an innovative multilayer design for both a logically and physically reversible QCA 8:1 multiplexer circuit. The novelty of this study is that the design can preserve reversibility throughout the entire circuit design process, from the synthesis level down to the layout level, throughout the design hierarchy. This design technique completely mitigates the loss of information and consequently produces circuits that have near-zero energy dissipation.

3. It is not clear to the reviewer how the single majority gate can be reversible. To be reversible, one should be able to understand the inputs from the outputs. The authors copy inputs A, B to the output to provide reversibility. However, the combinations A=B=C=1 and A=B=1, C=0 both provide the same outputs, thus A=B=1, M(A, B,C)=1. And there is no way to understand the inputs from the output. How can be the proposed device logically reversible?

The reversible majority gate, as demonstrated in Figure 2 in the manuscript, replicates the data for two inputs, labelled A and B, into two outputs, labelled A Copy and B Copy, resulting in an overall situation with equal numbers of binary inputs and outputs. The recycling of two input bits can make the QCA majority gate reversible [2,3]. The functionality of the majority gate is determined by the input labelled C, which allows it to act as either an 'AND' gate when given a '0' input value or an 'OR' gate when given a '1' input value.

4. The authors compare the energy dissipation of their proposed MUX with literature results. Yet, there is no information regarding the consistency of the comparison. Do the other works use similar methodologies and QCADesigner parameters? This point is crucial since the shown energy values are really small compared to present literature.

Yes, both in the present research and the previously comparative studies have used the QCADesigner standard technological characteristics outlined in Table 1, and the simulation parameters provided in Table 2.

5. The Authors do not address a specific technology. On the contrary, it is completely general. A technological-dependent analysis of the energy dissipation would permit the work to be more useful for the scientific literature. 

The technology characteristics used in this study is now more clearly stated and given in Table 1. Also, a new section (Section 2) has been added to the manuscript covering the technological-dependent aspects and a detailed discussion of the energy dissipation numerical calculations of the QCA system.

Minor points:

1. I would not say QCA is "nascent", it was born in 1993, 30 years ago.

The term "nascent" was substituted with "promising".

2. Pay attention to capitalization of acronyms, e.g., page 1, line 42, Very Large-Scale Integration, with capital first letters.

Done

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This study investigates the use of quantum-dot cellular automata (QCA) to develop a fully

reversible QCA 8:1 multiplexer circuit with extremely low energy dissipation. The authors

utilized the QCADesigner-E program to calculate the energy dissipation. The proposed

multiplexer designs have been compared to previously published studies in order to assess their

performance.

 

I think this article is well structured and appropriate to publish in the journal. However, I have

only a few minor suggestions to enhance clarity:

 

1- In Section 4, it is advisable to employ chart diagrams to illustrate the comparison

between the proposed work in this research and similar earlier studies.

2- For Table 6, Table 7, and Table 8, the title of the first column has to change from

Proposed Reversible QCA Multiplexer Circuits to QCA Multiplexer Circuits.

Author Response

Referee 2

This study investigates the use of quantum-dot cellular automata (QCA) to develop a fully reversible QCA 8:1 multiplexer circuit with extremely low energy dissipation. The authors utilized the QCADesigner-E program to calculate the energy dissipation. The proposed multiplexer designs have been compared to previously published studies in order to assess their performance.

I think this article is well structured and appropriate to publish in the journal. However, I have only a few minor suggestions to enhance clarity: 

• In Section 4, it is advisable to employ chart diagrams to illustrate the comparison between the proposed work in this research and similar earlier studies.

We have added chart diagrams (Figures 6 – 8) to visually display the comparison between the proposed work in this research and analogous previous research, to convey clearer information.

• For Table 6, Table 7, and Table 8, the title of the first column has to change from Proposed Reversible QCA Multiplexer Circuits to QCA Multiplexer Circuits.

Done.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Quantum-Dot Cellular Automata is a promising technology that can provide revolutionary development of microelectronics and computing. One of the main advantage of this technology is that it can significantly reduce the power dissipation in logic gates and circuits. That is why the presented sudy has topical interest and the authors made important steps toward acheiving this goal.  I have a remark related to the presentation of the material. To give more complete picture of the field the authors should give a physical picture of the dissipative processes  in the cells and to give references on this key subject. After revision in this point I recommend to publish the paper.

 

Author Response

Referee 3

Quantum-Dot Cellular Automata is a promising technology that can provide revolutionary development of microelectronics and computing. One of the main advantages of this technology is that it can significantly reduce the power dissipation in logic gates and circuits. That is why the presented study has topical interest and the authors made important steps toward achieving this goal.  I have a remark related to the presentation of the material. To give more complete picture of the field the authors should give a physical picture of the dissipative processes in the cells and to give references on this key subject. After revision in this point, I recommend publishing the paper.

We have added a new section (Section 2) to the manuscript to discuss the energy dissipation calculation for a QCA system, and we have included references on this subject.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This work exist from 2013 onwards i do not find any novelty in the proposed work. Similar works are available in literature from 2013 onwards. 

Comments on the Quality of English Language

Minor edits required

Author Response

Referee 4

This work exists from 2013 onwards I do not find any novelty in the proposed work. Similar works are available in literature from 2013 onwards. 

The multiplexer circuit has garnered significant attention in past research due to its essential role in constructing digital circuits for computing systems. High energy efficiency is a vital consideration in the development of computer circuits. Several previous studies have proposed different configurations for reversible QCA multiplexer circuits, in order to reduce energy dissipation. These studies addressed reversibility only at the synthesis level and neglected reversibility at the layout level, i.e., the physical incarnation of the circuit. However, maintaining reversibility, down to the physical level, is the only way to achieve significant energy reductions in reversible computing [1]. Therefore, in this study, we present an innovative multilayer reversible design both at the logically and physically level for a QCA 8:1 multiplexer circuit. The novelty of this study is that the design can preserve reversibility throughout the entire circuit design hierarchy, from the synthesis level down to the layout level. This design technique mitigates the loss of information and consequently produces circuits that have near-zero energy dissipation achieving ultra-high energy efficiency.

References

1. DeBenedictis, E.P.; Frank, M.P.; Ganesh, N.; Anderson, N.G. A path toward ultra-low-energy computing. In Proceedings of the 2016 IEEE International Conference on Rebooting Computing (ICRC), 2016; pp. 1-8.
2. Torres, F.S.; Niemann, P.; Wille, R.; Drechsler, R. Near Zero-Energy Computation Using Quantum-Dot Cellular Automata. ACM Journal on Emerging Technologies in Computing Systems 2020, 16, 1-16, doi:10.1145/3365394.
3. Lent, C.S.; Liu, M.; Lu, Y. Bennett clocking of quantum-dot cellular automata and the limits to binary logic scaling. Nanotechnology 2006, 17, 4240.

Author Response File: Author Response.pdf