Part of the reason, I think, is that there has been a lot of misinformation and misconceptions that have circulated around about this field for a while. But, there is no real substance behind this legend; all that we actually have from von Neumann on this is one brief remark he made during a lecture that was not backed up by any analysis.

He never published any peer-reviewed journal article on this topic, possibly because he realized that it was a mistake and had never actually proved it. Probably he was implicitly assuming that decision-making implied the creation of entropy, since an unknown outcome of the decision was being replaced by a known one, which would imply entropy creation elsewhere to satisfy the 2nd law of thermodynamics. But of course, a decision-making process can be deterministic, as most computations are; if the outcome is predetermined by the input, then there need be no change in entropy in the decision-making process.

And, even if you want the outcome of the decision-making process to be random, that only requires moving a bit of entropy from the environment into the computer, not generating any new entropy. A second rumor or urban legend against reversible computing is the claim that it would violate the central theorems proved by Claude Shannon, pioneer of the mathematical theory of information and communication, concerning the minimum power required for communication, at a given bandwidth and reliability. Absolutely all of his work only addresses power transmitted , but nowhere do his theorems establish that the power contained in a signal cannot later be recovered by suitable mechanisms.

In the design of reversible computing mechanisms, we explicitly show how the energy contained in any given pattern of physically encoded bits can be recovered, for example, by using the time-reverse of the exact same reversible process that created that bit-string in the first place. So, there is a bias against reversible computing that is based on the widespread misunderstanding or misinterpretation of the work of these respected pioneers.

But, each time the flaw in one of these skeptical arguments is pointed out, disproving its core objection definitively using a clear counterexample, the skeptics just keep coming up with new and different but still flawed arguments against reversible computing. I think that probably, the only way that many of these reversible computing skeptics will ever be convinced is if an already commercially-successful reversible computer is staring them in the faces — then they will no longer be able to deny it.

### Reward Yourself

After all, all of the theory in the world is useless until we are able to use it to start building practical machines. And to be fair, the challenges that still need to be faced in order to make reversible computing practical are substantial. But, the prevalent attitude does make it very difficult to get research funding. And without substantial funding — or top-level researchers who have the free time and inclination to solve the remaining foundational problems definitively — these problems will never be solved, and reversible computing will never become more than an obscure academic curiosity.

But, if adequate attention is paid to solving the key remaining problems, reversible computing has the potential to become the foundation of 21st century computer engineering. Certainly, we cannot make more than a modest amount of further progress in the power-performance of most computing applications without it. Luke : Can you say a bit about the history of reversible computing thus far?

## An algebra of reversible computation

What were the key pieces of conceptual progress after the initial demonstration of the Landauer limit? How did they build on each other, or on other results in physics or computing? The basic technique basically involves temporarily storing all of the intermediate data that would otherwise be thrown away, so it is somewhat space-intensive, but later, in , Bennett showed that more space-efficient variations on the technique were possible.

Finally, it was even shown in by Lange et al. It is probably the case that general reversible computations do require some amount of overhead in either space or time complexity; indeed, Ammer and I proved rigorously that this is true in a certain limited technical context.

## CNA - 混q进制、进位行电子计算机新一代技术方案 - Google Patents

But, the overheads of reversible algorithms can theoretically be overwhelmed by their energy-efficiency benefits, to improve overall cost-performance for large-scale computations. In terms of practical implementations, some early conceptual work was done by Fredkin and Toffoli at MIT in a proposal suggesting the use of inductors and capacitors to shuttle energy around between devices in a circuit to implement logic in a near dissipationless fashion.

In the early s, Koller and Athas developed a general adiabatic logic family, but it was only able to handle combinational not sequential logic. Finally, in Younis and Knight at MIT developed their general-purpose, adiabatic, sequential Split-Level Charge Recovery Logic — although even that one still contained a small bug limiting its energy efficiency, which we found and fixed in the late 90s , during my thesis work. I also invented another, simpler and bug-free universal adiabatic logic family called 2LAL at the University of Florida in 2.

In detailed simulations at UF, we found that 3 sequential 2LAL circuits could dissipate as little as 1 electron volt of energy per transistor per cycle, limited only by the leakage current in the particular device family we were simulating. This figure could be made even lower if other device families with reduced leakage were used. Whereas, the vast majority of other nanocomputing proposals that have been made, namely, all of the ones that totally ignore reversible computing, are all fundamentally doomed to failure, in that they will never be able to get many orders of magnitude beyond the limits of CMOS in terms of their energy efficiency — since they all ignore the fundamental limit on the energy efficiency of irreversible devices that follows from the requirement to maintain high reliability despite thermal noise.

Unfortunately, in my experience, there are far too few device physicists who seem to understand this basic fact. Luke : If a researcher wanted to make progress toward reversible computing, where would you recommend they start looking? What are the most promising avenues of research at this point, do you think? Mike : Well, as I mentioned earlier, I think that some fundamental breakthroughs in basic theory are still needed.

We are still lacking a comprehensive theoretical model demonstrating how a realistic quantum-mechanical system composed of many interacting subsystems can be made to coast along a complexly-constrained, deterministic trajectory through configuration space with negligible entropy increase per operation. Instead, we can presumably rely only on naturally stable a. It is a big challenge, but I think that someone will show us the way eventually. Theoretically reversible logic dissipates zero power since the input vector of reversible circuit can be uniquely recovered from the output vector.

This study presents an overview of the well-known reversible gates and discuss about their quantum implementation.

A new PFAG gate and its quantum implementation are presented. Finally, this study proposes a novel low cost quantum realization of reversible multiplier circuit and compares its superiority with the existing counterparts. Power dissipation is a very important factor in VLSI design. As we pack more and more logic elements into smaller and smaller volumes and clock them higher and higher frequencies, we dissipate more and more heat.

This creates at least three problems:. These logic operations are therefore called irreversible. This erasure is done very inefficiently and much more than kT is dissipated for each bit erased. If the revolution is continued in computer hardware performance we must continue to reduce the energy dissipated by each logic operation. Today, because we are dissipating much more than kT, we can do this by improving conventional methods, i. An alternative is to use logic operations that do not erase information. These are called reversible logic operations and according to Bennet zero energy dissipation would be possible only if the network consists of reversible gates.

Thus reversibility will become an essential property in future circuit design. Synthesis of reversible logic circuits differs significantly from classical logic circuits in many ways.

## A Valleytronics route towards future reversible computers

In reversible circuits there should be no fan-out, that is, each output will be used only once, for each input pattern there should be a unique output pattern and the resulting circuit must be acyclic Perkowski et al. Any reversible circuit realizes only the function that is reversible. Garbage is the number of outputs added to make an n-input k-output function, i. The word constant-input are the inputs added to an n, k function to make it reversible.

An algorithm is given by Islam to make an n, k function reversible.

### Background

Any efficient realization of reversible network should minimize the number of reversible gates, garbage outputs and constant inputs. The gate complexity should be kept as low as possible.

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Finally, the quantum realization cost of it in any nanotechnology should be optimized. Full-adder is the fundamental building block of many computational units. The compatible adder implementation in quantum technology is must. Any reversible gate that can work singly as a reversible full-adder unit will be beneficial to build other complex circuits in nanotechnology. This study presents a new reversible gate PFAG that can work singly as a reversible full-adder unit. The quantum realization of this reversible full-adder gate is also given.

Then a low cost quantum realization of reversible multiplier circuit using PFAG and Peres gate Peres, is presented. The objective of this study is that the proposed reversible multiplier circuit is superior to the existing designs in terms of gate count, garbage outputs, constant-inputs and hardware complexity. Moreover, the quantum realization of this multiplier circuit is readily available for use. Reversible gate: A gate or a circuit is called reversible if there is a one-to-one correspondence between its input and output assignments.

There exist many reversible gates in the literature. The quantum realizations of all these gates are not available in the literature. The detailed cost of a reversible gate depends on any particular realization of quantum logic. Generally, the cost is calculated as a total sum of 2x2 quantum primitives used. According to Perkowski et al. Reversible full-adder circuit: Full-adder is the fundamental building block of many computational units.

- Claw Back (Louis Kincaid).
- Reversible computing: fundamentals, quantum computing, and applications.
- An algebra of reversible computation.
- Center for Computing Research.
- Introduction to Reversible Computing!
- Traffic Jam.

The anticipated paradigm shift logic compatible with optical and quantum requires compatible adder implementations. Minimization of reversible full-adder circuits and their implementation issues has been discussed by Khan , Islam et al. Islam et al. They have realized a full-adder circuit with only two Peres gates and which is optimum in terms of gate count, garbage outputs, constant-input and efficient in terms of quantum cost and that can be technologically mapped.