arXiv subjects

Hannah Earley

Publications and source records attributed to Hannah Earley.

7 recordsLinked to original sources

arXiv2023

Reversible Bond Logic

The field of molecular programming allows for the programming of the structure and behavior of matter at the molecular level, even to the point of encoding arbitrary computation. However, current approaches tend to be wasteful in terms of monomers, gate complexes, and free energy. In response, we present a novel abstract model of molecular programming, Reversible Bond Logic (RBL), which exploits the concepts of reversibility and reversible computing to help address these issues. RBL systems permit very general manipulations of arbitrarily complex 'molecular' structures, and possess properties such as component reuse, modularity, compositionality. We will demonstrate the implementation of a common free-energy currency that can be shared across systems, initially using it to power a biased walker. Then we will introduce some basic motifs for the manipulation of structures, which will be used to implement such computational primitives as conditional branching, looping, and subroutines. Example programs will include logical negation, and addition and squaring of arbitrarily large numbers. As a consequence of reversibility, we will also obtain the inverse programs (subtraction and square-rooting) for free. Due to modularity, multiple instances of these computations can occur in parallel without cross-talk. Future work aims to further characterize RBL, and develop variants that may be amenable to experimental implementation.

cs.ET↗

arXiv2022

A Universal Constraint on Computational Rates in Physical Systems

Conventional computing has many sources of heat dissipation, but one of these--the Landauer limit--poses a fundamental lower bound of 1 bit of entropy per bit erased. 'Reversible Computing' avoids this source of dissipation, but is dissipationless computation possible? In this paper, a general proof is given for open quantum systems showing that a computer thermally coupled to its environment will necessarily dissipate entropy (and hence heat). Specifically, a lower bound is obtained that corresponds to the adiabatic regime, in which the amount of entropy dissipated per computational operation is proportional to the rate of computation.

quant-ph↗

arXiv2022

The $\aleph$-Calculus: A declarative model of reversible programming

A novel model of reversible computing, the $\aleph$-calculus, is introduced. It is declarative, reversible-Turing complete, and has a local term-rewriting semantics. Unlike previously demonstrated reversible term-rewriting systems, it does not require the accumulation of history data. Terms in the $\aleph$-calculus, in combination with the program definitions, encapsulate all program state. An interpreter was also written.

cs.PL↗

arXiv2021

Engines of Parsimony: Part I; Limits on Computational Rates in Physical Systems

We analyse the maximum achievable rate of sustained computation for a given convex region of three dimensional space subject to geometric constraints on power delivery and heat dissipation. We find a universal upper bound across both quantum and classical systems, scaling as $\sqrt{AV}$ where $V$ is the region volume and $A$ its area. Attaining this bound requires the use of reversible computation, else it falls to scaling as $A$. By specialising our analysis to the case of Brownian classical systems, we also give a semi-constructive proof suggestive of an implementation attaining these bounds by means of molecular computers. For regions of astronomical size, general relativistic effects become significant and more restrictive bounds proportional to $\sqrt{AR}$ and $R$ are found to apply, where $R$ is its radius. It is also shown that inhomogeneity in computational structure is generally to be avoided. These results are depicted graphically in Figure 1.

cond-mat.stat-mech↗

arXiv2021

Engines of Parsimony: Part II; Performance Trade-offs for Communicating Reversible Computers

In Part I of this series, the limits on the sustained performance of large reversible computers were investigated and found to scale as $\sqrt{AV}$ where $A$ is the convex bounding surface area of the system and $V$ its internal volume, compared to $A$ for an irreversible computer. This analysis neglected to consider interactions between components of the system however, instead focussing on raw computational power. In this part we extend this analysis to consider synchronisation events such as communication between independent reversible processors subject to a limiting supply of free energy. It is found that, whilst asynchronous computation can proceed at a rate $bλ$, synchronisation events proceed at the much slower rate $\sim b^2λ$; in these rate expressions, $λ$ is the gross transition rate for each processor and $b\sim\sqrt{A/V}\ll1$ is the 'computational bias' measuring the net fraction of transitions which are successful. Whilst derived for Brownian reversible computers, this result applies to all forms of reversible computer, including Quantum computers. In fact this result is an upper bound, and one must choose the phase space geometry of the synchronisation events carefully to avoid even worse performance. In the limit of large computers, communication will therefore tend to freeze out as $b\to0$; if, however, one is willing to restrict the number of processors permitted to share state at any given time then this rate can be ameliorated and performance on par with asynchronous computation can be recovered.

cond-mat.stat-mech↗

arXiv2021

The $\aleph$ Calculus

Motivated by a need for a model of reversible computation appropriate for a Brownian molecular architecture, the $\aleph$ calculus is introduced. This novel model is declarative, concurrent, and term-based--encapsulating all information about the program data and state within a single structure in order to obviate the need for a von Neumann-style discrete computational 'machine', a challenge in a molecular environment. The name is inspired by the Greek for 'not forgotten', due to the emphasis on (reversibly) learning and un-learning knowledge of different variables. To demonstrate its utility for this purpose, as well as its elegance as a programming language, a number of examples are presented; two of these examples, addition/subtraction and squaring/square-rooting, are furnished with designs for abstract molecular implementations. A natural by-product of these examples and accompanying syntactic sugar is the design of a fully-fledged programming language, alethe, which is also presented along with an interpreter. Efficiently simulating $\aleph$ on a deterministic computer necessitates some static analysis of programs within the alethe interpreter in order to render the declarative programs sequential. Finally, work towards a type system appropriate for such a reversible, declarative model of computation is presented.

cs.PL↗

arXiv2021

Engines of Parsimony: Part III; Performance Trade-offs for Reversible Computers Sharing Resources

This paper concludes a three-Part series on the limits the laws of physics place on the sustained performance of reversible computers. Part I concerned aggregate performance in terms of computational operations per unit time, but neglected to consider interactions among computational sub-units or between computational sub-units and shared resources such as memory or chemical species. Part II extended the analysis to consider the former set of interactions. In this Part we extend the analysis to consider the latter set, with a particular focus on resource distribution in the first half. It is found that most schemes imaginable fail to function effectively in the limit of vanishing 'computational bias' $b$, which measures the net fraction of transitions which are successful, and falls as the system grows in size. Driving thermodynamically unfavourable reactions, such as resource distribution, is a very general problem for such systems and can be solved by supplying a sufficient excess of free energy. We propose a scheme to dynamically supply enough free energy for a given reaction, automatically and rapidly adapting to changes in the disequilibrium state of said reaction--including the case when the favourable reaction direction switches. The overhead of this scheme is no worse than the overhead found in Part II for communicating reversible computers under the same regime.

cond-mat.stat-mech↗