Related papers: Towards a Theory of Conservative Computing
The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to…
This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case.…
The Conservation of Energy plays a pivotal part in the development of the physical sciences. With the growth of computation and the study of other discrete token based systems such as the genome, it is useful to ask if there are…
All computation is physically embedded. Reflecting this, a growing body of results embraces rate equations as the underlying mechanics of thermodynamic computation and biological information processing. Strictly applying the implied…
Reversible computation has been proposed as a future paradigm for energy efficient computation, but so far few implementations have been realised in practice. Quantum circuits, running on quantum computers, are one construct known to be…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
Our main models of computation (the Turing Machine and the RAM) make fundamental assumptions about which primitive operations are realizable. The consensus is that these include logical operations like conjunction, disjunction and negation,…
Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible…
Resent works of Hawking and Susskind suggested that information is conserved in the universe. We extend this thesis and propose that dynamics of information - computations can conserve in Anti-de-Sitter cosmological model. Information…
Conservation laws limit the accuracy of physical implementations of elementary quantum logic gates. If the computational basis is represented by a component of spin and physical implementations obey the angular momentum conservation law,…
Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of…
While often treated as abstract algorithmic properties, intelligence and computation are ultimately physical processes constrained by conservation laws. We introduce the Conservation-Congruent Encoding (CCE) framework as a unified,…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
In the paradigm of thermodynamic computing, instead of behaving deterministically, hardware undergoes a stochastic process in order to sample from a distribution of interest. While it has been hypothesized that thermodynamic computers may…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
Fault-tolerant quantum computation requires minimizing non-Clifford gates, whose implementation via magic state distillation dominates the resource costs. While $T$-count minimization is well-studied, dedicated $CCZ$ factories shift the…
We speculate whether the second law of thermodynamics has more to do with Turing machines than steam pipes. It states the logical reversibility of reality as a computation, i.e., the fact that no information is forgotten: nature computes…
Reversible computing is motivated by both pragmatic and foundational considerations arising from a variety of disciplines. We take a particular path through the development of reversible computation, emphasizing compositional reversible…
The relation between entropy and information has great significance for computation. Based on the strict reversibility of the laws of microphysics, Landauer (1961), Bennett (1973), Priese (1976), Fredkin and Toffoli (1982), Feynman (1985)…