Related papers: A complete set of transformation rules for reversi…
We introduce a set of eight universal Rules of Inference by which computer programs with known properties (axioms) are transformed into new programs with known properties (theorems). Axioms are presented to formalize a segment of Number…
Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
We consider the general problem of the optimal transformation of N uses of (possibly different) unitary channels to a single use of another unitary channel in any finite dimension. We show how the optimal transformation can be fully…
We introduce a reversible theory of exact entanglement manipulation by establishing a necessary and sufficient condition for state transfer under trace-preserving transformations that completely preserve the positivity of partial transpose…
Boolean reversible circuits are boolean circuits made of reversible elementary gates. Despite their constrained form, they can simulate any boolean function. The synthesis and validation of a reversible circuit simulating a given function…
We propose an interpretation of quantum separability based on a physical principle: local time reversal. It immediately leads to a simple characterization of separable quantum states that reproduces results known to hold for binary…
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.…
This PhD dissertation investigates garbage-free reversible computing systems from abstract design to physical gate-level implementation. Designed in reversible logic, we propose a ripple-block carry adder and work towards a reversible…
We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices…
An algorithm for reversible logic synthesis is proposed. The task is, for a given $n$-bit substitution map $P_n: \{0,1\}^n \rightarrow \{0,1\}^n$, to find a sequence of reversible logic gates that implements the map. The gate library…
Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be…
We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic…
Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in…
The paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits consisting of Toffoli gates with negative control lines. An asymptotically optimal synthesis algorithm for circuits…
Reversible sequential circuits are going to be the significant memory blocks for the forthcoming computing devices for their ultra low power consumption. Therefore design of various types of latches has been considered a major objective for…
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
Now a day reversible logic is an attractive research area due to its low power consumption in the area of VLSI circuit design. The reversible logic gate is utilized to optimize power consumption by a feature of retrieving input logic from…
The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven…