9,732 research outputs found
The origins and physical roots of life’s dual – metabolic and genetic – nature
This review paper aims at a better understanding of the origin and physical foundation of life’s dual – metabolic and genetic – nature. First, I give a concise ‘top-down’ survey of the origin of life, i.e., backwards in time from extant DNA/RNA/protein-based life over the RNA world to the earliest, pre-RNA stages of life’s origin, with special emphasis on the metabolism-first versus gene/replicator-first controversy. Secondly, I critically assess the role of minerals in the earliest origins of bothmetabolism and genetics. And thirdly, relying on the work of Erwin Schrödinger, Carl Woese and Stuart Kauffman, I sketch and reframe the origin of metabolism and genetics from a physics, i.e., thermodynamics, perspective. I conclude that life’s dual nature runs all the way back to the very dawn and physical constitution of life on Earth. Relying on the current state of research, I argue that life’s origin stems from the congregation of two kinds of sources of negentropy – thermodynamic and statistical negentropy. While thermodynamic negentropy (which could have been provided by solar radiation and/or geochemical and thermochemical sources), led to life’s combustive and/or metabolic aspect, the abundant presence of mineral surfaces on the prebiotic Earth – with their selectively adsorbing and catalysing (thus ‘organizing’) micro-crystalline structure or order – arguably provided for statistical negentropy for life to originate, eventually leading to life’s crystalline and/or genetic aspect. However, the transition from a prebiotic world of relatively simple chemical compounds including periodically structured mineral surfaces towards the complex aperiodic and/or informational structure, specificity and organization of biopolymers and biochemical reaction sequences remains a ‘hard problem’ to solve
The Birkhoff theorem for unitary matrices of prime-power dimension
The unitary Birkhoff theorem states that any unitary matrix with all row sums
and all column sums equal unity can be decomposed as a weighted sum of
permutation matrices, such that both the sum of the weights and the sum of the
squared moduli of the weights are equal to unity. If the dimension~ of the
unitary matrix equals a power of a prime , i.e.\ if , then the
Birkhoff decomposition does not need all possible permutation matrices, as
the epicirculant permutation matrices suffice. This group of permutation
matrices is isomorphic to the general affine group GA() of order only
The block-ZXZ synthesis of an arbitrary quantum circuit
Given an arbitrary unitary matrix , a powerful matrix
decomposition can be applied, leading to four different syntheses of a
-qubit quantum circuit performing the unitary transformation. The
demonstration is based on a recent theorem by F\"uhr and Rzeszotnik,
generalizing the scaling of single-bit unitary gates () to gates with
arbitrary value of~. The synthesized circuit consists of controlled 1-qubit
gates, such as NEGATOR gates and PHASOR gates. Interestingly, the approach
reduces to a known synthesis method for classical logic circuits consisting of
controlled NOT gates, in the case that is a permutation matrix.Comment: Improved (non-sinkhorn) algorithm to obtain the proposed circui
Logics between classical reversible logic and quantum logic
Classical reversible logic and quantum computing share the common feature that all computations are reversible, each result of a computation can be brought back to the initial state without loss of information
The Birkhoff theorem for unitary matrices of prime dimension
The Birkhoff's theorem states that any doubly stochastic matrix lies inside a
convex polytope with the permutation matrices at the corners. It can be proven
that a similar theorem holds for unitary matrices with equal line sums for
prime dimensions
Scaling a unitary matrix
The iterative method of Sinkhorn allows, starting from an arbitrary real
matrix with non-negative entries, to find a so-called 'scaled matrix' which is
doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and
with all line sums equal to 1. We conjecture that a similar procedure exists,
which allows, starting from an arbitrary unitary matrix, to find a scaled
matrix which is unitary and has all line sums equal to 1. The existence of such
algorithm guarantees a powerful decomposition of an arbitrary quantum circuit.Comment: A proof of the conjecture is now provided by Idel & Wolf
(http://arxiv.org/abs/1408.5728
The decomposition of an arbitrary unitary matrix into signed permutation matrices
Birkhoff's theorem tells that any doubly stochastic matrix can be decomposed
as a weighted sum of permutation matrices. A similar theorem reveals that any
unitary matrix can be decomposed as a weighted sum of complex permutation
matrices. Unitary matrices of dimension equal to a power of~2 (say )
deserve special attention, as they represent quantum qubit circuits. We
investigate which subgroup of the signed permutation matrices suffices to
decompose an arbitrary such matrix. It turns out to be a matrix group
isomorphic to the extraspecial group {\bf E} of order
. An associated projective group of order equally suffices.Comment: 4th paper in a series of Birkhoff decompositions for unitary matrices
[(1) arXiv:1509.08626; (2) arXiv:1606.08642; (3) arXiv:1812.08833
A technology based complexity model for reversible Cuccaro ripple-carry adder
Reversible logic provides an alternative to classical computing, that may overcome many of the power dissipation problems. The paper presents a simple complexity model, from the study of a cascade of Cuccaro adders processed in standard 0.35 micrometer CMOS technology
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