159,276 research outputs found
Noise Limited Computational Speed
In modern transistor based logic gates, the impact of noise on computation
has become increasingly relevant since the voltage scaling strategy, aimed at
decreasing the dissipated power, has increased the probability of error due to
the reduced switching threshold voltages. In this paper we discuss the role of
noise in a two state model that mimic the dynamics of standard logic gates and
show that the presence of the noise sets a fundamental limit to the computing
speed. An optimal idle time interval that minimizes the error probability, is
derived
Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
We apply the logic of the quench action to give an exact analytical
expression for the time evolution of the one-body density matrix after an
interaction quench in the Lieb-Liniger model from the ground state of the free
theory (BEC state) to the infinitely repulsive regime. In this limit there
exists a mapping between the bosonic wavefuntions and the free fermionic ones
but this does not help the computation of the one-body density matrix which is
sensitive to particle statistics. The final expression, given in terms of the
difference of the square root of two Fredholm determinants, can be numerically
evaluated and is valid in the thermodynamic limit and for all times after the
quench.Comment: 24 pages, 2 figur
Rapid flipping of parametric phase states
Since the invention of the solid-state transistor, the overwhelming majority
of computers followed the von Neumann architecture that strictly separates
logic operations and memory. Today, there is a revived interest in alternative
computation models accompanied by the necessity to develop corresponding
hardware architectures. The Ising machine, for example, is a variant of the
celebrated Hopfield network based on the Ising model. It can be realized with
artifcial spins such as the `parametron' that arises in driven nonlinear
resonators. The parametron encodes binary information in the phase state of its
oscillation. It enables, in principle, logic operations without energy transfer
and the corresponding speed limitations. In this work, we experimentally
demonstrate flipping of parametron phase states on a timescale of an
oscillation period, much faster than the ringdown time \tau that is often
(erroneously) deemed a fundamental limit for resonator operations. Our work
establishes a new paradigm for resonator-based logic architectures.Comment: 6 pages, 3 figure
Implications of the Landauer limit for quantum logic
The design of any system of quantum logic must take into account the implications of the Landauer limit for logical bits. Useful computation implies a deterministic outcome, and so any system of quantum computation must produce a final deterministic outcome, which in a quantum computer requires a quantum decision that produces a deterministic qubit. All information is physical, and any bit of information can be considered to exist in a physicality represented as a decision between the two wells of a double well potential in which the energy barrier between the two wells must be greater than kT·ln2. Any proposed system of quantum computation that does not result in such a deterministic outcome can only be considered stochastically as a probability distribution (i.e. a wave function). An example of such determinism in a quantum logic system is theorized to exist in the DNA molecule, where the decoherence of quantum decision results in an enantiomeric shift in the deoxyribose moiety that is appropriate to the Landauer limit
High visibility on-chip quantum interference of single surface plasmons
Quantum photonic integrated circuits (QPICs) based on dielectric waveguides
have been widely used in linear optical quantum computation. Recently, surface
plasmons have been introduced to this application because they can confine and
manipulate light beyond the diffraction limit. In this study, the on-chip
quantum interference of two single surface plasmons was achieved using
dielectric-loaded surface-plasmon-polariton waveguides. The high visibility
(greater than 90%) proves the bosonic nature of single plasmons and emphasizes
the feasibility of achieving basic quantum logic gates for linear optical
quantum computation. The effect of intrinsic losses in plasmonic waveguides
with regard to quantum information processing is also discussed. Although the
influence of this effect was negligible in the current experiment, our studies
reveal that such losses can dramatically reduce quantum interference visibility
in certain cases; thus, quantum coherence must be carefully considered when
designing QPIC devices.Comment: 6 pages, 4 figure
Semantics out of context: nominal absolute denotations for first-order logic and computation
Call a semantics for a language with variables absolute when variables map to
fixed entities in the denotation. That is, a semantics is absolute when the
denotation of a variable a is a copy of itself in the denotation. We give a
trio of lattice-based, sets-based, and algebraic absolute semantics to
first-order logic. Possibly open predicates are directly interpreted as lattice
elements / sets / algebra elements, subject to suitable interpretations of the
connectives and quantifiers. In particular, universal quantification "forall
a.phi" is interpreted using a new notion of "fresh-finite" limit and using a
novel dual to substitution.
The interest of this semantics is partly in the non-trivial and beautiful
technical details, which also offer certain advantages over existing
semantics---but also the fact that such semantics exist at all suggests a new
way of looking at variables and the foundations of logic and computation, which
may be well-suited to the demands of modern computer science
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