suppose and integer and is built from two unknown prime factors for example fifteen is
equal to three times five
if present a protocol how these factors can be determined by an experiment
imaging you have to try
we has it is great energy levels for a single particle a proportional to the
logarithm of the quantum number how can i help you to find the factors of
a given individual
we need to particles with the dimension less code the energy of logarithm of fifteen
then the particles may occupies the lattice number
three
and five
all you have to do now is to measure the energy of one of the
particles
from this would you like one of the factors
of course the second factor is followed by deviation of you rate you know the
two particles may occupy the lattice this number one and fifteen as well
that's is mean we have only a fifty chance to find the factors
no because we show in our paper that for large numbers and the probability to
find the fact that we are interested in is much larger than two fines to
detect those you met and
this is our first result
i seconds result is a proposal how to realise it to particle state with the
dimension of this energy of logarithm of and
we start with to code postonic atoms is a ground state and into we use
and are still aiding interaction between yet l two color segmentation into c desired state
the frequency only got a of the oscillating interaction is chosen to be resonant to
the frequency of the transition into the factor state in this way to the number
to be factor is coded into the frequency of the interaction
we solve this within a equation and find that the probabilities posted ground state and
the factor states are still eight
this is called rugby oscillation
on the typical it is evident that the measurement should be done vincent probability plots
of factors state is a rush we indicates it in the pickup by capital t
since values of this very the equation contains the factors p and q we want
to determine and therefore unfortunately the measurement time t also depends on unknown factors
our the result is that we found an approximation forty which depends only on the
number and we want to tactile
we have cm addition to factor numbers as large as possible but of course a
limitations on the experimental conditions
they all discussed in our paper i just mention one of them
since spacing of the energy nevis in the two particles spectrum decreases as n increases
because now of class and then transitions into a neighbouring states become more and more
probable over chance to fines affect the state becomes more for very large and
let me and ms a conclusion
we have developed a protocol that allows to find the factors of numbers of the
order of ten to the dog until tend to supports with the probability of about
ninety percent in a single run of the experiment
this estimation was based on parameters typical in two days and technology
thank you for your attention and enjoy reading all paper