0:00:03suppose and integer and is built from two unknown prime factors for example fifteen is
0:00:11equal to three times five
0:00:13if present a protocol how these factors can be determined by an experiment
0:00:21imaging you have to try
0:00:22we has it is great energy levels for a single particle a proportional to the
0:00:28logarithm of the quantum number how can i help you to find the factors of
0:00:33a given individual
0:00:36we need to particles with the dimension less code the energy of logarithm of fifteen
0:00:43then the particles may occupies the lattice number
0:00:49three
0:00:50and five
0:00:53all you have to do now is to measure the energy of one of the
0:00:58particles
0:00:59from this would you like one of the factors
0:01:02of course the second factor is followed by deviation of you rate you know the
0:01:08two particles may occupy the lattice this number one and fifteen as well
0:01:15that's is mean we have only a fifty chance to find the factors
0:01:20no because we show in our paper that for large numbers and the probability to
0:01:26find the fact that we are interested in is much larger than two fines to
0:01:31detect those you met and
0:01:34this is our first result
0:01:37i seconds result is a proposal how to realise it to particle state with the
0:01:43dimension of this energy of logarithm of and
0:01:47we start with to code postonic atoms is a ground state and into we use
0:01:52and are still aiding interaction between yet l two color segmentation into c desired state
0:01:59the frequency only got a of the oscillating interaction is chosen to be resonant to
0:02:05the frequency of the transition into the factor state in this way to the number
0:02:11to be factor is coded into the frequency of the interaction
0:02:16we solve this within a equation and find that the probabilities posted ground state and
0:02:22the factor states are still eight
0:02:24this is called rugby oscillation
0:02:27on the typical it is evident that the measurement should be done vincent probability plots
0:02:33of factors state is a rush we indicates it in the pickup by capital t
0:02:39since values of this very the equation contains the factors p and q we want
0:02:44to determine and therefore unfortunately the measurement time t also depends on unknown factors
0:02:52our the result is that we found an approximation forty which depends only on the
0:02:59number and we want to tactile
0:03:02we have cm addition to factor numbers as large as possible but of course a
0:03:08limitations on the experimental conditions
0:03:11they all discussed in our paper i just mention one of them
0:03:16since spacing of the energy nevis in the two particles spectrum decreases as n increases
0:03:23because now of class and then transitions into a neighbouring states become more and more
0:03:28probable over chance to fines affect the state becomes more for very large and
0:03:35let me and ms a conclusion
0:03:37we have developed a protocol that allows to find the factors of numbers of the
0:03:43order of ten to the dog until tend to supports with the probability of about
0:03:48ninety percent in a single run of the experiment
0:03:53this estimation was based on parameters typical in two days and technology
0:04:00thank you for your attention and enjoy reading all paper