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