<transcript><audio_51>log n with high probability so in our setting in this graph that I just showed in the previous slide your degree of your graph is bounded by your depth and then the probability that your</transcript><transcript><audio_52>vertex survives that a cubit remains non-de phased decays exponentially and and this is sort of important it's it's it's because like there's a certain</transcript> log n with high probability so in our setting in this graph that I just showed in the previous slide your degree of your graph is bounded by your depth and then the probability that your vertex survives that a cubit remains non-de phased decays exponentially and and this is sort of important it's it's it's because like there's a certain okay all right yeah probability there's a certain probability that survives the first layer then it survives the first and the second layer and the probability it survives D layers is exponentially decaying and D so the phase transition occurs when E power minus PD time D is less than one so you have an exponential decay caused by the noise and this linear growth in entanglement which characterizes the entanglement and when this is less than one you see percolation this will happen at a constant depth so after a constant depth all of your subcircuits are of size o of log n and you have a polinomial time classical simulation algorithm and I I want to emphasize this point here because it's sort of getting at the heart of what this classical simulation algorithm takes advantage of is that your entanglement in this iqp
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