<transcript><audio_45>because of this fact that I mentioned earlier that like some of these Gates become classically uh classical controlled Gates which don't int introduce in tanglement so each def phasing error removes all the edges of</transcript><transcript><audio_46>the corresponding vertex from the interaction graph so if this was your earlier interaction graph every time you have a def phasing error and you replace them of your cubits with zeros and ones those edges get removed from the graph your controlled phase gate becomes a</transcript><transcript><audio_47>classically controlled phase gate and you can classically simulate this there's there's no entanglement between the different regions the other thing you can notice here is that what used to be this giant connected component with entanglement stretching across the</transcript><transcript><audio_48>entire circuit is now split into smaller components because there's no entanglement across these two components you can simulate them independently and that's the the trick essentially we're going to check the depth at which all</transcript><transcript><audio_49>our circuit gets percolated into many small independent uh subcircuits that we can simulate independently so when does this happen so from graph percolation Theory we know that for any graph if Delta is</transcript> because of this fact that I mentioned earlier that like some of these Gates become classically uh classical controlled Gates which don't int introduce in tanglement so each def phasing error removes all the edges of the corresponding vertex from the interaction graph so if this was your earlier interaction graph every time you have a def phasing error and you replace them of your cubits with zeros and ones those edges get removed from the graph your controlled phase gate becomes a classically controlled phase gate and you can classically simulate this there's there's no entanglement between the different regions the other thing you can notice here is that what used to be this giant connected component with entanglement stretching across the entire circuit is now split into smaller components because there's no entanglement across these two components you can simulate them independently and that's the the trick essentially we're going to check the depth at which all our circuit gets percolated into many small independent uh subcircuits that we can simulate independently so when does this happen so from graph percolation Theory we know that for any graph if Delta is
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