<transcript><audio_27>with anti concentration in the average case over these an concentrated circuits if there's noise you're classically simulatable what our result shows is that at a constant depth and beyond that constant depth you get classical</transcript><transcript><audio_28>so I'm going to stress the generality of this result bit so it applies to arbitrary circuits including alt all connectivity it applies so I didn't Define the poly noise Channel explicitly because it applies to a a broad set of</transcript><transcript><audio_29>channels that include a def phasing component and what this means is if I can express my noise channel in a way that I can extract out a def phasing component then it fits into this uh classical simulation algorithm depolarizing noise for example is</transcript><transcript><audio_30>something that you can write as def phasing and bit flip noise so you could simulate a circuit with depolarizing noise um that's the math equation for that and it also applies for any iqp</transcript> with anti concentration in the average case over these an concentrated circuits if there's noise you're classically simulatable what our result shows is that at a constant depth and beyond that constant depth you get classical so I'm going to stress the generality of this result bit so it applies to arbitrary circuits including alt all connectivity it applies so I didn't Define the poly noise Channel explicitly because it applies to a a broad set of channels that include a def phasing component and what this means is if I can express my noise channel in a way that I can extract out a def phasing component then it fits into this uh classical simulation algorithm depolarizing noise for example is something that you can write as def phasing and bit flip noise so you could simulate a circuit with depolarizing noise um that's the math equation for that and it also applies for any iqp
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