<transcript><audio_31>circuits like any diagonal Gates Set you use to construct your iqp circuit as long it's on as as long as each gate acts locally so again I'll stress it doesn't require anti-concentration and since I didn't Define it before a loose like this is a little hand wavy but it</transcript><transcript><audio_32>it just tells you anti concentration sort of tells you over an ensemble of random circuit how flat is your distribution and this is sort of the formal definition of it it comes up in proofs of hardness and easiness um but it's something we're not going to need for our classical</transcript><transcript><audio_33>simulation algorithm so I won't go too much into it so to show you how it works I'm going to go through an example case so suppose you have an iqp circuit constructed with Tates and controlled phase Gates and</transcript><transcript><audio_34>you've interspersed def phasing noise the the proof the algorithm is going to work in three steps these are just the titles and I'm going to explain each step so the first fact we're going to use is that def phasing noise commutes with diagonal Gates so if you have your</transcript><transcript><audio_35>circuit and you have intersperse def phasing noise throughout your circuit you can take every single def phasing noise Channel commute it to the beginning of the circuit now you have this larger strength def phasing noise Channel at the beginning because your noise builds up and this is sort of taking advantage of the commuting</transcript><transcript><audio_36>structure of the iqp circuit the second fact we're going to use is that def phasing noise acts very predictably on this superposition state so the plus state is a superposition of your zero and one when you put def phasing noise on it it makes it a</transcript> circuits like any diagonal Gates Set you use to construct your iqp circuit as long it's on as as long as each gate acts locally so again I'll stress it doesn't require anti-concentration and since I didn't Define it before a loose like this is a little hand wavy but it it just tells you anti concentration sort of tells you over an ensemble of random circuit how flat is your distribution and this is sort of the formal definition of it it comes up in proofs of hardness and easiness um but it's something we're not going to need for our classical simulation algorithm so I won't go too much into it so to show you how it works I'm going to go through an example case so suppose you have an iqp circuit constructed with Tates and controlled phase Gates and you've interspersed def phasing noise the the proof the algorithm is going to work in three steps these are just the titles and I'm going to explain each step so the first fact we're going to use is that def phasing noise commutes with diagonal Gates so if you have your circuit and you have intersperse def phasing noise throughout your circuit you can take every single def phasing noise Channel commute it to the beginning of the circuit now you have this larger strength def phasing noise Channel at the beginning because your noise builds up and this is sort of taking advantage of the commuting structure of the iqp circuit the second fact we're going to use is that def phasing noise acts very predictably on this superposition state so the plus state is a superposition of your zero and one when you put def phasing noise on it it makes it a
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