<transcript><audio_37>mixture of your zero and one so in the block sphere picture what used to be on the boundary of your block sphere is now a shorter block Vector um which is a mixture between your zero your one and the plus state so the idea here is</transcript><transcript><audio_38>instead of simulating the shorter block Vector we're going to sample so your simulation algorithm is going to take your noise Channel and sample from it as either leaving the plus State intact or</transcript><transcript><audio_39>an error occurs and this error replaces it with a zero or a one so that's how we're going to simulate all of the noise that we built up at on the beginning of the circuit the second fact we're the third fact we're going to use is that diagonal</transcript><transcript><audio_40>Gates act classically on computational basis States so Tates introduce Global phase that can be ignored the controlled phase Gates become classically controlled phase Gates which don't introduce entanglement so once You' sampled your</transcript><transcript><audio_41>zeros and ones these AED locations the controlled phase gate that acts on these AED cubits acts classically you have a controlled phase a classically controlled phase so</transcript><transcript><audio_42>this has all been been known before to some extent that noise acts in a way that basically replaces some of your input states with with random zeros and ones but it takes a while like a large depth for you to get to the place where</transcript> mixture of your zero and one so in the block sphere picture what used to be on the boundary of your block sphere is now a shorter block Vector um which is a mixture between your zero your one and the plus state so the idea here is instead of simulating the shorter block Vector we're going to sample so your simulation algorithm is going to take your noise Channel and sample from it as either leaving the plus State intact or an error occurs and this error replaces it with a zero or a one so that's how we're going to simulate all of the noise that we built up at on the beginning of the circuit the second fact we're the third fact we're going to use is that diagonal Gates act classically on computational basis States so Tates introduce Global phase that can be ignored the controlled phase Gates become classically controlled phase Gates which don't introduce entanglement so once You' sampled your zeros and ones these AED locations the controlled phase gate that acts on these AED cubits acts classically you have a controlled phase a classically controlled phase so this has all been been known before to some extent that noise acts in a way that basically replaces some of your input states with with random zeros and ones but it takes a while like a large depth for you to get to the place where
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