<transcript><audio_9>examples of discrete gate sets that can generate such a diagonal unitary and you'll find a lot of these in literature um and finally you measure in the hadamar bases so you do your state prep and your measurement in this hadamar basis and then you do all of the</transcript><transcript><audio_10>intermediate Gates diagonally so uh what what was found like back in 2010 is that these circuits are hard to exactly sample from um after a depth of four and this makes them a good candidate for uh Quantum Supremacy</transcript><transcript><audio_11>experiments this was improved later on to show that it's hard to approximately sample from these in the average case under some conditions and all these like hardness statements usually rely on some complexity theoretic assumptions like</transcript><transcript><audio_12>the polinomial hierarchy um but the this is what's known sort of about this hardness and then another thing that makes it more practical is that it doesn't require a universal gate set so this hopefully makes it more amendable to near-term hardware and this is sort</transcript> examples of discrete gate sets that can generate such a diagonal unitary and you'll find a lot of these in literature um and finally you measure in the hadamar bases so you do your state prep and your measurement in this hadamar basis and then you do all of the intermediate Gates diagonally so uh what what was found like back in 2010 is that these circuits are hard to exactly sample from um after a depth of four and this makes them a good candidate for uh Quantum Supremacy experiments this was improved later on to show that it's hard to approximately sample from these in the average case under some conditions and all these like hardness statements usually rely on some complexity theoretic assumptions like the polinomial hierarchy um but the this is what's known sort of about this hardness and then another thing that makes it more practical is that it doesn't require a universal gate set so this hopefully makes it more amendable to near-term hardware and this is sort
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