please implement fully and in detail. please do not give chatgpt copy pasted answer as I can do that myself I am not paying this service for that. please do not give instructions but give full implementation. it's about quantum machine learning. here is the test cases fully:

test$\_$input: $[0\mathrm{.}863327072347624,0\mathrm{.}0167108057202516,0\mathrm{.}07991447085492759,0\mathrm{.}0854049026262154,0\mathrm{.}0167108057202516,0\mathrm{.}8237963773906136,-0\mathrm{.}07695947154193797,0\mathrm{.}03131548733285282,0\mathrm{.}07991447085492759,-0\mathrm{.}07695947154193795,0\mathrm{.}8355417021014687,-0\mathrm{.}11345916130631205,0\mathrm{.}08540490262621539,0\mathrm{.}03131548733285283,-0\mathrm{.}11345916130631205,0\mathrm{.}758156886827099]$

expected$\_$output: $0\mathrm{.}61745341$

test$\_$input: $[0\mathrm{.}32158897156285354,-0\mathrm{.}20689268438270836,0\mathrm{.}12366748295758379,-0\mathrm{.}11737425017261123,-0\mathrm{.}20689268438270836,0\mathrm{.}7747346055276305,-0\mathrm{.}05159966365446514,0\mathrm{.}08215539696259792,0\mathrm{.}12366748295758379,-0\mathrm{.}05159966365446514,0\mathrm{.}5769050487087416,0\mathrm{.}3853362904758938,-0\mathrm{.}11737425017261123,0\mathrm{.}08215539696259792,0\mathrm{.}3853362904758938,0\mathrm{.}3986256655167206]$

expected$\_$output: $0\mathrm{.}00246488$