Quantum Computing Simulator II

We are going to build our universal quantum computer in a slightly different way.

Suppose I have my simulator and it's storing my state like this:

myState=[
  (numpy.sqrt(0.1), '00'),
  (numpy.sqrt(0.4), '01') , 
  (-numpy.sqrt(0.5), '11' )
]

Go ahead and implement some functions that eat your state, apply a gate, and give out a new state

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def Hadamard(inWire,numWires,inputState):
# do something
   return outputState

To accomplish this, just go ahead and loop through you old state and apply the gate to every element of your old state:

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for element in inputState:
   newState.append(...)  # apply the gate to one basis element and get some new basis element(s)
   newState.append(...) 

(it's actually faster if you do this by loop comprehensions [newState(element) for element in inputState]

Don't worry if you end up having some duplicate states (like below)

myState=[
  (-numpy.sqrt(0.25), '11' )
  (numpy.sqrt(0.1), '00'),
  (numpy.sqrt(0.4), '01') , 
  (-numpy.sqrt(0.25), '11' )
]

Now just write some code which takes the state and removes duplicates (i.e. myState=RemoveDuplicates(myState) should give

myState=[
  (numpy.sqrt(0.1), '00'),
  (numpy.sqrt(0.4), '01') , 
  (-numpy.sqrt(0.5), '11' )
]

Make sure you remove any term which has an amplitude zero.

Now you have a simulator where you can start with some state, apply a gate, remove duplicates, apply a state, etc.

	Grading
	Run this new simulator on the typical suite of tests and paste the results into the document.