Operators.md

Operators (or Quantum Gates)

An operator serves to modify the state of a quantum state.
To create a new operator you have to specify a matrix which represent the operator:

myOp = Op([
    [-1,0],
    [0, 1]
    ])

To apply an operator to a quantum state you have 2 way:

• Use the method apply(Op):

  q = qbit(1,0)
  q.apply(myOp)
  print(q) # -1|0>

• Use the | operator:

  q = qbit(1,0)
  myOp | q
  print(q) # -1|0>

By default exists some common operator:

• Op.I
• Op.X
• Op.Y
• Op.Z
• Op.H
• Op.cnot
• Op.swap
• Op.sqrtSwap
• Op.phaseGate(phase, deg)
• Op.C(U) (the controlled-U gate)

---

To define an operator exists another way, that is specify how it modify the state of a basis.

For instance you can define an operator U in this way:

U such that:
    U|0> = |1>
    U|1> = |0>

You are surely glad to know that in logiq you can do this!

U = Op.build({
    '|0>' : '|1>',
    '|1>' : '|0>'
})

To build an operator you have to specify a dictionary {state : new state}

state and new state can be expressed in different way:

• vector
• number of state of a certain basis
• string

U = Op.build({
    0 : '|1>',
    1 : ket(1,0)
})

Of course you can specify a basis and work with it:

U = Op.build({
    '|+>' : '-|->',
    '|->' : '-|+>'
}, basis=hadamard)
q = qbit('|+>', basis=hadamard)
U | q
print(q) # -1|->

This method can be really useful to create dynamically an oracle (see this for an example of use)