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quantum-computingqiskit
Bob
Bob

Reputation: 1

In what state is this 3-qubit state?

So, I have a state of 3 qubits that is in one of the states in the picture. How can I find out which state it is in?

enter image description here

I tried to measure the qubits but the amplitudes are 1/3 for each, so...

Upvotes: 0

Views: 84

Answers (1)

Mariia Mykhailova
Mariia Mykhailova

Reputation: 2032

This is task 1.15 from the Measurements kata, so I'll outline the solution broadly and point you to the workbook for that task for the formulas and details that are painful to spell out on StackOverflow without LaTeX support.

When you need to distinguish two orthogonal quantum states, you can first apply a unitary to them to rotate them to two different orthogonal quantum states that are easy to distinguish - for example, states that have different basis states in their superposition makeup.

In this case,

  • We can first apply some rotation gates (R1 gate in Q# or similar gates) to the second and the third qubits to get rid of the 𝜔 amplitudes in the first state, converting it into the W state.
  • Then, apply adjoint of the transformation you'd use to prepare the W state from the |000⟩ state, so that this state ends up becoming the |000⟩ state.
  • Since the transformations you've applied are unitaries and they preserve the product of state vectors, you know that the vectors remain orthogonal after their application. This means that if you do the measurements now, you'll always get 000 for the first state, and some other basis state for the second one.

Upvotes: 1

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