Circuit to Create and Entangled State

[Kreizhn]

Homework Statement

In a quantum information setting:

I'm trying to find a circuit to construct the state

$$\frac1{\sqrt3} \left( |00\rangle + |01\rangle + |11 \rangle \right)$$

The Attempt at a Solution

This state is entangled, and so I've been playing with different input states to try and create this using the Bell EPR circuit. This hasn't worked so far, so if anyone has a better idea it would be much appreciated.

 

[jdwood983]

Now I don't know much about quantum computing, but if you have three terms in the state, don't you need three components to build that state? And doesn't the Bell circuit only have two components?

 

[Kreizhn]

The problem for me lies precisely in the fact that there's three components in the super-position. If the Bell circuit took three inputs though, we would have a superposition on three qubits rather than just two. Also, the Bell-circuit seemingly will only entangle for two components, since it's possible to create a four-component state but I don't think it's entangled.