Generate 3 qubit W state using standard quantum gates

Question

Starting from the state |000>, how can I generate the state (|100> + |010> + |001>)/sqrt(3) using only X,Y,Z,H,S,T,SWAP,TOFFOLI, rotation gates, QFT, and their controlled versions and any number of ancilla bits?

Answer 1

It is very painful to write quantum computing formulas on StackOverflow without formulas support, so I'll give you several links that cover this question quite extensively:

1. The same question on QuantumComputing StackExchange: https://quantumcomputing.stackexchange.com/questions/15506/three-qubits-w-state
2. A more general contstruction for N-qubit W state: https://quantumcomputing.stackexchange.com/questions/4350/general-construction-of-w-n-state
3. Superposition quantum kata has this task as one of its problems, and its workbook offers a very detailed description of the solution, as well as the Q# implementation.