Introduction to quantum error correction (QEC)

Suppose you want to send a single-bit message on a channel from which you know that the bit-flip error probability p = 0.25. How many repetitions are required to have a 99% that your message is received correctly? 

The number of times you need to send the message depends on the length of the message. 

You might have already heard about X, Y, and Z gates on single quantum bits, and that effect on their quantum state. In the field of Quantum Error Correction, we associate bit flips with X gates, as it turns a qubit from |0> into the |1> state. With what gate do you think we associate sign-flip errors? And why?

Sign flip errors are associated to Z-gates as they turn qubits from |0> into  |0>  and |1> into  -|1>.