Bitcoin Blockchain in the Quantum computing era
If quantum computers become viable and the approach of factorization of numbers which has been theoretically presented works, this means that Bitcoin will have to use a different way of signing transactions as through the use of quantum computers, it becomes easy (only polynomial time required) to calculate a private key from a public key.

Simply increasing the key length doesn't work. If you double the key length, a classical computer has to work twice as hard to encrypt or decrypt the message but it becomes much, much harder than twice as hard as before to crack the encryption. Signing, in this case, really is just encrypting a hash of a message. However, for a quantum computer, the problem of cracking the encryption, only becomes twice as hard. So you can't keep up with using longer and longer keys because then the increase in effort an attacker has to put in only increases as fast as the increase of effort you have to put into using the keys.

However, there are ways to approach the problem of the signatures currently in use being rendered useless by the advent of quantum computers. Namely, quantum digital signatures.

Because quantum computers aren't faster than classical computers but reduce some exponential problems to polynomial problems, and cryptographic hashes can't be broken using quantum computers, their advent won't impact the difficulty to find a new block.