The Merkle tree side won't be broken as 256-bit hash functions are not vulnerable to Grover's algorithm, and the digital signature algorithms used to sign transactions can be replaced with post quantum versions. So unfortunately we won't get rid of crypto currencies.

Example problem: Find out which two prime numbers were multiplied together to produce the following semiprime:

25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357

A sufficiently large Quantum Computer that runs Shor's algorithm solves this problem in polynomial time, i.e. in hours to days.

Your classic, digital electronic super computer running the best classical algorithm (General Number Field Sieve or GNFS for short) would crunch this problem until the universe dies of heat death.

The semiprime factoring problem is a at the heart of public key encryption algorithm known as RSA. There's also another algorithm in public key cryptography called Diffie-Hellman, that relies on a problem called discrete logarithm. DH can also be solved with an algorithm closely related to Shor's algorithm.

Computers rely almost exclusively on these two problems e.g. to verify authenticity of files, software updates etc, and to establish encryption keys over insecure channels.

The modern society depends on computers for everything so understandably this is a big and important topic, and the reason NIST just recently completed a competition to find so called post-quantum algorithms that the society can rely on for the next thousand years.

As per https://en.wikipedia.org/wiki/Integer_factorization_records#Records_for_efforts_by_quantum_computers, the largest number that Shor's algorithm has been used to factor, is 21.

Not to nitpick but the factors of a prime number are already known, e.g. the factors of 13 are 13 and 1. What you're usually factoring in these cases are semi-primes, that are the product of two prime numbers.

tl;dr No.

ELI5: The goal in quantum computers is to get many qubits into into a superposition where they are sort of connected to each other. As the number of qubits inside a single quantum computer is increased linearly, the problem size they can solve grows exponentially. If you add a second quantum computer, you're only doubling the computational power. With seven computers you can parallelize breaking of e.g. 7 keys, but the number of qubits inside a single quantum computer determine the size of the encryption key you're able to break.

Finally, I hope I didn't ruin some horcrux reference here, with the seven and all.

Yeah, the 1.6-bit improvement is roughly 3.03x improvement. It's interesting we haven't yet seen snake oil claims like "AES 66% broken". In layman's terms, it's kind of like having to eat a cake that's 1/3rd the size of our galaxy. Sure, you got rid of 2/3rds of the cake size but your stomach will only fit so much.

Also, SHA256 does lossy compression, and obtaining preimages larger than 256 bits can not be done at all, QC or not.

One extremely useful purpose is protein folding which is what IBM (that the article is about) is also doing: https://protein-folding-demo.mybluemix.net/

the tl;dr is it will result in much faster faster medicine/vaccine development.