If we invent quantum cryptography, business will continue on.

Otherwise, everybody's secret in the world can and will be cracked.

My brother-in-law is a physicist very involved in the world of research on quantum computing and I just asked him this question last week. All modern secure computing uses encryption based upon the same principals and if QC becomes a reality, all modern secure computing becomes insecure.

He thinks QC is a boondoggle and it reminds him of the government funded fusion research. A big money effort to something that may never happen and we are not even close.

If QC came into existence, he said we could use QC to encrypt and make this encryption impossible to crack by QC. And of course, the only 100% impossible to break encryption is one time pads.

QC doesn't just magically break all crypto, it makes it a lot easier possibly by several magnitudes,but many things could still be considered 'safe' for daily use.

Easier said than done.

Yes, it's nontrivial, but it could be done. My point is that QC wouldn't be the end of Bitcoin, and that we might be able to defend against it without having any quantum technology ourselves.

Perhaps with quantum technology it will be feasible not only to keep bitcoin alive, but to build a better bitcoin along the way.  For example, fully homomorphic encryption has recently just been shown to be possible, yet it is too slow for production use.  Perhaps something like that would be incorporated into the "next generation" bitcoin, thereby making bitcoin transactions verifiable, yet untraceable.

I'm currently working on a series of articles explaining the concepts used in Bitcoin, like proof-of-work and hashes. I would have to study a little bit before fully understanding exactly what quantum computers can do.

To answer the question: Not much. The BitCoin would just get to the 21 Million quicker.

But lets take a look at what would be needed. Considering this is an area that I am, what one could say, familiar with.  First we need ternary hardware, Russia kind of had the lead in this, and still have a few ternary computers around.  Basically it is hardware that is designed on 3 states not 2 or -0+ instead of 0101. One could run the logic on a binary system, but you loose the advantage of a ternary system. Guess who gets to use it first, The Government but hey they paid for it.  This actually start with University of Pennsylvania a long time ago. MIT has some musings on the subject.   

So the BitCoin would be safe in Quantum Computing, Hashes however, will be pretty useless. Just create a new key pair for each transaction, and get two or more confirmations, then it wont matter if the hash is cracked. It will only matter if you use the same Key pair for multiple transactions, meaning that they could crack your key pair.  But with PKC using Quantum Computing to generate Key pairs then you could just scale the system to keep the Odds of a crack off the charts.

How about using Quantum Pairing for sending and receiving between parties, instantaneously (even between Planets) and completely untraceable to boot.

A P2P Mesh network based on Quantum Pairs. Oh, baby. 

Did you read my post??

I don't think quantum computing is going to come out of left field. Many of the people paying attention to Bitcoin are heavy into crypto and will have a good idea of whether there's a major advance coming up.

Once it seems that quantum cryptanalysis is a real threat, all of these folks will start moving their money out of BTC and into other areas. And at least a few of them will be interested in inventing "Qubitcoin." Once that exists, smart money will move to Qubitcoin. Once folks notice the sudden inflation, even dumb money will move to Qubitcoin. A few slow movers will likely be left holding the pieces.

I'm curious about whether a Bitcoin-like currency could be minted with intrinsic value, so that even those last few won't be totally empty-handed. Encoding some sort of useful information that can only be accessed with the private key? But really I don't think this is anywhere close to the biggest threat to crypto-currency.