First, your understanding of quantum computers is wrong. Quantum computers are not faster as such, it's just that they can solve certain problems much faster than classical computers by using certain features of quantum mechanics.
While quantum computers indeed have some advantage in brute-forcing (due to Grover's algorithm), that advantage is merely quadratic; that is, just double your key size, and you're safe against a quantum computer with the same processing speed as a classical computer.
When you hear about quantum computers threatening cryptographic systems, this is about Shor's algorithm which is exponentially faster than what (we think that) classical computers can achieve. Which is relevant for cryptography because our current asymmetric cryptography (like SSH and SSL/TLS) is mostly based on the difficulty of factoring large numbers. The algorithm being exponentially faster means that a doubling of your key length only adds a fixed amount of additional time to break the key.
However at the time quantum computers are released, this will be a non-issue, for two reasons:
First, there are already cryptographic algorithms that are believed to be secure against quantum computing (if you think "are believed to be" is too weak, remember that factorizing integers is also only believed to be hard for classical computers; we don't have a proof for it, and in principle we cannot exclude the possibility that tomorrow someone will publish an efficient algorithm to do it on a classical computer).
And second, asymmetric (public key) encryption is mainly used for communication; and for that quantum mechanics also offers a solution: Quantum encryption. Quantum encryption can be broken neither by classical nor by quantum computers (and unlike for public key encryption, you actually can prove it!). The only way to attack quantum encryption is to attack the hardware.
Note that quantum cryptography is already commercially available today, and surely by the time a quantum computer capable of breaking current cryptography is available, those quantum cryptography systems will already be in wide use.
So in short: The way to safely release quantum computers to the world will be easy: Just release them. People who care will already be prepared.
If you have indication that people are not sufficiently prepared, just announce that you will release them, wait for some reasonable time for everyone who cares to update their cryptography, and then release them,