There's no good reason to believe that quantum computers will break modern cryptography.
Shor's algorithm requires that a quantum Fourier transform is applied to the integer to be factored. The QFT essentially takes quantum data with a representation that mirrors ordinary binary, and maps it to a representation that encodes information in quantum phase (an angle).
The precision in phase needed to perform an accurate QFT scales EXPONENTIALLY with the number of qubits you're trying to transform. You manage to develop a quantum computer capable of factoring my keys? Fine, I'll add 11 bits to my key length, come back when you've developed a computer with 2000x the phase precision.
Shor's algorithm requires that a quantum Fourier transform is applied to the integer to be factored. The QFT essentially takes quantum data with a representation that mirrors ordinary binary, and maps it to a representation that encodes information in quantum phase (an angle).
The precision in phase needed to perform an accurate QFT scales EXPONENTIALLY with the number of qubits you're trying to transform. You manage to develop a quantum computer capable of factoring my keys? Fine, I'll add 11 bits to my key length, come back when you've developed a computer with 2000x the phase precision.