"Since the invention of a ground-breaking factoring algorithm by Peter Shor  in 1994 and the (not proven) availability
of quantum computer hardware capable of running the algorithm efficiently , , the scientific interest in finding a
“Post-Quantum Key Exchange” - a key exchange that resists quantum computer attacks, is immense. Shor’s algorithm
 is capable of factoring a number on quantum computer hardware with an execution time that is “only” polynomial
in the number of bits. The operating principle was first verified experimentally in 2001 .
"Quantum computers with approximately 512 qubits are now claimed to be available to companies like Lockheed
Martin and government agencies like the CIA, NSA and NASA  . This has fuelled speculations about the actual
code-breaking capabilities of government organizations like the NSA. In order to break keys with 2,048 bit key length,
approximately 6,150 qubits are although required. Quantum control and correction accounts for an even higher number
of qubits that are required to mount an attack on 2,048 bit keys so that, depending on the chosen strategy, 20,000 ..
332,100 qubits must be present. The output of the quantum computer is not the desired solution. An additional step using conventional computers with time complexity O(bits 3 ) is required to identify the actual key, provided the
quantum system finishes in coherent state. Decoherence (change of state caused by spontaneous decay or interaction
with the environment of a quantum system) drags the probability of the success of the quantum computation step down
as the quantum lifetime is limited by experimental conditions, and eventually by the Heisenberg uncertainty principle
in general. This problem increases with increasing number of bits used for the encryption because the number of
quantum operations and, therefore, the computation time, increases with O(bits 3 ) as well. The greater the size of the key
that is attacked, the less the number of useful quantum computer results."
(Yes, the article has foot-notes. Deal with it.)