  The quantum computer is supposed to process information by applying unitary
transformations to the complex amplitudes defining the state of N qubits. A
useful machine needing N=1000 or more, the number of continuous parameters
describing the state of a quantum computer at any given moment is much greater
than the number of protons in the Universe. However, the theorists believe that
the feasibility of large-scale quantum computing has been proven via the
threshold theorem. Like for any theorem, the proof is based on a number of
assumptions considered as axioms. However, in the physical world none of these
assumptions can be fulfilled exactly. Any assumption can be only approached
with some limited precision. So, the rather meaningless
error-per-qubit-per-gate threshold must be supplemented by a list of the
precisions with which all assumptions behind the threshold theorem should hold.
Such a list still does not exist. The theory also seems to ignore the undesired
free evolution of the quantum computer caused by the energy differences of
quantum states entering any given superposition. Another important point is
that the hypothetical quantum computer will be a system of at least a thousand
of qubits plus an extremely complex and monstrously sophisticated classical
apparatus. This huge and strongly nonlinear system will generally exhibit
instabilities and chaotic behavior.
