  Decoherence is the main obstacle to quantum computation. The decoherence rate
per qubit is typically assumed to be constant. It is known, however, that
quantum registers coupling to a single reservoir can show a decoherence rate
per qubit that increases linearly with the number of qubits. This effect has
been referred to as superdecoherence, and has been suggested to pose a threat
to the scalability of quantum computation. Here, we show that superdecoherence
is absent when the spectrum of the single reservoir is continuous, rather than
discrete. The reason of this absence, is that, as the number of qubits is
increased, a quantum register inevitably becomes susceptible to an ever
narrower bandwidth of frequencies in the reservoir. Furthermore, we show that
for superdecoherence to occur in a reservoir with a discrete spectrum, one of
the frequencies in the reservoir has to coincide exactly with the frequency the
quantum register is most susceptible to. We thus fully resolve the conditions
that determine the presence or absence of superdecoherence. We conclude that
superdecoherence is easily avoidable in practical realizations of quantum
computers.
