  In a number of recent experiments it has been demonstrated that in
ultra-narrow superconducting channels quantum fluctuations of the order
parameter, alternatively called quantum phase slips, are responsible for the
finite resistance well below the critical temperature. The acceptable agreement
between those experiments and the models describing quantum fluctuations in
quasi-one-dimensional superconductors has been established. However the very
concept of the phase slip is justified when these fluctuations are the
relatively rare events, meaning that the effective resistance of the system
should be much smaller than the normal state equivalent. In this paper we study
the limit of the strong quantum fluctuations where the existing models are not
applicable. In particular case of ultra-thin titanium nanowires it is
demonstrated that below the expected critical temperature the resistance does
not demonstrate any trend towards the conventional for a superconductor
zero-resistivity state even at negligibly small measuring currents. Application
of a small magnetic field leads to an unusual negative magnetoresistance, which
becomes more pronounced at lower temperatures. The origin of the negative
magnetoresistance effect is not clear.
