its an open problem subject to cutting edge research whether quantum algorithms will ever be faster than "classical" algorithms both on the theoretical and applied levels. in complexity theory it is reflected in the question eg BQP =? P ie whether quantum computing "P" class is equivalent or not to the classical P (Polynomial time) class & there are many other related open questions.
there is one very intriguing & significant datapoint: the award-winning Shors algorithm factors numbers in P quantum time, but it is still not known whether there exists a P-time classical factoring algorithm.
a new direction over last few years is work in adiabatic quantum computing which is easier to implement/engineer than other standard methods involving qbit transport (but yet still extremely difficult to implement).
the only quantum computer(s) ever built to date is by Dwave systems and is currently subject to intense scientific scrutiny and controversy regarding its actual quantum effects & performance; it is very expensive and basically does not outperform a desktop computer, when the classical code is fully (human-/hand-) optimized. however it can be fairly stated no other corporate, government, or university research entities appear to be anywhere close to their level of applied/technical/engineering advancement so far.
the scientific outlook is cloudy at the moment & some scientific experts/critics/skeptics eg Dyakonov have long believed/argue strongly that scalable QM computers will never materialize due to insurmountable technical difficulties and/or barriers.