Hu et al. just posted An efficient quantum search engine on unsorted database. They refer to an older paper by Patel (2001), Quantum database search can do without sorting. Apparently without any data structure or preprocessing, logarithmic-time search queries are possible in quantum databases.
Even if we did have affordable quantum computers, this would not be a big selling point. Building B-trees or sorting tables is hardly prohibitive.
I would be more interested in how quantum databases can handle low selectivity queries. For example, can a quantum computer sum up a large array of numbers in near-constant time? Our current technology solves these problems with a mix of parallelism, compression and brute-force.
All I know about quantum computers is that we do not think they can solve NP-hard problems in polynomial time. Is there any reason to see a bright future in quantum databases?