Which results make quantum space interesting? Time-bounded quantum computation is obviously very interesting. What about space-bounded quantum computation?

I know many interesting results for quantum computation with sublogarithmic space bounds and various kind of quantum automata models.

On the other hand, it was shown that unbounded-error probabilistic and quantum space are equivalent for any space constructable $ s(n) \in \Omega(\log(n)) $ (Watrous, 1999 and 2003). 

I wonder whether there are some specific results making quantum space interesting (by excluding sublogarithmic-space and automata models).

(I am aware of this entry: Quantum analogues of SPACE complexity classes.)
I think Amnon Ta-Shma's new result is a good answer to my own question.


Amnon Ta-Shma: Inverting well conditioned matrices in quantum logspace. STOC 2013: 881-890. (copy from author's website)



  ...  We show that the inverse of a well conditioned matrix can be approximated in quantum logspace with intermediate measurements. This should be compared with the best known classical algorithm for the problem that requires $\Omega(\log^2 n)$ space. We also show how to approximate the spectrum of a normal matrix, or the singular values of an arbitrary matrix, with $\epsilon$ additive accuracy, and how to approximate the singular value decomposition (SVD) of a matrix whose singular values are well separated. ...