Are there any useful deterministic quantum algorithms for decision problems?
There are some query complexity results that mention exact quantum algorithms. See this blog post about the paper "Separations in Query Complexity Based on Pointer Functions":


  a total boolean function $g$ on $n$ variables that has [...] exact quantum query complexity [...] $Q_E(g) = \tilde O(\sqrt n)$.




More generally, the complexity class you're looking for is called EQP: Exact Quantum Polynomial-Time.

EQP is not a very "nice" complexity class, especially compared to BQP. There's two big reasons for that:


Theoretical-side, there's no universal set of gates. EQP circuits may require a gate with irrational coefficients such as $\begin{bmatrix} \cos(10^\circ) &amp; -\sin(10^\circ)\\ \sin(10^\circ) &amp; \cos(10^\circ)\end{bmatrix}$, and approximations via other gates aren't allowed. So you end up with a bunch of different $\text{EQP}_{my\_favorite\_gate\_set}$s instead of a nice unified one.
Practical-side, there's no possibility of error correction. EQP lives in a world without errors, because otherwise it wouldn't be exact. Error correction is expected to be a necessity in practice, so if you care about actual implementation then you don't care much about EQP.