Broken promises and quantum algorithms (pp131-145)
         Adam Brazier and Martin B. Plenio
          doi: https://doi.org/10.26421/QIC5.2-4
Abstracts: In the black-box model, problems constrained by a "promise" are the only ones that admit a quantum exponential speedup over the best classical algorithm in terms of query complexity. The most prominent example of this is the Deutsch-Jozsa algorithm. More recently, Wim van Dam put forward an algorithm for unstrucred problems (i.e., those without a promise). We consider the Deutsch-Jozsa algorithm with a less restrictive (or "broken") promise and study the transition to an unstructured problem. We compare this to the success of van Dam's algorithm. These are both compared with a standard classical sampling algorithm. The Deutsch-Jozsa algorithm remains good as the problem initially becomes less structured, but the van Dam algorithm can be adapted so as to become superior to the Deutsch-Jozsa algorithm as the promise is weakened. 
Key words: quantum algorithms, broken promises