Determine whether the amplitude-amplification transducer can be time-efficient

Determine whether the error-free amplitude-amplification transducer developed in the paper can be implemented time-efficiently, rather than only analyzed in the query-complexity model.

Background

The paper develops an amplitude-amplification transducer that avoids producing garbage, a property needed for its quantum-walk applications. Its query complexity is analyzed through adversary-bound and transducer techniques.

The authors contrast this construction with an earlier transducer that is time-efficient but produces garbage. Thus, establishing time efficiency for the new garbage-free construction would strengthen the practical and algorithmic scope of the transducer framework.

References

The downside of our construction is that we do not currently know if it is possible to implement this transducer time-efficiently, in contrast with the transducer constructed in . We leave this for future work.

— Improved quantum volume estimation with transducers and amortized quantum walks  (2609.40217 - Cornelissen et al., 30 Sep 2026) in Section 2, subsection 2.1 (Amplitude amplification with transducers), opening discussion

The algorithms presented in this work are optimal or efficient in terms of quantum query complexity, but we do not study time or space complexity: as constructed, the transducing algorithms that we obtain might involve unitaries that are hard to implement. We leave as open problem for future work how to make these transducing algorithms time or space efficient.

— Optimal transducers using symmetries  (2610.02133 - Dubus et al., 1 Oct 2026) in Section 1, Introduction