A Tight Lower Bound for Index Erasure

@inproceedings{Lindzey2020ATL,
  title={A Tight Lower Bound for Index Erasure},
  author={N. Lindzey and A. Rosmanis},
  booktitle={ITCS},
  year={2020}
}
  • N. Lindzey, A. Rosmanis
  • Published in ITCS 2020
  • Mathematics, Computer Science, Physics
  • The Index Erasure problem asks a quantum computer to prepare a uniform superposition over the image of an injective function given by an oracle. We prove a tight $\Omega(\sqrt{n})$ lower bound on the quantum query complexity of the non-coherent case of the problem, where, in addition to preparing the required superposition, the algorithm is allowed to leave the ancillary memory in an arbitrary function-dependent state. This resolves an open question of Ambainis, Magnin, Roetteler, and Roland… CONTINUE READING

    Figures and Topics from this paper.

    On the Algebraic Combinatorics of Injections and its Applications to Injection Codes

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 25 REFERENCES
    Quantum Adversary Lower Bound for Element Distinctness with Small Range
    • 6
    • PDF
    A note on the quantum collision and set equality problems
    • 73
    • PDF
    Negative weights make adversaries stronger
    • 179
    • PDF
    Understanding Quantum Algorithms via Query Complexity
    • 22
    • PDF
    Quantum Query Complexity of State Conversion
    • 120
    • PDF
    Quantum lower bounds for the collision and the element distinctness problems
    • 300
    • PDF