The structure of promises in quantum speedups
Name
892733342-MIT.pdf
Description
Full printable version
Size
1.13 MB
Format
Adobe PDF
Checksum (MD5)
80d0eb89a36a6c8de2ab2085d757fc80
Author(s)
Ben David, Shalev
Advisor(s)
Scott Aaronson.
Date Issued
2014
Publisher
Massachusetts Institute of Technology
Abstract
It has long been known that in the usual black-box model, one cannot get super-polynomial quantum speedups without some promise on the inputs. In this thesis, we examine certain types of symmetric promises, and show that they also cannot give rise to super-polynomial quantum speedups. We conclude that exponential quantum speedups only occur given "structured" promises on the input. Specifically, we show that there is a polynomial relationship of degree 12 between D(f) and Q(f) for any function f defined on permutations (elements of {0, 1, ... , M - 1}1 in which each alphabet element occurs exactly once). We generalize this result to all functions f defined on orbits of the symmetric group action S., (which acts on an element of {0, 1, . . . , M - I}f by permuting its entries). We also show that when M is constant, any function f defined on a "symmetric set" - one invariant under Sn - satisfies R(f) = O(Q(f)12(M-1)).
Description
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (page 35).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
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