2026-09-19T22:51:48Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/910972022-01-13T07:54:01Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Scott Aaronson.
Ben David, Shalev
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2014-10-21T17:25:52Z
2014-10-21T17:25:52Z
2014
2014
http://hdl.handle.net/1721.1/91097
892733342
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).
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)).
by Shalev Ben David.
S.M.
35 pages
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
The structure of promises in quantum speedups
Thesis
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<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)).</Abstract>
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