UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

A Generalized Adversary Method for Quantum Query Complexity

dc.contributor.authorSoiffer, Rory
dc.date.accessioned2022-05-20T18:52:42Z
dc.date.available2022-05-20T18:52:42Z
dc.date.issued2022-05-20
dc.date.submitted2022-05-10
dc.description.abstractQuantum query complexity measures the minimum number of queries a quantum algorithm needs to make to some input string to compute a function of that input. Query complexity models are widely used throughout quantum computing, from setting limits on quantum algorithms to analyzing post-quantum cryptography. This thesis studies quantum adversary methods, a group of mathematical tools that prove lower bounds on quantum query complexity. I introduce a new general-purpose framework for adversary methods that generalizes over both the negative weight and multiplicative adversary methods. This framework unifies the lower bound proofs of both methods, even in the general case of quantum state conversion. This generalized method also gives a new formula for the multiplicative adversary method based on max-relative entropy. This new definition is more concise and easier to reason about than existing definitions in the literature. I verify this by reproving several known results about the multiplicative adversary method. I also use this to reprove the strong direct product theorem for quantum query complexity.en
dc.identifier.urihttp://hdl.handle.net/10012/18317
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectquantum computingen
dc.subjectquery complexityen
dc.subjectadversary methodsen
dc.titleA Generalized Adversary Method for Quantum Query Complexityen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentDavid R. Cheriton School of Computer Scienceen
uws-etd.degree.disciplineComputer Scienceen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.embargo.terms0en
uws.contributor.advisorBen-David, Shalev
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

Files

Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Soiffer_Rory.pdf
Size:
375.47 KB
Format:
Adobe Portable Document Format
Description:
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
6.4 KB
Format:
Item-specific license agreed upon to submission
Description: