{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/61269"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/61269","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Evaluation of boolean formulas with restricted inputs","abstract":"In this thesis, I will investigate the running time of quantum algorithms for evaluating boolean functions when the input is promised to satisfy certain conditions. The two quantum algorithms considered in this paper are the quantum walk algorithm for NAND trees given by Farhi and Gutmann [2], and an algorithm for more general boolean formulas based on span programs, given by Reichardt and Spalek [6]. I will show that these algorithms can run much faster on a certain set of inputs, and that there is a super-polynomial separation between the quantum algorithm and the classical lower bound on this problem. I will apply this analysis to quantum walks on decision trees, as described in [3], giving a class of decision trees that can be penetrated quickly by quantum walk but may not be efficiently searchable by classical algorithms.","abstract_html":"In this thesis, I will investigate the running time of quantum algorithms for evaluating boolean functions when the input is promised to satisfy certain conditions. The two quantum algorithms considered in this paper are the quantum walk algorithm for NAND trees given by Farhi and Gutmann [2], and an algorithm for more general boolean formulas based on span programs, given by Reichardt and Spalek [6]. I will show that these algorithms can run much faster on a certain set of inputs, and that there is a super-polynomial separation between the quantum algorithm and the classical lower bound on this problem. I will apply this analysis to quantum walks on decision trees, as described in [3], giving a class of decision trees that can be penetrated quickly by quantum walk but may not be efficiently searchable by classical algorithms.","abstract_has_math":false,"creators":["Zhan, Bohua"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Physics.","school":null,"contributors":[],"advisors":["Edward Farhi."],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-22T22:22:25Z","subjects":["Physics."],"languages":["eng"],"rights":["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."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/61269","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Edward Farhi."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Physics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. 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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."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/61269"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 61)."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, I will investigate the running time of quantum algorithms for evaluating boolean functions when the input is promised to satisfy certain conditions. The two quantum algorithms considered in this paper are the quantum walk algorithm for NAND trees given by Farhi and Gutmann [2], and an algorithm for more general boolean formulas based on span programs, given by Reichardt and Spalek [6]. I will show that these algorithms can run much faster on a certain set of inputs, and that there is a super-polynomial separation between the quantum algorithm and the classical lower bound on this problem. I will apply this analysis to quantum walks on decision trees, as described in [3], giving a class of decision trees that can be penetrated quickly by quantum walk but may not be efficiently searchable by classical algorithms."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.B."]},{"key":"dc:title","label":"Title","values":["Evaluation of boolean formulas with restricted inputs"]}]}],"canonical_facts":{"dc:contributor.advisor":["Edward Farhi."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Physics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Physics."],"dc:creator":["Zhan, Bohua"],"dc:date.accessioned":["2011-02-23T14:39:17Z"],"dc:date.available":["2011-02-23T14:39:17Z"],"dc:date.issued":["2010"],"dc:description":["Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 61)."],"dc:description.abstract":["In this thesis, I will investigate the running time of quantum algorithms for evaluating boolean functions when the input is promised to satisfy certain conditions. The two quantum algorithms considered in this paper are the quantum walk algorithm for NAND trees given by Farhi and Gutmann [2], and an algorithm for more general boolean formulas based on span programs, given by Reichardt and Spalek [6]. I will show that these algorithms can run much faster on a certain set of inputs, and that there is a super-polynomial separation between the quantum algorithm and the classical lower bound on this problem. I will apply this analysis to quantum walks on decision trees, as described in [3], giving a class of decision trees that can be penetrated quickly by quantum walk but may not be efficiently searchable by classical algorithms."],"dc:description.degree":["S.B."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/61269"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["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."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Physics."],"dc:title":["Evaluation of boolean formulas with restricted inputs"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:22:25Z"}