{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/36127"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/36127","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Simulations of error in quantum adiabatic computations of random 2-SAT instances","abstract":"This thesis presents a series of simulations of quantum computations using the adiabatic algorithm. The goal is to explore the effect of error, using a perturbative approach that models 1-local errors to the Hamiltonian and estimates transition probabilities out of the ground state. The data show that a perturbation in the z-direction, parallel to the alignment of the computational basis, causes a greater error than one in the x-direction, and show with good confidence (X2/[nu] = 1.7) that the variation is as sin [theta] where [theta] is the angle of the error term. An attempt to explore the change in error with the number of qubits was inconclusive--there was no measurable variation.","abstract_html":"This thesis presents a series of simulations of quantum computations using the adiabatic algorithm. The goal is to explore the effect of error, using a perturbative approach that models 1-local errors to the Hamiltonian and estimates transition probabilities out of the ground state. The data show that a perturbation in the z-direction, parallel to the alignment of the computational basis, causes a greater error than one in the x-direction, and show with good confidence (X2/[nu] = 1.7) that the variation is as sin [theta] where [theta] is the angle of the error term. An attempt to explore the change in error with the number of qubits was inconclusive--there was no measurable variation.","abstract_has_math":false,"creators":["Gill, Jay S. (Jay Singh)"],"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":2006,"date_issued":"2006","date_published":"2006","updated_at":"2026-07-22T22:20:58Z","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/1721.1/36127","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. Dept. of Physics."]},{"key":"dc:creator","label":"Author","values":["Gill, Jay S. (Jay Singh)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2007-02-21T11:34:58Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2007-02-21T11:34:58Z"]},{"key":"dc:date.issued","label":"Date","values":["2006"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["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."]},{"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/1721.1/36127"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.","Includes bibliographical references (p. 45)."]},{"key":"dc:description.abstract","label":"Abstract","values":["This thesis presents a series of simulations of quantum computations using the adiabatic algorithm. The goal is to explore the effect of error, using a perturbative approach that models 1-local errors to the Hamiltonian and estimates transition probabilities out of the ground state. The data show that a perturbation in the z-direction, parallel to the alignment of the computational basis, causes a greater error than one in the x-direction, and show with good confidence (X2/[nu] = 1.7) that the variation is as sin [theta] where [theta] is the angle of the error term. An attempt to explore the change in error with the number of qubits was inconclusive--there was no measurable variation."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.B."]},{"key":"dc:title","label":"Title","values":["Simulations of error in quantum adiabatic computations of random 2-SAT instances"]}]}],"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":["Gill, Jay S. (Jay Singh)"],"dc:date.accessioned":["2007-02-21T11:34:58Z"],"dc:date.available":["2007-02-21T11:34:58Z"],"dc:date.issued":["2006"],"dc:description":["Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.","Includes bibliographical references (p. 45)."],"dc:description.abstract":["This thesis presents a series of simulations of quantum computations using the adiabatic algorithm. The goal is to explore the effect of error, using a perturbative approach that models 1-local errors to the Hamiltonian and estimates transition probabilities out of the ground state. The data show that a perturbation in the z-direction, parallel to the alignment of the computational basis, causes a greater error than one in the x-direction, and show with good confidence (X2/[nu] = 1.7) that the variation is as sin [theta] where [theta] is the angle of the error term. An attempt to explore the change in error with the number of qubits was inconclusive--there was no measurable variation."],"dc:description.degree":["S.B."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/36127"],"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":["Simulations of error in quantum adiabatic computations of random 2-SAT instances"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:20:58Z"}