Hamilton's turns as a visual tool kit for designing single-qubit unitary gates

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dc.contributor.authorSimon, B. Neethi
dc.contributor.authorChandrashekar, C. M.
dc.contributor.authorSimon, Sudhavathani
dc.date.accessioned2017-08-22T10:30:38Z
dc.date.available2017-08-22T10:30:38Z
dc.date.issued2012
dc.description.abstractUnitary evolutions of a qubit are traditionally represented geometrically as rotations of the Bloch sphere, but the composition of such evolutions is handled algebraically through matrix multiplication [of SU(2) or SO(3) matrices]. Hamilton's construct, called turns, provides for handling the latter pictorially through the addition of directed great circle arcs on the unit sphere S-2 subset of R-3, resulting in a non-Abelian version of the parallelogram law of vector addition of the Euclidean translation group. This construct is developed into a visual tool kit for handling the design of single-qubit unitary gates. As an application, it is shown, in the concrete case wherein the qubit is realized as polarization states of light, that all unitary gates can be realized conveniently through a universal gadget consisting of just two quarter-wave plates (QWP) and one half-wave plate (HWP). The analysis and results easily transcribe to other realizations of the qubit: The case of NMR is obtained by simply substituting pi/2 and pi pulses respectively for QWPs and HWPs, the phases of the pulses playing the role of the orientation of fast axes of these plates.en
dc.description.statusPeer revieweden
dc.description.versionPublished Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.articleid22323
dc.identifier.citationSimon, B. N., Chandrashekar, C. M. and Simon, S. (2012) 'Hamilton's turns as a visual tool kit for designing single-qubit unitary gates', Physical Review A, 85(2), 022323 (11pp). doi: 10.1103/PhysRevA.85.022323en
dc.identifier.doi10.1103/PhysRevA.85.022323
dc.identifier.issn2469-9926
dc.identifier.issn2469-9934
dc.identifier.issued2
dc.identifier.journaltitlePhysical Review Aen
dc.identifier.urihttps://hdl.handle.net/10468/4504
dc.identifier.volume85
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.urihttps://journals.aps.org/pra/abstract/10.1103/PhysRevA.85.022323
dc.rights© 2012, American Physical Societyen
dc.subjectQuantum kinematic approachen
dc.subjectGeometric phaseen
dc.subjectPolarization opticsen
dc.subjectBargmann invariantsen
dc.subjectPancharatnam phaseen
dc.subjectLorentz groupen
dc.subjectSU(2) gadgeten
dc.subjectComputationen
dc.subjectLighten
dc.subjectRepresentationen
dc.titleHamilton's turns as a visual tool kit for designing single-qubit unitary gatesen
dc.typeArticle (peer-reviewed)en
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