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

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dc.contributor.author Simon, B. Neethi
dc.contributor.author Chandrashekar, C. M.
dc.contributor.author Simon, Sudhavathani
dc.date.accessioned 2017-08-22T10:30:38Z
dc.date.available 2017-08-22T10:30:38Z
dc.date.issued 2012
dc.identifier.citation Simon, 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.85.022323 en
dc.identifier.volume 85
dc.identifier.issued 2
dc.identifier.issn 2469-9926
dc.identifier.issn 2469-9934
dc.identifier.uri http://hdl.handle.net/10468/4504
dc.identifier.doi 10.1103/PhysRevA.85.022323
dc.description.abstract Unitary 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.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher American Physical Society en
dc.relation.uri https://journals.aps.org/pra/abstract/10.1103/PhysRevA.85.022323
dc.rights © 2012, American Physical Society en
dc.subject Quantum kinematic approach en
dc.subject Geometric phase en
dc.subject Polarization optics en
dc.subject Bargmann invariants en
dc.subject Pancharatnam phase en
dc.subject Lorentz group en
dc.subject SU(2) gadget en
dc.subject Computation en
dc.subject Light en
dc.subject Representation en
dc.title Hamilton's turns as a visual tool kit for designing single-qubit unitary gates en
dc.type Article (peer-reviewed) en
dc.internal.authorcontactother Chandrashekar Madaiah, Physics, University College Cork, Cork, Ireland. +353-21-490-3000. Email: cmadaiah@phys.ucc.ie en
dc.internal.availability Full text available en
dc.description.version Published Version en
dc.internal.wokid WOS:000300417700002
dc.description.status Peer reviewed en
dc.identifier.journaltitle Physical Review A en
dc.internal.IRISemailaddress cmadaiah@phys.ucc.ie en
dc.identifier.articleid 22323


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