Feder, David L.Ji, Jiawei2019-01-252019-01-252019-01-24Ji, J. (2019). The Hubbard Model for Universal Quantum Computation (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.http://hdl.handle.net/1880/109852Quantum circuits based only on matchgates are able to perform non-trivial (but not universal) quantum algorithms. Because matchgates can be mapped to non-interacting fermions, these circuits can be efficiently simulated on a classical computer. One can perform universal quantum computation by adding any non-matchgate parity-preserving gate, implying that interacting fermions are natural candidates for universal quantum computation. Most work to date has focused on Majorana fermions, which are difficult to realize and manipulate in the laboratory, despite the advantage of topologically protecting quantum information. We instead show that universal quantum computation can be implemented using interacting spinless (spin-polarized) fermions and further propose a scheme for achieving universal quantum computation with the Hubbard model, which may be realized in the laboratory based on current experimental techniques.enUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.universal quantum computationoptical latticeultracold atomHubbard modelPhysics--AtomicCondensed MatterPhysics--Theorymaster thesis10.11575/PRISM/36111