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Quantum Algorithmic Techniques for Fault-Tolerant Quantum Computers

dc.contributor.authorKieferova, Maria
dc.date.accessioned2019-10-01T14:31:25Z
dc.date.available2019-10-01T14:31:25Z
dc.date.issued2019-10-01
dc.date.submitted2019-09-23
dc.description.abstractQuantum computers have the potential to push the limits of computation in areas such as quantum chemistry, cryptography, optimization, and machine learning. Even though many quantum algorithms show asymptotic improvement compared to classical ones, the overhead of running quantum computers limits when quantum computing becomes useful. Thus, by optimizing components of quantum algorithms, we can bring the regime of quantum advantage closer. My work focuses on developing efficient subroutines for quantum computation. I focus specifically on algorithms for scalable, fault-tolerant quantum computers. While it is possible that even noisy quantum computers can outperform classical ones for specific tasks, high-depth and therefore fault-tolerance is likely required for most applications. In this thesis, I introduce three sets of techniques that can be used by themselves or as subroutines in other algorithms. The first components are coherent versions of classical sort and shuffle. We require that a quantum shuffle prepares a uniform superposition over all permutations of a sequence. The quantum sort is used within the shuffle and as well as in the next algorithm in this thesis. The quantum shuffle is an essential part of state preparation for quantum chemistry computation in first quantization. Second, I review the progress of Hamiltonian simulations and give a new algorithm for simulating time-dependent Hamiltonians. This algorithm scales polylogarithmic in the inverse error, and the query complexity does not depend on the derivatives of the Hamiltonian. A time-dependent Hamiltonian simulation was recently used for interaction picture simulation with applications to quantum chemistry. Next, I present a fully quantum Boltzmann machine. I show that our algorithm can train on quantum data and learn a classical description of quantum states. This type of machine learning can be used for tomography, Hamiltonian learning, and approximate quantum cloning.en
dc.identifier.urihttp://hdl.handle.net/10012/15190
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectquantum computingen
dc.subjectquantum informationen
dc.subjectquantum algorithmsen
dc.subjectHamiltonian simulationen
dc.titleQuantum Algorithmic Techniques for Fault-Tolerant Quantum Computersen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentPhysics and Astronomyen
uws-etd.degree.disciplinePhysics (Quantum Information)en
uws-etd.degree.grantorUniversity of Waterlooen
uws.comment.hiddenAnother copy of this thesis will be submitted at Macquarie University, Australia as a part of a cotutelle agreement.en
uws.contributor.advisorMosca, Michele
uws.contributor.advisorBerry, Dominic
uws.contributor.affiliation1Faculty of Scienceen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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