Algorithmic Quantum Channel Simulation

atmire.migration.oldid3568
dc.contributor.advisorSanders, Barry C.
dc.contributor.authorWang, Dongsheng
dc.date.accessioned2015-09-18T21:01:19Z
dc.date.available2015-11-20T08:00:40Z
dc.date.issued2015-09-18
dc.date.submitted2015en
dc.description.abstractQuantum simulation, which is generically the task to employ quantum computers to simulate quantum physical models, has been one of the most significant motivations of quantum computing. Quantum dynamics, unitary or nonunitary Markovian dynamics driven by local interactions, has been proved to be efficiently simulatable on quantum computers. Extending the underlying models from unitary to nonunitary evolution, and from continuous-time to discrete-time evolution is essential not only for quantum simulation of more general processes, e.g., dissipative processes with evident non-Markovian effects, but also for developing alternative quantum computing models and algorithms. In this thesis, we explore quantum simulation problems mainly from the following three themes. First, we extend quantum simulation framework of Hamiltonian-driven evolution to quantum simulation of quantum channels, combined with the scheme of algorithmic simulation that accepts a promised simulation accuracy, hence algorithmic quantum channel simulation. Our simulation scheme contains a classical preprocessing part, i.e. a classical algorithm for quantum-circuit design, and a quantum part that is the execution of a quantum circuit for the quantum channel simulator. Second, we employ simulation algorithms for arbitrary quantum channels beyond the dilation method. We explore channel decomposition in terms of convex combination of smaller channels, known as generalized extreme channels, which is known as a nontrivial open problem. To attack this problem, we develop an optimization algorithm for approximate decomposition into a convex sum of generalized extreme channels. We provide an ansatz that proves to be able to yield arbitrary generalized extreme channels and allows a precise quantum circuit description. Furthermore, our numerical simulation has demonstrated the validity of our optimization algorithm for low-dimensional quantum channels. Third, by considering quantum simulation problems beyond the rough distinction between digital and analog simulations, and beyond the quantum-state generation problem, we define uniform, strong, and weak quantum simulations from the point view of operator topology. Besides strong simulation of quantum channels, we define a general weak quantum simulation problem, which simulates observable effects instead of the effects on state generation. Also we study the channel simulation problem in the quantum query model, and provide the query complexity by employing uniform quantum simulation method.en_US
dc.identifier.citationWang, D. (2015). Algorithmic Quantum Channel Simulation (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24767en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/24767
dc.identifier.urihttp://hdl.handle.net/11023/2466
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity 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.
dc.subjectPhysics--Theory
dc.subject.classificationQuantum channelen_US
dc.subject.classificationQuantum simulationen_US
dc.titleAlgorithmic Quantum Channel Simulation
dc.typedoctoral thesis
thesis.degree.disciplinePhysics and Astronomy
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
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