<p>We studied two topics: i) how much physical resources are needed to store information and ii) decoherent histories theory applied to Grover search. Given a system consisting of <i>d</i> degrees of freedom each of mass <i>m</i> to store an amount <i>S</i> of information, we find that its average energy, ⟨<i>H</i>⟩, or size, ⟨<i>r</i><sup>2</sup>⟩, can be made arbitrarily small individually, but its product ⟨P⟩ = ⟨<i>H</i>⟩⟨<i> r</i><sup>2</sup>⟩ is bounded below by (exp{<i>S/d</i>} − 1)<sup>2</sup><i>d</i><sup>2</sup>/<i>m.</i> This result is obtained in a nonrelativistic, quantum mechanical setting, and it is independent of earlier thermodynamical results such as the Bekenstein bound on the entropy of black holes. </p><p> The second topic is decoherent histories applied to the Grover search problem. The theory of decoherent histories is an attempt to derive classical physics from positing only quantum laws at the fundamental level without notions of a classical apparatus or collapse of the wave-function. Searching for a marked target in a list of <i>N</i> items requires Ω(<i> N</i>) oracle queries when using a classical computer, while a quantum computer can accomplish the same task in <i>O</i>([special characters omitted]) queries using Grover's quantum algorithm. We study a closed quantum system executing Grover algorithm in the framework of decoherent histories and find it to be an exactly solvable model, thus yielding an alternate derivation of Grover's famous result. We also subject the Grover-executing computer to a generic external influence without needing to know the specifics of the Hamiltonian insofar as the histories decohere. Depending on the amount of decoherence, which is captured in our model by a single parameter related to the amount of information obtained by the environment, the search time can range from quantum to classical. Thus, we identify a key effect induced by the environment that can adversely affect a quantum computer's performance and demonstrate exactly how classical computing can emerge from quantum laws. </p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:3612010 |
| Date | 26 March 2014 |
| Creators | Nguyen, Hieu Duy |
| Publisher | University of California, Santa Barbara |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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