Continuous-Variable Quantum Computation of Oracle Decision Problems
| atmire.migration.oldid | 535 | |
| dc.contributor.advisor | Sanders, Barry Cyril | |
| dc.contributor.advisor | Hoyer, Peter Christian | |
| dc.contributor.author | Adcock, Mark Richard Ashley | |
| dc.date.accessioned | 2013-01-07T22:50:41Z | |
| dc.date.available | 2013-06-15T07:01:42Z | |
| dc.date.issued | 2013-01-07 | |
| dc.date.submitted | 2012 | en |
| dc.description.abstract | Quantum information processing is appealing due its ability to solve certain problems quantitatively faster than classical information processing. Most quantum algorithms have been studied in discretely parameterized systems, but many quantum systems are continuously parameterized. The field of quantum optics in particular has sophisticated techniques for manipulating continuously parameterized quantum states of light, but the lack of a code-state formalism has hindered the study of quantum algorithms in these systems. To address this situation, a code-state formalism for the solution of oracle decision problems in continuously-parameterized quantum systems is developed. In discrete-variable quantum computation, oracle decision problems exploit quantum parallelism through the use of the Hadamard transform. The challenge in continuous-variable quantum computation is to exploit similar quantum parallelism by generalizing the Hadamard transform to the continuous Fourier transform while avoiding non-renormalizable states. This straightforward relationship between the operators in the discrete and continuous settings make oracle decision problems the ideal test-bed. However, as the formalism results in a representation of discrete information strings as proper code states, the approach also allows for the study of a wider range of quantum algorithms in continuously-parameterized quantum systems having both finite- and infinite-dimensional Hilbert spaces. In the infinite-dimensional case, we study continuous-variable quantum algorithms for the solution of the Deutsch--Jozsa oracle decision problem implemented within a single harmonic-oscillator. Orthogonal states are used as the computational bases, and we show that, contrary to a previous claim in the literature, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform. We further demonstrate that orthogonal encoding bases are not unique, and using the coherent states of the harmonic oscillator as the computational bases, our formalism enables quantifying the relative performances of different choices of the encoding bases. We extend our formalism to include quantum algorithms in the continuously parameterized yet finite-dimensional Hilbert space of a coherent spin system. We show that the highest-squeezed spin state possible can be approximated by a superposition of two states thus transcending the usual model of using a single basis state as algorithm input. As a particular example, we show that the close Hadamard oracle-decision problem, which is related to the Hadamard codewords of digital communications theory, can be solved quantitatively more efficiently using this computational model than by any known classical algorithm. | en_US |
| dc.identifier.citation | Adcock, M. R. (2013). Continuous-Variable Quantum Computation of Oracle Decision Problems (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25442 | en_US |
| dc.identifier.doi | http://dx.doi.org/10.11575/PRISM/25442 | |
| dc.identifier.uri | http://hdl.handle.net/11023/387 | |
| dc.language.iso | eng | |
| dc.publisher.faculty | Graduate Studies | |
| dc.publisher.institution | University of Calgary | en |
| dc.publisher.place | Calgary | en |
| dc.rights | University 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.subject | Physics--Theory | |
| dc.subject.classification | Quantum | en_US |
| dc.subject.classification | Physics | en_US |
| dc.subject.classification | Algorithms | en_US |
| dc.subject.classification | Information | en_US |
| dc.title | Continuous-Variable Quantum Computation of Oracle Decision Problems | |
| dc.type | doctoral thesis | |
| thesis.degree.discipline | Physics and Astronomy | |
| thesis.degree.grantor | University of Calgary | |
| thesis.degree.name | Doctor of Philosophy (PhD) | |
| ucalgary.item.requestcopy | true |