Keywords

quantum computer, quantum algorithm, quantum information, time-correlated error, stabilizer code

Abstract

Quantum computation has been a rich field of study for decades because it promises possible spectacular advances, some of which may run counter to our classically rooted intuitions. At the same time, quantum computation is still in its infancy in both theoretical and practical areas. Efficient quantum algorithms are very limited in number and scope; no real breakthrough has yet been achieved in physical implementations. Grover's search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems can be reformulated to take advantage of quantum parallelism and entanglement leading to algorithms which show a square root speedup over their classical counterparts. This dissertation discusses a systematic way to formulate such problems and gives as an example a quantum scheduling algorithm for an R||C_max problem. This thesis shows that quantum solution to such problems is not only feasible but in some cases advantageous. The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting only a single error per error correction cycle. Yet, time-correlated errors are common for physical implementations of quantum systems; an error corrected during a certain cycle may reoccur in a later cycle due to physical processes specific to each physical implementation of the qubits. This dissertation discusses quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm proposed allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code, perfect or non-perfect, and simplified the circuit complexity significantly comparing to the classic quantum error correction codes.

Notes

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Graduation Date

2007

Semester

Fall

Advisor

Marinescu, Dan

Degree

Doctor of Philosophy (Ph.D.)

College

College of Engineering and Computer Science

Department

Electrical Engineering and Computer Science

Degree Program

Computer Science

Format

application/pdf

Identifier

CFE0001873

URL

http://purl.fcla.edu/fcla/etd/CFE0001873

Language

English

Release Date

December 2007

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Restricted to the UCF community until December 2007; it will then be open access.

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