 Announcing the Final Examination of Mr. Feng Lu for the degree of Doctor of Philosophy Date: October 18, 2007 STUDIES OF A QUANTUM SCHEDULING ALGORITHM AND ON QUANTUM ERROR CORRECTION 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, and lead to algorithms which show a square root speedup over their classical counterparts. We discuss a systematic way to formulate such problems and gives as an example a quantum scheduling algorithm for an $R||C_{max}$ problem. We show 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. We discuss 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. Outline of Studies: Educational Career: Committee in Charge: Approved for distribution by Dr. Dan C. Marinescu, Committee Chair, on October 10, 2007. The public is welcome to attend.
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