Quantum error correcting codes have been introduced to encode the data bits
in extra redundant bits in order to accommodate errors and correct them. However,
due to the delicate nature of the quantum states or faulty gate operations, there is
a possibility of catastrophic spread of errors which might render the error correction
techniques ineffective. Hence, in this thesis we concentrate on how various operations
can be carried out fault-tolerantly so that the errors are not propagated in the same
block. We prove universal fault-tolerance for nonbinary CSS codes. This thesis is
focussed only on nonbinary quantum codes and all the results pertain to nonbinary
codes.
Efficient error detection and correction techniques using fault-tolerant techniques
can help as long as we ensure that the gate error probability is below a certain
threshold. The calculation of this threshold is therefore important to see if quantum
computations are realizable or not, even with fault-tolerant operations. We derive an
expression to compute the gate error threshold for nonbinary quantum codes and test
this result for different classes of codes, to get codes with best threshold results.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/2714 |
| Date | 01 November 2005 |
| Creators | Kanungo, Aparna |
| Contributors | Klappenecker, Andreas |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | 265662 bytes, electronic, application/pdf, born digital |
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