Threshold analysis with fault-tolerant operations for nonbinary quantum error correcting codes
Year: 2005
Type: dissertation
Abstract: Quantum error correcting codes have been introduced to encode the data bits\nin extra redundant bits in order to accommodate errors and correct them. However,\ndue to the delicate nature of the quantum states or faulty gate operations, there is\na possibility of catastrophic spread of errors which might render the error correction\ntechniques ineffective. Hence, in this thesis we concentrate on how various operations\ncan be carried out fault-tolerantly so that the errors are not propagated in the same\nblock. We prove universal fault-tolerance for nonbinary CSS codes. This thesis is\nfocussed only on nonbinary quantum codes and all the results pertain to nonbinary\ncodes.\nEfficient error detection and correction techniques using fault-tolerant techniques\ncan help as long as we ensure that the gate error probability is below a certain\nthreshold. The calculation of this threshold is therefore important to see if quantum\ncomputations are realizable or not, even with fault-tolerant operations. We derive an\nexpression to compute the gate error threshold for nonbinary quantum codes and test\nthis result for different classes of codes, to get codes with best threshold results.
Author: Aparna Kanungo
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2744325214