Quantum Computation and Quantum Theory of error correction.

Name: José Victor Soares Scursulim
Type: MSc dissertation
Publication date: 22/11/2021
Advisor:

Namesort descending Role
Galen Mihaylov Sotkov Advisor *
Ulysses Camara da Silva Co-advisor *

Examining board:

Namesort descending Role
Galen Mihaylov Sotkov Advisor *
Itzhak Roditi External Examiner *
Jardel da Costa Brozeguini External Examiner *
Jorge Luis Gonzalez Alfonso Internal Examiner *
Ulysses Camara da Silva Co advisor *

Summary: The quantum computing must be the initial mark of the second technological revolution caused by the deepening knowledge of the humankind about the peculiar features of the quantum mechanics. If we want to unlock all the potential of this new technology, a development of a fault-tolerant quantum computing will be needed. In order to reach this stage, it is necessary an implementation of quantum error correcting codes that guarantee an exponential suppression of the errors at each step of the execution of an algorithm. Besides that, we need to learn how to isolate our qubits aiming a suppression of the decoherence effects. Quantum mechanics imposes various constraints to the process
of construction of the error correction codes, one of them is the impossibility of using copies as redundancy mechanism, once no-cloning theorem does not allow the creation of an universal copy machine of quantum states. Another issue to be noted within this context, is that the measurement process causes a collapse in the quantum state, thus
leading to a corruption of the information encoded in the state. Fortunately, there are some ways to bypass the problems pointed out through the entanglement and the stabilizer formalism, the first one allows us to recover the redundancy through the delocalization of
the information in the Hilbert spaces of the parts that share quantum correlations, while the second one provides a process of gathering information about the errors that can occur in the quantum state without measuring it. The surface codes are one of the quantum
codes that use the features highlighted to correct the errors, this type of code is one of the main candidates to be experimentally implemented on a large scale and it presents promising results in the preliminary studies.

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