Quantum error-correction theory during logical gates and finitetime syndrome measurements

Author(s)

Leonardo Andreta de Castro

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT)
• Defense date: 2012-02-17

Examining board members

Reginaldo de Jesus Napolitano; Celso Jorge Villas Bôas; Leonardo Kleber Castelano

• Advisor: Reginaldo de Jesus Napolitano

Abstract

In this work, we study the theory of quantum error correction, one of the main methods of preventing loss of information in a quantum computer. This method, however, is normally studied under ideal conditions in which the operation of the quantum gates that constitute the quantum algorithm do not interefere with the kind of error the system undergoes. Moreover, the syndrome measurements employed in the traditional method are considered instantaneous. Our aims with this work are to evaluate how altering these two suppositions would modify the quantum error correction process. In respect with the first objective, we verify that, for errors caused by external environments, the action of a logical gate simultaneously to the noise can provoke errors that, in principle, may not be correctable by the code employed. We subsequently propose a short-step correction method that can be used to render negligible the uncorrectable errors, besides being capable of reducing the probability of occurrence of correctable errors. For the second objective, we first study how finite-time measurements affect the decoherence of a single qubit, concluding that this kind of measurement can actually protect the state under scrutiny. Motivated by that, we demonstrate, that, in certain cases, finite syndrome measurements performed concurrently with the noise are capable of protecting more efficiently the state of the qubits against errors than if the measurements had been performed instantaneously at the the end of the process. (AU)

• FAPESP's process: 09/12460-0 - Quantum error-correction theory during logical operations and finite-duration syndrome measurements
• Grantee: Leonardo Andreta de Castro
• Support Opportunities: Scholarships in Brazil - Master