3 June 2011 Logical zeros for the seven-qubit quantum error correction code
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Abstract
In this work we compare the accuracy of two methods used to construct a logical zero state appropriate for the [7, 1, 3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment. The first method is to apply error correction, via syndrome measurement, on seven physical qubits all in the state zero. To do the syndrome measurements in a fault-tolerant fashion requires the construction of four qubit Shor states. These Shor states are also assumed to be constructed in a non-equiprobable Pauli operator error environment and it is these that are used to implement the syndrome measurement. The second construction method is to implement the [7, 1, 3] encoding gate sequence, also in the nonequiprobable Pauli operator error environment. The fidelity of the output states is calculated for each of these methods. With respect to the Shor state construction we find that the implementation of (noisy) parity based verifications does not necessarily raise the fidelity of the resulting Shor state. We also find that the second logical zero construction method outputs a seven qubit state with a respectfully higher fidelity than the first (fault tolerant) method. However, the fidelity of the single qubit of stored information has almost equivalent fidelity from the two construction methods.
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G. Gilbert, G. Gilbert, Y. S. Weinstein, Y. S. Weinstein, } "Logical zeros for the seven-qubit quantum error correction code", Proc. SPIE 8057, Quantum Information and Computation IX, 80570D (3 June 2011); doi: 10.1117/12.884024; https://doi.org/10.1117/12.884024
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