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Title: Fidelity of an encoded [7,1,3] logical zero

Abstract

I calculate the fidelity of a [7,1,3] Calderbank-Shor-Steane quantum error correction code logical zero state constructed in a nonequiprobable Pauli operator error environment for two methods of encoding. The first method is to apply fault-tolerant error correction to an arbitrary state of seven qubits utilizing Shor states for syndrome measurement. The Shor states are themselves constructed in the nonequiprobable Pauli operator error environment, and their fidelity depends on the number of verifications done to ensure multiple errors will not propagate into the encoded quantum information. Surprisingly, performing these verifications may lower the fidelity of the constructed Shor states. The second encoding method is to simply implement the [7,1,3] encoding gate sequence also in the nonequiprobable Pauli operator error environment. Perfect error correction is applied after both methods to determine the correctability of the implemented errors. I find that which method attains higher fidelity depends on which of the Pauli operators errors is dominant. Nevertheless, perfect error correction applied after the encoding suppresses errors to at least first order for both methods.

Authors:
 [1]
  1. Quantum Information Science Group, Mitre, 260 Industrial Way West, Eatontown, New Jersey 07724 (United States)
Publication Date:
OSTI Identifier:
22038629
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRECTIONS; ERRORS; PARITY; QUANTUM COMPUTERS; QUBITS; RANDOMNESS; VERIFICATION

Citation Formats

Weinstein, Yaakov S. Fidelity of an encoded [7,1,3] logical zero. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.012323.
Weinstein, Yaakov S. Fidelity of an encoded [7,1,3] logical zero. United States. doi:10.1103/PHYSREVA.84.012323.
Weinstein, Yaakov S. Fri . "Fidelity of an encoded [7,1,3] logical zero". United States. doi:10.1103/PHYSREVA.84.012323.
@article{osti_22038629,
title = {Fidelity of an encoded [7,1,3] logical zero},
author = {Weinstein, Yaakov S.},
abstractNote = {I calculate the fidelity of a [7,1,3] Calderbank-Shor-Steane quantum error correction code logical zero state constructed in a nonequiprobable Pauli operator error environment for two methods of encoding. The first method is to apply fault-tolerant error correction to an arbitrary state of seven qubits utilizing Shor states for syndrome measurement. The Shor states are themselves constructed in the nonequiprobable Pauli operator error environment, and their fidelity depends on the number of verifications done to ensure multiple errors will not propagate into the encoded quantum information. Surprisingly, performing these verifications may lower the fidelity of the constructed Shor states. The second encoding method is to simply implement the [7,1,3] encoding gate sequence also in the nonequiprobable Pauli operator error environment. Perfect error correction is applied after both methods to determine the correctability of the implemented errors. I find that which method attains higher fidelity depends on which of the Pauli operators errors is dominant. Nevertheless, perfect error correction applied after the encoding suppresses errors to at least first order for both methods.},
doi = {10.1103/PHYSREVA.84.012323},
journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 84,
place = {United States},
year = {2011},
month = {7}
}