README file for 'Research Data: Quantum Topological Error Correction Codes Are Capable of Improving the Performance of Clifford Gates'

Dataset DOI: https://doi.org/10.5258/SOTON/D1051

README Author: Daryus Chandra, University of Southampton. [https://orcid.org/0000-0003-2406-7229]

This dataset supports the publication:
Chandra, D., Babar, Z., Nguyen, H.V., Alanis, D., Botsinis, P. Ng, S.X., & Hanzo, L. (Accepted/In press). Quantum Topological Error Correction Codes Are Capable of Improving the Performance of Clifford Gates. IEEE Access. 

Abstract: 
The employment of quantum error correction codes (QECCs) within quantum computers potentially offers a reliability improvement for both quantum computation and communications tasks. However, incorporating quantum gates for performing error correction potentially introduces more sources of quantum decoherence into the quantum computers. In this scenario, the primary challenge is to find the sufficient condition required by each of the quantum gates for beneficially employing QECCs in order to yield reliability improvements given that the quantum gates utilized by the QECCs also introduce quantum decoherence. In this treatise, we approach this problem by firstly presenting the general framework of protecting quantum gates by the amalgamation of the transversal configuration of quantum gates and quantum stabilizer codes (QSCs), which can be viewed as syndrome-based QECCs. Secondly, we provide examples of the advocated framework by invoking quantum topological error correction codes (QTECCs) for protecting both transversal Hadamard gates and CNOT gates. The simulation and analytical results explicitly show that by utilizing QTECCs, the fidelity of the quantum gates can be beneficially improved, provided that quantum gates satisfying a certain minimum depolarization fidelity threshold (Fth) are available. For instance, for protecting transversal Hadamard gates, the minimum fidelity values required for each of the gates in order to attain fidelity improvements are 99.74%, 99.73%, 99.87%, and 99.86%, when they are protected by colour, rotated-surface, surface, and toric codes, respectively. These specific Fth values are obtained for a very large number of physical qubits (n → ∞), when the quantum coding rate of the QTECCs approaches zero (rQ → 0). Ultimately, the framework advocated can be beneficially exploited for employing QSCs to protect large-scale quantum computers.

This dataset contains:

* Figure 13: The qber_rep_hadamard.mat is used for plotting the quantum bit error ratio (QBER) versus depolarizing probability (p) curves of the transversal Hadamard gates protected by 1/3-, 1/5-, and 1/7-rate quantum repetition codes.

* Figure 14: The qber_rep_cnot.mat is used for plotting the quantum bit error ratio (QBER) versus depolarizing probability (p) curves of the transversal CNOT gates protected by 1/3-, 1/5-, and 1/7-rate quantum repetition codes.

* Figure 15 (a, b, c): The qber_topo3_hadamard.mat is used for plotting the QBER versus p of transversal Hadamard gates protected by selected distance-3 QTECCs for both analytical expression and simulation results.

* Figure 16 (a, b, c, d): The qber_topo_hadamard.mat is used for plotting the upper-bound and lower-bound analytical QBER performance curves of transversal Hadamard gates protected by various QTECCs exhibiting various minimum distances.

* Figure 17 (a, b, c): The qber_topo3_cnot.mat is used for plotting the QBER versus p of transversal CNOT gates protected by selected distance-3 QTECCs for both analytical expression and simulation results.

* Figure 18 (a, b, c, d): The qber_topo_cnot.mat is used for plotting the upper-bound and lower-bound analytical QBER performance curves of transversal CNOT gates protected by various QTECCs exhibiting various minimum distances.

All figures in the manuscript are plotted using MATLAB.

Information about geographic location of data collection: University of Southampton, U.K.

Licence: CC BY

Acknowledgements: 
The financial support of the EPSRC under the grant EP/L018659/1 and the COALESCE project, that of the European Research Council, Advanced Fellow Grant QuantCom and that of the Royal Society’s Global Research Challenges Fund (GRCF) is gratefully acknowledged. Additionally, the authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work. 

Date that the file was created: August 19, 2019