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arXiv · 2207.04996

Construction of non-CSS quantum codes using measurements on cluster states

Swayangprabha Shaw·Harsh Gupta·Shahid Mehraj Shah·Ankur Raina
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Abstract

The Measurement-based quantum computation provides an alternate model for quantum computation compared to the well-known gate-based model. It uses qubits prepared in a specific entangled state followed by single-qubit measurements. The stabilizers of cluster states are well defined because of their graph structure. We exploit this graph structure extensively to design non-CSS codes using measurement in a specific basis on the cluster state. % We aim to construct $[[n,1]]$ non-CSS code from a $(n+1)$ qubit cluster state. The procedure is general and can be used specifically as an encoding technique to design any non-CSS codes with one logical qubit. We show there exists a $(n+1)$ qubit cluster state which upon measurement gives the desired $[[n,1]]$ code.

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Swayangprabha Shaw, Harsh Gupta, Shahid Mehraj Shah, Ankur Raina. 2022-07-11. Construction of non-CSS quantum codes using measurements on cluster states. https://arxiv.org/abs/2207.04996

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