Constructing Quantum Surface Codes for Arbitrary Surface Forms

Abstract

Quantum technology has been considered as one of the key enablers for the sixth-generation (6G) wireless commu-nication systems. Since we rely on vulnerable quantum states, the main challenge in quantum communication is to compute and send information in a reliable manner, which requires highly reliable quantum error corrections (QEC) with high fidelity. This paper proposes counter-clockwise standard forms to construct quantum surface codes for arbitrary surface forms. We show that our procedure can give result to the same codes as the currently available quantum surface codes. We investigate the matrix generated from Roffe $[[5,1,2]]$ quantum surface codes and compare to that of the proposed $[[5,1,2]]$ quantum surface codes. We perform a series of computer simulations to evaluate the codes in terms of quantum word error rate (QWER) under depolarizing channel model. Our results confirm that we can construct good performance quantum surface codes using counter-clockwise standard forms that helps the design of any arbitrary forms of quantum surface codes.