Decoding algorithms for surface codes

Quantum technologies have the potential to solve computationally hardproblems that are intractable via classical means. Unfortunately, the unstablenature of quantum information makes it prone to errors. For this reason,quantum error correction is an invaluable tool to make quantum informationreliable and enable the ultimate goal of fault-tolerant quantum computing.Surface codes currently stand as the most promising candidates to build errorcorrected qubits given their two-dimensional architecture, a requirement ofonly local operations, and high tolerance to quantum noise. Decoding algorithmsare an integral component of any error correction scheme, as they are taskedwith producing accurate estimates of the errors that affect quantuminformation, so that it can subsequently be corrected. A critical aspect ofdecoding algorithms is their speed, since the quantum state will sufferadditional errors with the passage of time. This poses a connundrum-liketradeoff, where decoding performance is improved at the expense of complexityand viceversa. In this review, a thorough discussion of state-of-the-artsurface code decoding algorithms is provided. The core operation of thesemethods is described along with existing variants that show promise forimproved results. In addition, both the decoding performance, in terms of errorcorrection capability, and decoding complexity, are compared. A review of theexisting software tools regarding surface code decoding is also provided.