October 30, 2023

Decoding algorithms for surface codes

Quantum technologies have the potential to solve computationally hard problems that are intractable via classical means.

Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing.

Surface codes currently stand as the most promising candidates to build error corrected qubits given their two-dimensional architecture, a requirement of only local operations, and high tolerance to quantum noise.

Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that it can subsequently be corrected.

A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum-like tradeoff, where decoding performance is improved at the expense of complexity and viceversa.

In this review, a thorough discussion of state-of-the-art surface code decoding algorithms is provided. The core operation of these methods is described along with existing variants that show promise for improved results.

In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface code decoding is also provided.