A large-scale quantum computer is envisioned to leverage the theoretical guarantees of the fault-tolerant accuracy threshold theorem to ensure that long computations be carried out reliably, even in the presence of noise. Quantum Error Correction (QEC) is an integral part of an FT protocol specifying noise-resilient quantum information storage. Quantum error-correcting codes encode information in entangled states of many physical qubits. Topological stabilizer codes are a widely studied class of quantum error-correcting codes wherein the physical qubits are associated with a tessellation of a surface. The geometric locality of physical qubits in topological codes has both advantages and drawbacks. On the positive side, it simplifies the engineering challenges of implementing them on certain hardware platforms. However, it imposes a strict limitation on the scaling of the fraction of logical qubits that can be encoded per physical qubit. In general, it is useful to know several parameters of a surface code to deem its usefulness.
In this presentation, I will introduce a generalized formalism for the study of a specific subclass of topological codes called surface codes. Based on findings from [1], I will demonstrate an efficient method to compute the number of logical qubits and the distance of a generalized surface code. Additionally, I will discuss results from [2], showing how to effectively benchmark the performance of generalized surface codes under the error model described by quantum erasures. Lastly, I will present a tool from [3] that facilitates the analysis of generalized surface codes.
Related works:
[1]: Generalized surface codes and packing of logical qubits. Nicolas Delfosse, Pavithran Iyer, David Poulin. https://arxiv.org/abs/1606.07116
[2]: A linear-time benchmarking tool for generalized surface codes. Nicolas Delfosse, Pavithran Iyer, David Poulin.
https://arxiv.org/abs/1611.04256.
[3]: SQUAB: A Fast Benchmarking Software for Surface Quantum Computing
Architectures. http://quantum-squab.com [1].
