Research on mitigating errors in computing and communication systems has grown with their widespread use. In quantum computing, error correction is crucial as errors can quickly propagate, undermining results and the theoretical speedup over classical systems. Quantum error-correcting codes, particularly topological codes, are a key focus. These codes map parity check matrices to graphs on d-dimensional surfaces, with our research centered on the 3D toric code. Effective decoders must be robust to noise, with performance improving as code size increases, but their complexity should scale polynomially with lattice size for practicality. We propose a neural network with inductive bias, leveraging equivariance to generalize efficiently from a smaller input subset. Additionally, we explore transformer networks for error correction and compare these methods to existing techniques for decoding errors in the 3D toric code, highlighting their strengths and limitations.
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep learning. We provide a general prescription for the training of the network and a decoding strategy that is applicable to a wide variety of stabilizer codes with very little specialization. We demonstrate the neural decoder numerically on the well-known two-dimensional toric code with phase-flip errors.
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need to reiterate the method used to deal with errors. Within the field of quantum computing, error correction is getting a lot of attention since errors can propagate fast and invalidate results, which makes the theoretical exponential speed increase in computation time, compared to traditional systems, obsolete. To correct errors in quantum systems, error-correcting codes are used. A subgroup of codes, topological codes, is currently the focus of many research papers. Topological codes represent parity check matrices corresponding to graphs embedded on a
d-dimensional surface. For our research, the focus lies on the toric code with a 3D square lattice. The goal of any decoder is robustness to noise, which can increase with code size. However, a reasonable decoder performance scales polynomially with lattice size. As error correction is a time-sensitive operation, we propose a neural network using an inductive bias: equivariance. This allows the network to learn from a rather small subset of the exponentially growing training space of possible inputs. In addition, we investigate how transformer networks can help in correction. These methods will be compared with various configurations and previously published methods of decoding errors in the 3D toric code.