Related papers: Local decoder for the toric code via signal exchan…
Local decoders, also known as cellular-automaton decoders, offer a promising path toward real-time quantum error correction by replacing centralized classical decoding, with inherent hardware constraints, by a natively parallel and…
We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and G\'acs. Our decoder is a circuit of strictly local quantum operations preserving a logical state for…
Kitaev's toric code is arguably the most studied quantum code and is expected to be implemented in future generations of quantum computers. The renormalisation decoders introduced by Duclos-Cianci and Poulin exhibit one of the best…
In recent years, there have been many studies on local stabilizer codes. Under the assumption of translation and scale invariance Yoshida classified such codes. His result implies that translation invariant 2D color codes are equivalent to…
We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and…
Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to…
The Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation. However, direct methods to increase its logical dimensions, such as lattice surgery or introducing…
Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to…
Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes which affects code performance and ease of physical realization. For device architectures restricted to 2D local gates,…
The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of…
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…
A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within…
We study the quantum error correction threshold of Kitaev's toric code over the group Z_d subject to a generalized bit-flip noise. This problem requires novel decoding techniques, and for this purpose we generalize the renormalization group…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
In a recent work, Bombin, Duclos-Cianci, and Poulin showed that every local translationally invariant 2D topological stabilizer code is locally equivalent to a finite number of copies of Kitaev's toric code. For 2D color codes, Delfosse…
In the torn paper channel, a transmitted codeword is broken at random locations into fragments that arrive at the decoder in an unordered manner. A central theoretical challenge within this model is global alignment -- the task of…
Quantum error correction is a key ingredient for large scale quantum computation, protecting logical information from physical noise by encoding it into many physical qubits. Topological stabilizer codes are particularly appealing due to…
We still do not have perfect decoders for topological codes that can satisfy all needs of different experimental setups. Recently, a few neural network based decoders have been studied, with the motivation that they can adapt to a wide…
To avoid prohibitive overheads in performing fault-tolerant quantum computation, the decoding problem needs to be solved accurately and at speeds sufficient for fast feedback. Existing decoding systems fail to satisfy both of these…
We introduce a family of 2D topological subsystem quantum error-correcting codes. The gauge group is generated by 2-local Pauli operators, so that 2-local measurements are enough to recover the error syndrome. We study the computational…