Related papers: Quantum error correction with fractal topological …
Real-time decoding plays a crucial role in practical fault-tolerant quantum computing. Window decoding, in which the decoding problem is divided into windows, is a promising approach. While reducing the window size is desirable for faster…
Polar codes are a class of channel capacity achieving codes that has been selected for the next generation of wireless communication standards. Successive-cancellation (SC) is the first proposed decoding algorithm, suffering from mediocre…
SC-Flip (SCF) decoding algorithm shares the attention with the common polar code decoding approaches due to its low-complexity and improved error-correction performance. However, the inefficient criterion for locating the correct…
Steane code is one of the most widely studied quantum error-correction codes, which is a natural choice for fault-tolerant quantum computation (FTQC). However, the original Steane code is not fault-tolerant because the CNOT gates in an…
We introduce the spanning tree matching (STM) decoder for surface codes, which guarantees the error correction capability up to the code's designed distance by first employing an instance of the minimum spanning tree on a subset of ancilla…
Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer…
Quantum low-density parity-check (qLDPC) codes have emerged as a promising approach for realizing low-overhead logical quantum memories. Recent theoretical developments have established shift automorphisms as a fundamental building block…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…
Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) based method. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose. Here we propose a two-level (low…
Finite alphabet iterative decoders (FAIDs) for LDPC codes were recently shown to be capable of surpassing the Belief Propagation (BP) decoder in the error floor region on the Binary Symmetric channel (BSC). More recently, the technique of…
Fault-tolerant complexes describe surface-code fault-tolerant protocols from a single geometric object. We first introduce fusion complexes that define a general family of fusion-based quantum computing (FBQC) fault-tolerant quantum…
The error floor phenomenon observed with LDPC codes and their graph-based, iterative, message-passing (MP) decoders is commonly attributed to the existence of error-prone substructures -- variously referred to as near codewords, trapping…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
Quantum Error Correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
In order to build a scalable quantum computer error correction will be required to reduce the impact of errors. Implementing error correction in the framework of measurement based computation manifests itself as the construction of fault…
Quantum computation promises significant computational advantages over classical computation for some problems. However, quantum hardware suffers from much higher error rates than in classical hardware. As a result, extensive quantum error…
Quantum low-density parity-check (qLDPC) codes are a promising construction for drastically reducing the overhead of fault-tolerant quantum computing (FTQC) architectures. However, all of the known hardware implementations of these codes…
We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of $Z$- or $X$-rotations of individual qubits. We find that, similarly to the case of incoherent bit- and phase-flips, a trade-off between…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…