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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…
Utilizing present and futuristic Quantum Computers to solve difficult problems in different domains has become one of the main endeavors at this moment. Of course, in arriving at the requisite solution both quantum and classical computers…
Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…
To address the issue of increased bit error rates during the later stages of linear search in denoising diffusion error correction codes, we propose a novel method that optimizes denoising diffusion error correction codes (ECC) using cosine…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
In fault-tolerant quantum computing, quantum algorithms are implemented through quantum circuits capable of error correction. These circuits are typically constructed based on specific quantum error correction codes, with consideration…
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…
We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by…
Lowering the resource overhead needed to achieve fault-tolerant quantum computation is crucial to building scalable quantum computers. We show that adapting conventional maximum likelihood (ML) decoders to a small subset of efficiently…
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…
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
In this paper we investigate the behavior of iteratively decoded low-density parity-check codes over the binary erasure channel in the so-called ``waterfall region." We show that the performance curves in this region follow a very basic…
Identifying the best families of quantum error correction (QEC) codes for near-term experiments is key to enabling fault-tolerant quantum computing. Ideally, such codes should have low overhead in qubit number, high physical error…
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
Parity check matrices (PCMs) are used to define linear error correcting codes and ensure reliable information transmission over noisy channels. The set of codewords of such a code is the null space of this binary matrix. We consider the…
Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced…
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…