Related papers: Construction and Decoding of Quantum Margulis Code…
We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. While conventional constructions using circulant permutation matrices are limited to girth…
For a high-rate case, it is difficult to randomly construct good low-density parity-check (LDPC) codes of short and moderate lengths because their Tanner graphs are prone to making short cycles. Also, the existing high-rate quasi-cyclic…
Quantum low-density parity check (qLDPC) codes offer higher encoding rate than topological codes, e.g. surface codes, making them favourable for practical, fault-tolerant quantum computing with low overhead. These codes are particularly…
In this paper, we consider how to partition the parity-check matrices (PCMs) to reduce the hardware complexity and computation delay for the row layered decoding of quasi-cyclic low-density parity-check (QC-LDPC) codes. First, we formulate…
Real-time decoding is crucial for fault-tolerant quantum computing but likely requires specialized hardware such as field-programmable gate arrays (FPGAs), whose parallelism can alter relative algorithmic performance. We analyze…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
Low-density parity check (LDPC) codes are an important class of codes with many applications. Two algebraic methods for constructing regular LDPC codes are derived -- one based on nonprimitive narrow-sense BCH codes and the other directly…
We discuss error-correction properties for families of quantum low-density parity check (LDPC) codes with relative distance that tends to zero in the limit of large blocklength. In particular, we show that any family of LDPC codes, quantum…
Hypergraph products are quantum low-density parity-check (LDPC) codes constructed from two classical LDPC codes. Although their dimension and distance depend only on the parameters of the underlying classical codes, optimizing their…
We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$…
In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes as ingredient codes for a quantum error-correcting code is proposed. That is, we find quantum regular LDPC codes with various weight distributions. Furthermore our…
Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand,…
Quantum-classical interfaces (QCIs) for fault-tolerant quantum computing must manage simultaneous, real-time decoding across thousands to millions of logical qubits. Scaling these architectures necessitates sharing expensive decoding…
Quantum low density parity check (QLDPC) codes are useful primitives for quantum information processing because they can be encoded and decoded efficiently. Besides, the error correcting capability of a few QLDPC codes exceeds the quantum…
In this paper, we propose a belief-propagation (BP)-based decoder, termed the Multiple-Bases Belief-Propagation List Decoder (MBBP-LD), for quantum low-density parity-check (QLDPC) codes. The key idea is to generate \emph{structured…
We introduce univariate bicycle (UB) codes, a structured subclass of generalized bicycle (GB) quantum low-density parity-check (LDPC) codes obtained via a Frobenius relation. This construction reduces the code design space from a…
The ultimate goal of quantum error correction is to create logical qubits with very low error rates (e.g. 1e-12) and assemble them into large-scale quantum computers capable of performing many (e.g. billions) of logical gates on many (e.g.…
We study a construction of Quantum LDPC codes proposed by MacKay, Mitchison and Shokrollahi. It is based on the Cayley graph of Fn together with a set of generators regarded as the columns of the parity-check matrix of a classical code. We…
Quantum computing requires effective error correction strategies to mitigate noise and decoherence. Quantum Low-Density Parity-Check (QLDPC) codes have emerged as a promising solution for scalable Quantum Error Correction (QEC) applications…
We construct a new explicit family of good quantum low-density parity-check codes which additionally have linear time decoders. Our codes are based on a three-term chain $(\mathbb{F}_2^{m\times m})^V \quad \xrightarrow{\delta^0}\quad…