Related papers: Check-weight-constrained quantum codes: Bounds and…
Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and…
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of LDPC codes with a simple construction facilitating hardware implementation while achieving excellent performance. In this paper, we introduce an algorithm that…
Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result…
This work applies earlier results on Quasi-Cyclic (QC) LDPC codes to the codes specified in six separate IEEE 802 standards, specifying wireless communications from 54 MHz to 60 GHz. First, we examine the weight matrices specified to upper…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
Quantum error-correcting codes (QECCs) sit between noisy quantum hardware and reliable computation, so the code parameters used in practice must be trustworthy. The single number that summarizes a code's strength is its distance, yet…
A method to construct girth-12 (3,L) quasi-cyclic low-density parity-check (QC-LDPC) codes with all lengths larger than a certain given number is proposed, via a given girth-12 code subjected to some constraints. The lengths of these codes…
Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so called qudit…
The average weight distribution of a regular low-density parity-check (LDPC) code ensemble over a finite field is thoroughly analyzed. In particular, a precise asymptotic approximation of the average weight distribution is derived for the…
We present a new family of low-density parity-check (LDPC) convolutional codes that can be designed using ordered sets of progressive differences. We study their properties and define a subset of codes in this class that have some desirable…
The discovery of the family of balanced product codes was pivotal in the subsequent development of 'good' low density quantum error correcting codes that have optimal scaling of the key parameters of distance and storage density. We review…
While low-density parity-check (LDPC) codes are near capacity-achieving when paired with iterative decoders, these decoders may not output a codeword due to the existence of pseudocodewords. Thus, pseudocodewords have been studied to give…
Quantum low-density parity-check (QLDPC) codes offer a promising path to low-overhead fault-tolerant quantum computation but lack systematic strategies for exploration. In this Letter, we establish a topological framework for studying the…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…
We introduce Decision Tree Decoders (DTDs), which rely only on the sparsity of the binary check matrix, making them broadly applicable for decoding any quantum low-density parity-check (qLDPC) code and fault-tolerant quantum circuits. DTDs…
Quantum error correction (QEC) with single-shot decoding enables reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum…
This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
Joint encryption-encoding schemes have been released to fulfill both reliability and security desires in a single step. Using Low Density Parity Check (LDPC) codes in joint encryption-encoding schemes, as an alternative to classical linear…
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…