Related papers: An efficient decoder for a linear distance quantum…
Quantum LDPC codes may provide a path to build low-overhead fault-tolerant quantum computers. However, as general LDPC codes lack geometric constraints, na\"ive layouts couple many distant qubits with crossing connections which could be…
Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to…
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…
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…
Quantum computers hold the potential to surpass classical computers in solving complex computational problems. However, the fragility of quantum information and the error-prone nature of quantum operations make building large-scale,…
The error correction performance of low-density parity-check (LDPC) codes under iterative message-passing decoding is degraded by the presence of certain harmful objects existing in their Tanner graph representation. Depending on the…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
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…
The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary…
Quantum low-density parity-check (qLDPC) codes are promising for realizing scalable fault-tolerant quantum computation due to their potential for low-overhead protocols. A common approach to decoding qLDPC codes is to use the belief…
Low-Density Parity-Check (LDPC) codes received much attention recently due to their capacity-approaching performance. The iterative message-passing algorithm is a widely adopted decoding algorithm for LDPC codes \cite{Kschischang01}. An…
We solve the problem of designing powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather…
Quantum low-density parity-check (LDPC) codes, a class of quantum error correcting codes, are considered a blueprint for scalable quantum circuits. To use these codes, one needs efficient decoding algorithms. In the classical setting, there…
Quantum low-density parity-check (QLDPC) codes have been proven to achieve higher minimum distances at higher code rates than surface codes. However, this family of codes imposes stringent latency requirements and poor performance under…
A major challenge in fault-tolerant quantum computation (FTQC) is to reduce both space overhead -- the large number of physical qubits per logical qubit -- and time overhead -- the long physical gate sequences per logical gate. We prove…
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 $[[n,k,d]]$…
Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this…
Quantum low-density parity-check (QLDPC) codes have emerged as a promising technique for quantum error correction. A variety of decoders have been proposed for QLDPC codes and many of them utilize belief propagation (BP) decoding in some…
We propose the use of certain low-density generator-matrix (LDGM) codes as syndrome measurement (SM) codes for quantum low-density parity check (QLDPC) codes. We use an efficient progressive-edge-growth-like algorithm to create LDGM SM…
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…