Related papers: Automorphism Ensemble Decoding of Quantum LDPC Cod…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
Erasures are the primary type of errors in physical systems dominated by leakage errors. While quantum error correction (QEC) using stabilizer codes can combat erasure errors, it remains unknown which constructions achieve capacity…
In this study, we report that quantum quasi-cyclic low-density parity-check codes decoded via joint belief propagation (BP) exhibit steep error-rate curves, despite the presence of error floors. To the best of our knowledge, this is the…
The recent success in constructing asymptotically good quantum low-density parity-check (QLDPC) codes makes this family of codes a promising candidate for error-correcting schemes in quantum computing. However, conventional belief…
The automorphism groups of various linear codes are extensively studied yielding insights into the respective code structure. This knowledge is used in, e.g., theoretical analysis and in improving decoding performance, motivating the…
Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This…
We study the decoding problem for quantum Tanner codes and propose to exploit the underlying local code structure by grouping check nodes into more powerful generalized check nodes for enhanced iterative belief propagation (BP) decoding by…
Quantum Tanner codes are a recently developed family of quantum error-correcting codes characterized by favorable asymptotic performance characteristics. Despite their theoretical potential, practical decoding algorithms that effectively…
Quantum low-density parity-check (QLDPC) codes are among the most promising candidates for future quantum error correction schemes. However, a limited number of short to moderate-length QLDPC codes have been designed and their decoding…
We describe an empirical approach to identify low-weight combinations of columns of the decoding matrices of a quantum circuit-level noise model, for which belief-propagation (BP) algorithms converge possibly very slowly. Focusing on the…
(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…
Fault-tolerant quantum computers will depend crucially on the performance of the classical decoding algorithm which takes in the results of measurements and outputs corrections to the errors inferred to have occurred. Machine learning…
Hardware-friendly quantum low-density parity-check (QLDPC) decoders are commonly built upon belief propagation (BP) processing. Yet, quantum degeneracy often prevents BP from achieving reliable convergence. To overcome this fundamental…
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…
Many quantum systems are being investigated in the hope of building a large-scale quantum computer. All of these systems suffer from decoherence, resulting in errors during the execution of quantum gates. Quantum error correction enables…
Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is appealing due to its low complexity, yet it often exhibits convergence issues due to quantum degeneracy and short cycles that exist in the Tanner graph.…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
An efficient decoder is essential for quantum error correction, and data-driven neural decoders have emerged as promising, flexible solutions. Here, we introduce a diffusion model framework to infer logical errors from syndrome measurements…
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…