Related papers: Quantum-enhanced belief propagation for LDPC decod…
Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems.…
Quantum computers have now surpassed classical simulation limits, yet noise continues to limit their practical utility. As the field shifts from proof-of-principle demonstrations to early deployments, there is no standard method for…
We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph product. To this end, we run numerical simulations of the…
Weighted belief propagation (WBP) for the decoding of linear block codes is considered. In WBP, the Tanner graph of the code is unrolled with respect to the iterations of the belief propagation decoder. Then, weights are assigned to the…
Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum heuristics for combinatorial optimization. While QAOA has been shown to perform well on small-scale instances and to provide an asymptotic speedup over…
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,…
Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems, especially for Distributed Energy Resources (DERs) dominant cyber-physical systems that have been widely developed to…
The syndrome decoding problem is known to be NP-complete. The goal of the decoder is to find an error of low weight that corresponds to a given syndrome obtained from a parity-check matrix. We use the quantum approximate optimization…
We introduce a two-stage decimation process to improve the performance of neural belief propagation (NBP), recently introduced by Nachmani et al., for short low-density parity-check (LDPC) codes. In the first stage, we build a list by…
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…
Quantum devices use qubits to represent information, which allows them to exploit important properties from quantum physics, specifically superposition and entanglement. As a result, quantum computers have the potential to outperform the…
As quantum computing moves toward fault-tolerant architectures, quantum error correction (QEC) decoder performance is increasingly critical for scalability. Understanding the impact of transitioning from floating-point software to…
Quantum computers are expected to offer significant advantages in solving complex optimization problems that are challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class…
In this paper, we propose a framework of the mutual information-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes by using simple mappings and fixed-point additions. Our decoding method is generic in the sense…
We illustrate the utility of the recently developed loop calculus for improving the Belief Propagation (BP) algorithm. If the algorithm that minimizes the Bethe free energy fails we modify the free energy by accounting for a critical loop…
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 propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy…
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 error correction (QEC) is a cornerstone of quantum computing, enabling reliable information processing in the presence of noise. Sparse stabilizer codes -- referred to generally as quantum low-density parity-check (QLDPC) codes --…
We consider near maximum-likelihood (ML) decoding of short linear block codes. In particular, we propose a novel decoding approach based on neural belief propagation (NBP) decoding recently introduced by Nachmani et al. in which we allow a…