51ÂÜÀò

Synchronization errors, arising from both synthesis and sequencing noise, present a fundamental challenge in DNA-based data storage systems. These errors are often modeled as insertion-deletion-substitution (IDS) channels, for which maximum-likelihood decoding is quite computationally expensive. In this work, we propose a data-driven approach based on neural polar decoders (NPDs) to design decoders with reduced complexity for channels with synchronization errors.

As a potential implementation of data storage using DNA molecules, multiple strands of DNA are stored unordered in a liquid container. When the data are needed, an array of DNA readers will sample the strands with replacement, producing a Poisson-distributed number of noisy reads for each strand. The primary challenge here is to design an algorithm that reconstructs data from these unsorted, repetitive, and noisy reads.

An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical n,k,d≥m+1 binary linear code with certain additional properties, we show that pure [n,k,m+1]]2 quantum error-correcting codes (QECCs) can be constructed within the codeword stabilized (CWS) code framework. As illustrations, we construct pure [[22r-1,22r-2r-3,3]]2 and [[(24r-1)2,(24r-1)2-32r-7,5]]2 QECCs.

The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms.