Related papers: Local decoder for the toric code via signal exchan…
We present an error correcting protocol that enhances the lifetime of stabilizer code based qubits which are susceptible to the creation of pairs of localized defects (due to string-like error operators) at finite temperature, such as the…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
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…
We show how to convert an arbitrary stabilizer code into a bipartite quantum code. A bipartite quantum code is one that involves two senders and one receiver. The two senders exploit both nonlocal and local quantum resources to encode…
The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We…
We propose a nonuniform quantized decoder for polar codes. The design metric of the quantizers is to minimize the distortion incurred by quantization. The quantizers are obtained via dynamic programming and the optimality of the quantizer…
The rapidly improving performance of modern hardware renders convolutional codes obsolete, and allows for the practical implementation of more sophisticated correction codes such as low density parity check (LDPC) and turbo codes (TC). Both…
Quantum low density parity check (qLDPC) codes are an attractive alternative to the surface code due to their relatively high code rate and distance. However, unlike the surface code which has simple, geometrically local, stabilizer checks,…
Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a…
Active error decoding and correction of topological quantum codes - in particular the toric code - remains one of the most viable routes to large scale quantum information processing. In contrast, passive error correction relies on the…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with code distance being the linear system size, is decomposed by a local Clifford…
We propose a quantized decoding algorithm for low- density parity-check codes where the variable node update rule of the standard min-sum algorithm is replaced with a look-up table (LUT) that is designed using an information-theoretic…
We investigate layer codes, a family of three-dimensional stabilizer codes that can achieve optimal scaling of code parameters and a polynomial energy barrier, as candidates for self-correcting quantum memories. First, we introduce two…
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…
We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…