Related papers: Decoding color codes by projection onto surface co…
The surface code is one of the leading quantum error correction codes for realizing large-scale fault-tolerant quantum computing (FTQC). One major challenge in realizing surface-code-based FTQC is the extremely large number of qubits…
Current work presents a new approach to quantum color codes on compact surfaces with genus $g \geq 2$ using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
We present a general framework for constructing error-correcting codes using distributed graph coloring under the LOCAL model. Building on the correspondence between independent sets in the confusion graph and valid codes, we show that the…
We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower…
Quantum computation promises significant computational advantages over classical computation for some problems. However, quantum hardware suffers from much higher error rates than in classical hardware. As a result, extensive quantum error…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
Generation of logical zero states encoded with a quantum error-correcting code is the first step for fault-tolerant quantum computation, but requires considerably large resource overheads in general. To reduce such overheads, we propose an…
Stall patterns are known to cause an error floor in hard decision decoding of the OFEC code. We propose a novel stall pattern removal algorithm that lowers the error floor of state-of-the-art algorithms by an order of magnitude
Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then,…
The states needed in a quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an…
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…
In this paper we concentrate on rate-1/3 systematic parallel concatenated convolutional codes and their rate-1/2 punctured child codes. Assuming maximum-likelihood decoding over an additive white Gaussian channel, we demonstrate that a…
Product codes (PCs) and staircase codes (SCCs) are conventionally decoded based on bounded distance decoding (BDD) of the component codes and iterating between row and column decoders. The performance of iterative BDD (iBDD) can be improved…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions…
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error…
In classical computing, error-correcting codes are well established and are ubiquitous both in theory and practical applications. For quantum computing, error-correction is essential as well, but harder to realize, coming along with…