Related papers: Trellis Decoding For Qudit Stabilizer Codes And It…
In this work we develop a general tensor network decoder for 2D codes. Specifically, we propose a decoder that approximates maximally likelihood decoding for 2D stabiliser and subsystem codes subject to Pauli noise. For a code consisting of…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be…
We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit,…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
Trellis-coded modulation (TCM) is a power and bandwidth efficient digital transmission scheme which offers very low structural delay of the data stream. Classical TCM uses a signal constellation of twice the cardinality compared to an…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
We present a fault-tolerant [[8, 1, 3]] non-CSS quantum error correcting code and study its logical error rates. We choose the unitary encoding procedure for stabilizer codes given by Gottesman and modify it to suit the setting of a class…
To unleash the potential of quantum computers, noise effects on qubits' performance must be carefully managed. The decoders responsible for diagnosing noise-induced computational errors must use resources efficiently to enable scaling to…
Tensor-network codes enable the construction of large stabilizer codes out of tensors describing smaller stabilizer codes. An application of tensor-network codes was an efficient and exact decoder for holographic codes. Here, we show how to…
We utilize the symmetry groups of regular tessellations on two-dimensional surfaces of different constant curvatures, including spheres, Euclidean planes and hyperbolic planes, to encode a qubit or qudit into the physical degrees of freedom…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
We demonstrate that the performance of quantum error correction can be improved with noise-aware decoders that are calibrated to the likelihood of physical error configurations in a device. We show that noise-aware decoding increases the…
We study the resources needed to construct topological 2D stabilizer codes as a way to estimate in part their efficiency and this leads us to perform a comparative study of surface codes and color codes. This study clarifies the…
Color codes are a class of topological quantum codes with a high error threshold and large set of transversal encoded gates, and are thus suitable for fault tolerant quantum computation in two-dimensional architectures. Recently,…
We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15-qubit Reed-Muller code to obtain a $[\![10,1,2]\!]$ code that is the smallest known stabilizer code…
In this paper, two classes of twisted generalized Reed-Solomon (TGRS) codes with multi-twists are studied. Firstly, some sufficient and necessary conditions for these codes to be self-orthogonal and self-dual are established. Then several…
We describe a class of "neighboring-blocks" stabilizer quantum error correction codes and demonstrate that such class of codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit…
In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further…
This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution. A key part of this work involves representing the deletion channel using a trellis…
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…