Related papers: On the Construction of New Toric Quantum Codes and…
We analyze the four dimensional toric code in a hyperbolic space and show that it has a classical error correction procedure which runs in almost linear time and can be parallelized to almost constant time, giving an example of a quantum…
In this paper, we provide a framework for constructing entanglement-assisted quantum error-correcting codes (EAQECCs) from classical additive codes over a finite commutative local Frobenius ring $\mathcal{R}$. At the heart of the framework,…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
We study the four-dimensional Z_2 random-plaquette lattice gauge theory as a model of topological quantum memory, the toric code in particular. In this model, the procedure of quantum error correction works properly in the ordered (Higgs)…
The toric code can be constructed as a gauge theory of finite groups on oriented two dimensional lattices. Here we construct analogous models with the gauge fields belonging to groupoids, which are categories where every morphism has an…
One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing on QC codes…
Quantum computers are predicted to utilize quantum states to perform memory and to process tasks far faster than those of conventional classical computers. In this paper we show a new road towards building fault tolerance quantum computer…
A class of powerful $q$-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are $q$-ary block codes that encode $k$…
Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error…
Lattice surgery protocols allow for the efficient implementation of universal gate sets with two-dimensional topological codes where qubits are constrained to interact with one another locally. In this work, we first introduce a decoder…
Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst…
There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, seems to be a difficult problem in general. In this paper,…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of…
Local decoders provide a promising approach to real-time quantum error-correction by replacing centralized classical decoding, with significant hardware constraints, by a fully distributed architecture based on a simple, local update rule.…
Bosonic systems offer unique advantages for quantum error correction, as a single bosonic mode provides a large Hilbert space to redundantly encode quantum information. However, previous studies have been limited to exploiting symmetries in…
One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized…
We study Algebraic Geometry codes producing quantum error-correcting codes by the CSS construction. We pay particular attention to the family of Castle codes. We show that many of the examples known in the literature in fact belong to this…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
We derive two families of EA-QC quantum LDPC (EA-QC-QLDPC) codes by tiling permutation matrices of prime and composite orders. The unassisted portion of the Tanner graphs corresponding to these codes, constructed from two distinct classical…