Related papers: Layer Codes
The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either…
This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to…
The surface code is a two-dimensional stabiliser code with parameters $[[n,1,\Theta(\sqrt{n})]]$. To this day, no stabiliser code with growing distance is know to live in less than two dimensions. In this note we show that no such code can…
The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…
We introduce tile codes, a simple yet powerful way of constructing quantum codes that are local on a planar 2D-lattice. Tile codes generalize the usual surface code by allowing for a bit more flexibility in terms of locality and stabilizer…
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…
An economy of scale is found when storing many qubits in one highly entangled block of a topological quantum code. The code is defined by construction of a topologically convoluted 2-d surface and does not work by compressing redundancy in…
The surface code is a spin-1/2 lattice system that can exhibit non-trivial topological order when defects are punctured in the lattice and thus can be used as a stabiliser code. The protocols developed to create defects in the system have…
We use the recently introduced lifted product to construct a family of Quantum Low Density Parity Check Codes (QLDPC codes). The codes we obtain can be viewed as stacks of surface codes that are interconnected, leading to the name…
The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher…
A linear error correcting code is a subspace of a finite-dimensional space over a finite field with a fixed coordinate system. Such a code is said to be locally recoverable with locality $r$ if, for every coordinate, its value at a codeword…
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…
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 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…
One of the leading quantum computing architectures is based on the two-dimensional (2D) surface code. This code has many advantageous properties such as a high error threshold and a planar layout of physical qubits where each physical qubit…
Amongst quantum error-correcting codes the surface code has remained of particular promise as it has local and very low-weight checks, even despite only encoding a single logical qubit no matter the lattice size. In this work we discuss new…
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…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some…
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a…