Related papers: Boundaries for the Honeycomb Code
In this paper, we design a series of matching boundary conditions for a two-dimensional compound honeycomb lattice, which has an explicit and simple form, high computing efficiency and good effectiveness of suppressing boundary reflections.…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
We improve the planar honeycomb code by describing boundaries that need no additional physical connectivity, and by optimizing the shape of the qubit patch. We then benchmark the code using Monte Carlo sampling to estimate logical error…
Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
We provide upper and lower bounds on the least-perimeter way to enclose and separate n regions of equal area in the plane. Along the way, inside the hexagonal honeycomb, we provide minimizers for each n .
A new construction for moderate density parity-check (MDPC) codes using finite geometry is proposed. We design a parity-check matrix for this family of binary codes as the concatenation of two matrices: the incidence matrix between points…
In this paper we introduce a variant of the honeycomb lattice in which we create defects by randomly exchanging adjacent bonds, producing a random tiling with a distribution of polygon edges. We study the percolation properties on these…
A protocol called the "honeycomb code", or generically a "Floquet code", was introduced by Hastings and Haah in \cite{hastings_dynamically_2021}. The honeycomb code is a subsystem code based on the honeycomb lattice with zero logical qubits…
In this paper, I present a way to compile the surface code into two-body parity measurements ("pair measurements"), where the pair measurements run along the edges of a Cairo pentagonal tiling. The resulting circuit improves on prior work…
Quantum low-density parity-check (qLDPC) codes can be implemented by measuring only low-weight checks, making them compatible with noisy quantum hardware and central to the quest to build noise-resilient quantum computers. A fundamental…
Quantum low-density parity-check codes are promising candidates for quantum error correcting codes as they might offer more resource-efficient alternatives to surface code architectures. In particular, bivariate bicycle codes have recently…
Recently, Hastings & Haah introduced a quantum memory defined on the honeycomb lattice. Remarkably, this honeycomb code assembles weight-six parity checks using only two-local measurements. The sparse connectivity and two-local measurements…
Low-density parity check (LDPC) codes are a significant class of classical codes with many applications. Several good LDPC codes have been constructed using random, algebraic, and finite geometries approaches, with containing cycles of…
The main purpose of this paper is to further study the structure, parameters and constructions of the recently introduced minimal codes in the sum-rank metric. These objects form a bridge between the classical minimal codes in the Hamming…
The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where…
A new method to compute the symplectic structure of a quantum field theory with non trivial boundary conditions is proposed. Following the suggestion in \cite{ho:gnus, ardalan}, we regard that the boundary conditions are second class…
In this paper we introduce a novel way to speed up the discovery of counterexamples in bounded model checking, based on parallel runs over versions of a system in which features have been randomly disabled. As shown in previous work, adding…
We introduce a new type of boundary conditions, {\it smooth boundary conditions}, for numerical studies of quantum lattice systems. In a number of circumstances, these boundary conditions have substantially smaller finite-size effects than…
On conformally compact manifolds of arbitrary signature, we use conformal geometry to identify a natural (and very general) class of canonical boundary problems. It turns out that these encompass and extend aspects of already known…