Related papers: Quantum Codes on Graphs
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also…
In this work, we generalize several three-dimensional Z2 stabilizer models--including the X-cube model, the three-dimensional toric code, and Haah's code--to their ZN counterparts. Under periodic boundary conditions, we analyze their ground…
Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which…
We discuss encodings of fermionic many-body systems by qubits in the presence of symmetries. Such encodings eliminate redundant degrees of freedom in a way that preserves a simple structure of the system Hamiltonian enabling quantum…
Flag codes generalize constant dimension codes by considering sequences of nested subspaces with prescribed dimensions as codewords. A comprehensive construction, which unites cyclic orbit flag codes, yields two families of flag codes on…
Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for…
Quantum LDPC codes may provide a path to build low-overhead fault-tolerant quantum computers. However, as general LDPC codes lack geometric constraints, na\"ive layouts couple many distant qubits with crossing connections which could be…
We propose to construct large quantum graph codes by means of superconducting circuits working at the ultrastrong coupling regime. In this physical scenario, we are able to create a cluster state between any pair of qubits within a fraction…
We introduce a construction for protocols for fault-tolerant quantum computing based on code concatenation and transversal gates. These protocols can be interpreted as families of quantum circuits of low-weight stabilizer measurements…
The hypergraph product creates a quantum stabilizer code from two input classical linear codes; a paradigmatic example being the surface code as a hypergraph product of two classical repetition codes. Many properties of the hypergraph…
We show how graph theory concepts can provide an insight into the origin of slow dynamics in systems with kinetic constraints. In particular, we observe that slow dynamics is related to the presence of strong hierarchies between nodes on…
We construct a new graph on 120 vertices whose quantum and classical independence numbers are different. At the same time, we construct an infinite family of graphs whose quantum chromatic numbers are smaller than the classical chromatic…
In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…
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…
In the present article, we consider Algebraic Geometry codes on some rational surfaces. The estimate of the minimum distance is translated into a point counting problem on plane curves. This problem is solved by applying the upper bound…
We introduce a class of models, dubbed paired twist-defect networks, that generalize the structure of Kitaev's honeycomb model for which there is a direct equivalence between: i) Floquet codes (FCs), ii) adiabatic loops of gapped…
The problem of computing distances of error-correcting codes is fundamental in both the classical and quantum settings. While hardness for the classical version of these problems has been known for some time (in both the exact and…
We discuss families of approximate quantum error correcting codes which arise as the nearly-degenerate ground states of certain quantum many-body Hamiltonians composed of non-commuting terms. For exact codes, the conditions for error…
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…