Related papers: A local automaton for the 2D toric code

We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…

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 propose a unifying paradigm for analyzing and constructing topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. To this end, we relate such circuits to discrete fixed-point…

This paper concerns $d$-dimensional cellular automata with the von Neumann neighborhood that conserve the sum of the states of all their cells. These automata, called number-conserving or density-conserving cellular automata, are of…

We present a quantum error correcting code with dynamically generated logical qubits. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act…

Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…

Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remains largely unexplored. In this work, we focus on the…

Over discrete memoryless channels (DMC), linear decoders (maximizing additive metrics) afford several nice properties. In particular, if suitable encoders are employed, the use of decoding algorithm with manageable complexities is…

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…

Quantum error correction is a key ingredient for large scale quantum computation, protecting logical information from physical noise by encoding it into many physical qubits. Topological stabilizer codes are particularly appealing due to…

We analyze the properties of a 2D topological code derived by concatenating the [[4, 2, 2]] code with the toric/surface code, or alternatively by removing check operators from the 2D square-octagon or 4.8.8 color code. We show that the…

We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these…

We study the robustness of 3D intrinsic topogical order under external perturbations by investigating the paradigmatic microscopic model, the 3D toric code in an external magnetic field. Exact dualities as well as variational calculations…

We give an explicit realization of the 4d local operator / 2d conformal block correspondence of Costello and Paquette in the case of gauge theories. This is accomplished by lifting the 4d local operators to non-local operators in twistor…

We introduce a class of 3D color codes, which we call stacked codes, together with a fault-tolerant transformation that will map logical qubits encoded in two-dimensional (2D) color codes into stacked codes and back. The stacked code allows…

Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…

A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates…

Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…

Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the…

We present a generalization of the double semion topological quantum field theory to higher dimensions, as a theory of $d-1$ dimensional surfaces in a $d$ dimensional ambient space. We construct a local Hamiltonian which is a sum of…