Related papers: Generalized matching decoders for 2D topological t…
For reliable large-scale quantum computation, quantum error correction (QEC) is essential to protect logical information distributed across multiple physical qubits. Taking advantage of recent advances in deep learning, neural network-based…
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…
We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a…
Decoding a quantum error correction code is generally NP-hard, but corrections must be applied at a high frequency to suppress noise successfully. Matchable codes, like the surface code, exhibit a special structure that makes it possible to…
We propose fault-tolerant encoders for quantum low-density parity check (LDPC) codes. By grouping qubits within a quantum code over contiguous blocks and applying preshared entanglement across these blocks, we show how transversal…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
Surface codes are a popular error-correction route to fault-tolerant quantum computation. The so-called exponential backlog problem that can arise when one has to do logical $T$-gates within the surface code demands real-time decoding of…
A Viterbi-like decoding algorithm is proposed in this paper for generalized convolutional network error correction coding. Different from classical Viterbi algorithm, our decoding algorithm is based on minimum error weight rather than the…
Iterative decoders for finite length quantum low-density parity-check (QLDPC) codes are attractive because their hardware complexity scales only linearly with the number of physical qubits. However, they are impacted by short cycles,…
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…
In this paper, we revisit the Image-to-Image (I2I) translation problem with transition consistency, namely the consistency defined on the conditional data mapping between each data pairs. Explicitly parameterizing each data mappings with a…
Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators,…
Discovering low-overhead quantum error-correcting codes is of significant interest for fault-tolerant quantum computation. For hardware capable of long-range connectivity, the bivariate bicycle codes offer significant overhead reduction…
We propose a general framework for decoding quantum error-correcting codes with generative modeling. The model utilizes autoregressive neural networks, specifically Transformers, to learn the joint probability of logical operators and…
In numerical simulations of classical and quantum lattice systems, 2d corner transfer matrices (CTMs) and 3d corner tensors (CTs) are a useful tool to compute approximate contractions of infinite-size tensor networks. In this paper we show…
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…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum…
Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that…