Related papers: Bias-Aware BP Decoding of Quantum Codes via Direct…
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions…
Polar codes are a channel coding scheme for the next generation of wireless communications standard (5G). The belief propagation (BP) decoder allows for parallel decoding of polar codes, making it suitable for high throughput applications.…
We describe message-passing and decimation approaches for lossy source coding using low-density generator matrix (LDGM) codes. In particular, this paper addresses the problem of encoding a Bernoulli(0.5) source: for randomly generated LDGM…
Measuring fibre dispersion in white matter with diffusion magnetic resonance imaging (MRI) is limited by an inherent degeneracy between fibre dispersion and microscopic diffusion anisotropy (i.e., the diffusion anisotropy expected for a…
Backpropagation (BP) of errors is the backbone training algorithm for artificial neural networks (ANNs). It updates network weights through gradient descent to minimize a loss function representing the mismatch between predictions and…
Here, we study the problem of decoding information transmitted through unknown quantum states. We assume that Alice encodes an alphabet into a set of orthogonal quantum states, which are then transmitted to Bob. However, the quantum channel…
Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show…
Belief propagation (BP) provides a scalable heuristic for contracting tensor networks on loopy graphs, but its success in quantum many-body settings has largely rested on empirical evidence. Developing upon a recently introduced…
The back-propagation (BP) algorithm has been considered the de-facto method for training deep neural networks. It back-propagates errors from the output layer to the hidden layers in an exact manner using the transpose of the feedforward…
Highly efficient quantum dense coding for continuous variables has been experimentally accomplished by means of exploiting bright EPR beam with anticorrelation of amplitude quadratures and correlation of phase quadratures, which is…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
Known for their capacity-achieving abilities, polar codes have been selected as the control channel coding scheme for 5G communications. To satisfy the needs of high throughput and low latency, belief propagation (BP) is chosen as the…
There is an increasing interest in scaling tensor network methods through belief propagation (BP), as well as increasing the accuracy of BP through tensor network methods. We develop a unification framework that takes an arbitrary graphical…
We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing…
We consider decoding of binary Tanner codes using message-passing iterative decoding and linear programming (LP) decoding in MBIOS channels. We present new certificates that are based on a combinatorial characterization for local-optimality…
We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted…
We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by…
In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order…
To enable fault tolerance on millions of qubits in real time, scalable decoding is necessary, which motivates this paper. Existing decoding algorithms (decoders), such as clustering, matching, belief propagation (BP), and neural networks,…
Degeneracies arising from uninformative geometry are known to deteriorate LiDAR-based localization and mapping. This work introduces a new probabilistic method to detect and mitigate the effect of degeneracies in point-to-plane error…