Implementation of the propagator approach

Jean‐Philippe Bouchaud, Julius Bonart, Jonathan Donier +1 more

Arvid B. van den Brink, Oğuz Meteer, Marco J.G. Bekooij

The belief propagation algorithm is one of the preferred algorithms for a polar code based decoder that can potentially achieve the lowest latency. Although belief propagation polar code algorithms have the ability for a highly parallelized implementation, they require more iterations to achieve a comparable frame error rate and bit error rate compared to the successive cancellation polar code algorithm. The iterative nature of the belief propagation algorithms also results in a higher computational complexity, i.e. O(N(2log2N-1)) compared to the computational complexity O(Nlog2N) of the successive cancellation decoder algorithm. In this paper we propose several software implementations of belief propagation polar code decoders using the computational complexity reduced belief propagation algorithm and the enhanced loop-weakened belief propagation algorithm, to increase the number of decoded codes per second. Compared to a baseline belief propagation implementation, our proposed radix-2 and radix-4 implementations increase the throughput by approximately 15.4% and 22.04% respectively. This gain is the result of a reduction of arithmetic operations, i.e., additions, compares, and multiplications, which is obtained without a loss in error-correcting performance.

Jens Oddershede

Hrishikesh Belagali, Ryan LaRose

We introduce Propaq, a performant and flexible Python package implementing Heisenberg propagation techniques for classically simulating quantum circuits. Propaq is compatible with major quantum software packages like Qiskit and Cirq, and matches or outperforms similar state-of-the-art packages for Heisenberg propagation. Beyond this, Propaq has multiple distinguishing features for simulation and research. These include Heisenberg propagation in any basis, hybrid Schrödinger-Heisenberg simulation, custom truncation and noisy simulation methods, and detailed logging information for analyzing simulation accuracy, runtime, and memory usage. We describe these features, how to use Propaq for research, and its backend implementation.

Robert van Leeuwe Stan Nils Erik Dahlen

While the use of Green's function techniques has a long tradition in quantum chemistry, the possibility of propagating the Kadanoff-Baym equations has remained largely unexplored. We have implemented the time-propagation for atoms and diatomic molecules, starting from a system in the groundstate. The initial stage of the calculation requires solving the Dyson equation self-consistently for the equilibrium Green's function. This Green's function contains a huge amount of information, and we have found it particularly interesting to compare the self-consistent total energies to the results of variational energy functionals of the Green's function. We also use time-propagation for calculating linear response functions, as a means for obtaining the excitation energies of the system. We have presently implemented the propagation for the second Born approximation, while the GW approximation has now been implemented for the ground state calculations.

Philipp Schläfer, Stefan Scholl, E. Leonardi +1 more

LDPC codes are commonly decoded by conventional belief propagation algorithms like the min-sum algorithm. However especially for small block lengths belief propagation performs poorly in comparison to maximum likelihood decoding. In this paper we propose a new decoding algorithm, that is inspired by augmented belief propagation from literature and present hardware architectures and implementations for 28nm ASIC technology. The new decoder has a much higher complexity, but provides a gain of up to 1.2 dB signal-to-noise ratio compared to conventional belief propagation decoding.