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Paper 1

Examples of minimal-memory, non-catastrophic quantum convolutional encoders

Mark M. Wilde, Monireh Houshmand, Saied Hosseini-Khayat

Year

2010

Journal

arXiv preprint

DOI

arXiv:1011.5535

arXiv

1011.5535

One of the most important open questions in the theory of quantum convolutional coding is to determine a minimal-memory, non-catastrophic, polynomial-depth convolutional encoder for an arbitrary quantum convolutional code. Here, we present a technique that finds quantum convolutional encoders with such desirable properties for several example quantum convolutional codes (an exposition of our technique in full generality will appear elsewhere). We first show how to encode the well-studied Forney-Grassl-Guha (FGG) code with an encoder that exploits just one memory qubit (the former Grassl-Roetteler encoder requires 15 memory qubits). We then show how our technique can find an online decoder corresponding to this encoder, and we also detail the operation of our technique on a different example of a quantum convolutional code. Finally, the reduction in memory for the FGG encoder makes it feasible to simulate the performance of a quantum turbo code employing it, and we present the results of such simulations.

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Paper 2

Coarse-Grained Mapping of Fluid Particles via Evolutionary Fuzzy Clustering: Membership-Evolution Term as a Pressure Correction Mechanism.

Han J, Feng Y, Wu J, Fang H

Year

2026

Journal

Journal of chemical theory and computation

DOI

10.1021/acs.jctc.5c01867

arXiv

-

Coarse-graining is an effective approach for bridging atomistic and mesoscopic descriptions of fluid particle systems. However, fixed coarse-grained (CG) mappings do not account for the unbundled nature of fluid particles. We propose an entropy-regularized fuzzy clustering method with temporal smoothness constraints, examining in detail the role of the evolution of fuzzy particle-cluster membership degrees throughout the coarse-graining process. Entropy regularization controls the level of spatial fuzziness, while the temporal smoothness constraints enhance the continuity of cluster position evolution. Within a bottom-up force-matching framework, the interactions between clusters are decomposed into two contributions: a particle-interaction term, which is the weighted sum of interactions between particles, and a membership-evolution term, which originates from the temporal variation of membership degrees. Analyses based on the Lennard-Jones (L-J) fluid particle system and the water molecule system show that an intermediate level of fuzziness yields the most pronounced structural features in the radial distribution functions. The particle-interaction term exhibits system-dependent characteristics, whereas the membership-evolution term consistently provides a repulsive contribution across different systems. Moreover, CG dynamics simulations of the L-J fluid demonstrate that including the membership-evolution term effectively restores the system pressure, which could be interpreted as a pressure correction scheme. This finding provides a physical perspective on the transition from microscopic particle interactions to macroscopic fluid pressure constraints and reveals a bottom-up origin for incorporating additional pressure corrections into fluid CG dynamics, which could be beneficial for the future design of coarse-graining strategies.

Open paper