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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

Rapid Prediction of Hot-Carrier Relaxation by Learning of Nonadiabatic Hamiltonians with Graph Neural Networks.

Meng K, Lu H, Xu X, Prezhdo OV, Long R

Year

2026

Journal

Journal of chemical theory and computation

DOI

10.1021/acs.jctc.5c02178

arXiv

-

An electron-vibrational Hamiltonian fully encodes corresponding quantum dynamics; however, extracting the dynamics still relies on time and memory-consuming trajectory-based nonadiabatic molecular dynamics (NAMD) simulations, typically stochastic surface hopping. Here, we develop a general graph neural network, artificial intelligence ab initio NAMD (AINAMD) that establishes an end-to-end mapping from Hamiltonian to hot carrier relaxation dynamics. We validated the generality of AINAMD across multiple materials, including a zero-dimensional Si quantum dot (QD), a one-dimensional carbon nanotube (CNT), a two-dimensional twisted MoS/WS bilayer, and a three-dimensional soft-lattice MAPbI perovskite. With only 10% training data, AINAMD can rapidly and accurately generate picosecond energy decay curves for hot electron and hot hole relaxation for the remaining 90% Hamiltonians, while delivering a computational speed-up of more than 6 orders of magnitude compared to standard CPU-based NAMD simulations. Moreover, AINAMD can also map directly the Hamiltonian to the carrier relaxation time, bypassing generation of the energy decay curves and demonstrating the ability to handle complex NAMD tasks. Further, by projecting high-dimensional Hamiltonian encoding features into a two-dimensional space with unsupervised learning, we demonstrate that AINAMD can effectively distinguish Hamiltonian types, verifying its ability to identify a particular system (QD, CNT, MoS/WS and MAPbI) and a charge carrier (electron or hole). Overall, the developed AINAMD approach provides a novel computational methodology and a conceptual framework for accelerating NAMD simulations with machine learning by many orders of magnitude.

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