Ninnat Dangniam

Apimuk Sornsaeng, Ninnat Dangniam, Thiparat Chotibut

Next Generation Reservoir Computing (NG-RC) is a modern class of model-free machine learning that enables an accurate forecasting of time series data generated by dynamical systems. We demonstrate that NG-RC can accurately predict full many-body quantum dynamics in both integrable and chaotic systems. This is in contrast to the conventional application of reservoir computing that concentrates on the prediction of the dynamics of observables. In addition, we apply a technique which we refer to as skipping ahead to predict far future states accurately without the need to extract information about the intermediate states. However, adopting a classical NG-RC for many-body quantum dynamics prediction is computationally prohibitive due to the large Hilbert space of sample input data. In this work, we propose an end-to-end quantum algorithm for many-body quantum dynamics forecasting with a quantum computational speedup via the block-encoding technique. This proposal presents an efficient model-free quantum scheme to forecast quantum dynamics coherently, bypassing inductive biases incurred in a model-based approach.

Apimuk Sornsaeng, Ninnat Dangniam, Pantita Palittapongarnpim et al.

Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many applications, DM has been successfully applied to discover relevant order parameters in many-body systems, enabling automatic classification of quantum phases of matter. However, classical DM algorithm is computationally prohibitive for a large dataset, and any reduction of the time complexity would be desirable. With a quantum computational speedup in mind, we propose a quantum algorithm for DM, termed quantum diffusion map (qDM). Our qDM takes as an input $N$ classical data vectors, performs an eigen-decomposition of the Markov transition matrix in time $O(\log^3 N)$, and classically constructs the diffusion map via the readout (tomography) of the eigenvectors, giving a total expected runtime proportional to $N^2 \text{polylog}\, N$. Lastly, quantum subroutines in qDM for constructing a Markov transition matrix, and for analyzing its spectral properties can also be useful for other random walk-based algorithms.