Quantum mechanics has stirred interest in a number of research fields over the last years, including data processing. This is especially due to the promise of Quantum computers (QC) to solve specific problems faster and more efficient than conventional classical algorithms. Following this direction, our team focuses on different ways to exploit subfields of quantum mechanics, such as QC and quantum machine learning (QML), for earth observation (EO) tasks and explores how they can help shape the future of large scale data processing and classification.
Fundamental research — Complexity and simulability of quantum states
As of now it has proven difficult to determine whether for a given computational problem a fast quantum algorithm exists that outperforms classical algorithms running on (super) computers. Many computational tasks, like the simulation of quantum systems, can oftentimes be efficiently executed on classical computers through cleverly designed Monte Carlo algorithms. Thus, a precise description of the boundary between quantum and classical simulability remains difficult. To shed light on this important question, part of our team studies the complexity of quantum states and their classical simulability. To be precise, we investigate different notions of complexity and their use in examples such as quantum walks. Furthermore, we study the classical simulability of quantum systems through Monte Carlo sampling techniques. The outcome of these investigations promises to help us understand the circumstances under which quantum computational resources are essential and must be deployed.
Quantifying the complexity of a given quantum state is a fundamental problem.
Here we explored the notion of the Krylov complexity of quantum states in the setting of quantum walks.
Applied Theory — Quantum machine learning in EO data classification
Quantum circuit for QC-CNN model (slightly altered from the published version):
1) white for qL qubits (spatial information encoding), gray for qC qubit (color information encoding), green for qK qubits (kernel index encoding), and yellow for qR qubits (feature map information encoding); 2) dot markers in the circuit highlight the involved qubits in the applied quantum gates or the measured qubits in the specific layers; 3) the model contains m convolution layers and each layer involves 2k kernels; and 4) |9i⟩ and |9m⟩ are the outputs from the encoding layer and quantum convolution layers, respectively
Credit:
F. Fan, Y. Shi, T. Guggemos and X. X. Zhu, "Hybrid Quantum-Classical Convolutional Neural Network Model for Image Classification," in IEEE Transactions on Neural Networks and Learning Systems, doi: 10.1109/TNNLS.2023.3312170. https://ieeexplore.ieee.org/abstract/document/10254235
Another challenge with respect to QC is the fact that today's functional prototypes only consist of a very limited number of quantum bits, which restricts the size of the input information. Thus the second focus of our team is to determine if and how these 'small' quantum computers can be used to enhance EO data processing and classification. To be precise, we focus on QML algorithms, which combine quantum computing with machine learning, to tackle this task.
In particular, we explore two different strategies:
1. Use classical preprocessing to extract a small number of features and subsequently employ QML to classify the image based on these features
2. Use QML to preprocess the image to extract relevant features and a classical convolutional neural networt (CNN) for classification. This approach is called Quantum Classical Convolutional Neural Network (QC-CNN)
1. QML for classification
This strategy is investigated for different QML platforms such as quantum annealers and gate based quantum computers. The efficiency of this approach can then be tested on various test data sets and so far usually seems to be on par with its classical counterparts, even outperforming it in certain circumstances. For further enhancing we are researching in decreasing or even circumventing the required amount of classical preprocessing.
2. QC-CNN
The combination of feature extraction with QML and subsequent classification with a classical CNN was first successfully demonstrated for radically downscaled (8 by 8 bit pixels) grey-scale EO images. Since then our focus has shifted on how to encode larger multi-spectral images using enhanced ‘superpixel’ preprocessing to avoid lossy downscaling and different techniques such as MCQI and FRQI to encode and process multiple spectral bands at the same time. We have since been able to implement both improvements and demonstrate their advantages compared to both classical and other quantum schemes. However, we are determined to try to find new ways to increase the efficiency and functionality of our scheme.
Land cover maps produced by the trained QML models with the best performance for Berlin covering about 30 × 30 km2 and the GSD of each map is 10 m:
(a) the cloud removed Sentinel-2 image of Berlin; (b) MQCNN model with the overall accuracy 0.92; (c) FQCNN with the overall accuracy 0.90; (d) CNN with the overall accuracy 0.90; (e) QCNN with the overall accuracy 0.91;
Credit:
F. Fan, Y. Shi and X. X. Zhu, "Urban Land Cover Classification from Sentinel-2 Images with Quantum-Classical Network," 2023 Joint Urban Remote Sensing Event (JURSE), Heraklion, Greece, 2023, pp. 1-4, doi: 10.1109/JURSE57346.2023.10144213. https://ieeexplore.ieee.org/document/10144213
We are part of a European team dedicated to combine High Performance Computers (HPC) with Quantum Computers, to make QC relevant and accessible for other research fields. This combination of HPC and QC could prove useful for a number of applications such as energy anomaly detection, vegetation management, transport route optimization and image classification. While our focus regarding this project will be on the last topic, we believe that we will be able to contribute largely to the general idea and implementation of this promising crossover of high level classical and quantum computing.
In collaboration with the DLR_School_Labs, we plan to use this research as an outreach platform for schools and the general public. We believe that the study of earth sciences is a great motivation to learn about the concepts of quantum mechanics and quantum computing.
Example for a hybrid HPC-QC network.
While the HPC is mainly used for pre- and postprocessing and feedback loops, the QC employs quantum effects to enhance the efficiency of the main computations.
The chip consists of three main parts: the source for producing the needed quantum states, the state evolution layer also used to encode the image information, and the measurement layer to read out the results.
The last pillar of our research is the actual experimental implementation of QML. In a collaboration together with the University of Vienna we aim to implement QML algorithms for EO data processing and classification on a photonic chip. To this end we consider Quantum Kernel Methods, Quantum Neural Networks and Quantum Reservoir Computing as promising candidates. The final goal is thus to not only test different preexisting universal quantum hardware for EO tasks but to also design and fabricate a photonic chip specifically for our precise applications.
