Abstracts-QSP-EN

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CUAOA: A Novel CUDA-Accelerated Simulation Framework for the Quantum Approximate Optimization Algorithm

CUAOA: A Novel CUDA-Accelerated Simulation Framework for the Quantum Approximate Optimization Algorithm

Abstract:

The Quantum Approximate Optimization Algorithm (QAOA) is a prominent quantum algorithm designed to find approximate solutions to combinatorial optimization problems. In the current era, where quantum hardware is constrained by noise and limited qubit availability, simulating QAOA remains essential for research. However, existing state-of-the-art simulation frameworks suffer from long execution times or lack comprehensive functionality, usability, and versatility, often requiring users to implement essential features themselves. Additionally, these frameworks are restricted to Python, limiting their use within safer and faster languages like Rust, which offer, e.g., advanced parallelization capabilities. This thesis presents the development of a new GPU-accelerated QAOA simulation framework utilizing the NVIDIA CUDA toolkit.

This framework offers a complete interface for QAOA simulations, enabling the calculation of (exact) expectation values, direct access to the state-vector, fast sampling, and high-performance optimization methods using an advanced state-of-the-art gradient calculation technique. The framework is designed for use in Python and Rust, providing flexibility for integration into a wide range of applications, including those requiring fast algorithm implementations leveraging the QAOA at its core. Such an algorithm, specifically the QAOA^2 , a divide-and-conquer algorithm, is implemented using the new QAOA simulation framework to showcase its usage in a possibly parallized application. The new QAOA simulation framework’s performance is rigorously benchmarked using various random graphs for the MaxCut problem and compared against current state-of-the-art general-purpose quantum circuit simulation frameworks and a specialized QAOA simulation tool. The evaluation shows that the developed simulator can outperform the current state-of-the-art simulators in terms of runtime, with a speedup of up to multiple orders of magnitude. Furthermore, the framework’s capabilities are evaluated within the divide-and-conquer algorithm utilizing the QAOA at its core. This implementation significantly outperforms the reference implementation using the current state-of-the-art simulators for a large problem instance.

Author:

Jonas Felix Blenninger

Advisors:

Claudia Linnhoff-Popien, Jonas Stein, Maximilian Zorn

Student Thesis | Published September 2024 | Copyright © QAR-Lab
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A Reinforcement Learning Environment for directed Quantum Circuit Synthesis

A Reinforcement Learning Environment for directed Quantum Circuit Synthesis

Abstract:

Fueled by recent advances in quantum computing technologies, the design of optimized quantum circuits including reliable quantum state preparation are topics gaining more and more importance. Common approaches often require a high amount of Know-How and manual calculation hampering implementation, especially if the involved circuits increase in qubit number and gate count. Hence, addressing the rise in possible gate-to- qubit combinations by utilizing machine learning techniques represents a promising step in the development of the field. The following study aims to provide a reinforcement learning environment enabling the training of agents on the directed quantum-circuit design for the preparation of quantum states. Thus, the trained agents are enabled to create quantum circuits facilitating the preparation of desired target states, which can be handed over as inputs. In the course of this, all generated quantum-circuits are built utilizing gates from the Clifford+T gate set only. Based on the implemented environment, we conducted experiments to investigate the relation between the depth of the reconstructed quantum circuits and the involved target state parameters. The explored parameter-space included the respective qubit number and circuit-depth used for the target initialization. By providing a division of the parameter-space into several difficulty regions and a collection of well-known states, we facilitated benchmarking of different reinforcement learning algorithms on the quantum-circuit synthesis problem. Specific findings of the study include the generation of PPO-algorithm-based agents, which outperform the random-baseline. Through the application of the trained agents on the benchmarking tests we show their ability to reliably design minimal quantum-circuits for a selection of 2-qubit Bell states.

Author:

Tom Schubert

Advisors:

Claudia Linnhoff-Popien, Michael Kölle, Philipp Altmann

Student Thesis | Published November 2023 | Copyright © QAR-Lab
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Anomaly Detection using Quantum Circuit Born Machines (en)

Anomaly Detection using Quantum Circuit Born Machines

Abstract:

Anomaly detection is a critical component in various fields, including finance, medical diagnosis, and fraud detection. As datasets become increasingly complex and larger, traditional computers face limitations in processing power. In contrast, quantum computers oer promising solutions through the physical properties of their qubits, such as entanglement and superposition. The emergence of quantum machine learning, particularly the quantum circuit born machines (QCBMs), is introduced as a promising approach to tackle such complex problems. QCBMs are parameterized quantum circuits that can be trained to generate samples from a target distribution. The goal of this work is to leverage this ability for detecting anomalies that have a distribution dierent from that of normal data points. The effectiveness of QCBMs for anomaly detection is explored using a dataset generated by the make_blobs method from the Scikit-learn package in Python, where some outliers can be clearly distinguished from the clusters. And its performance is compared with an autoencoder model using the ROC-curve and the Matthews correlation coecient (MCC). These metrics are used to evaluate the models’ ability to detect anomalies and avoid false positives. The results show that QCBMs outperform the autoencoder when trained with a smaller dataset, indicating that QCBMs are more eective in dealing with data and can learn the underlying distribution more eciently than the autoencoder. However, both models can learn the distribution when trained with the full dataset.

Author:

Ahmad Almohamad Alissa

Advisors:

Jonas Stein, Danielle Schumann, Claudia Linnhoff-Popien

Student Thesis | Published April 2023 | Copyright © QAR-Lab
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Efficient Quantum Circuit Architecture for Coined Quantum Walks on many Bipartite Graphs (en)

Efficient Quantum Circuit Architecture for Coined Quantum Walks on many Bipartite Graphs

Abstract:

Quantum walks, a quantum analog of classical random walks, have emerged as a powerful paradigm in quantum computation and simulation. While classical random walks rely on stochastic processes to explore systems, quantum walks leverage the unique properties of quantum mechanics to perform these tasks more efficiently. In particular, discrete-time quantum walks (DTQWs) have been studied extensively for their applications in graph theory, such as graph isomorphism, graph connectivity, and graph-based search problems. Despite their potential, implementing DTQWs on near-term quantum devices remains challenging. While previous works have focused on quantum circuit implementations for DTQWs with uniform coin operators, implementing non-homogeneous coin sets is a complex task that requires new approaches. This thesis presents an efficient quantum circuit architecture for implementing coined DTQWs with non-homogeneous, position-dependent coin sets on a large subset of bipartite graphs. A novel edge labeling scheme, Gray Code Directed Edges encoding, is introduced, taking advantage of Gray code for position encoding and the bipartite structure of the underlying graph to minimize the complexity of the quantum circuits representing coin and shift operators. This optimization leads to fewer gate operations, reducing the impact of noise and errors in near-term quantum devices. A labeling scheme is developed for various graph topologies, including cycle graphs, chained cylinder graphs, and square grid graphs, which are especially relevant for reinforcement learning applications. These findings offer a new perspective on the implementation of coined quantum walks and lay a foundation for future research on quantum walks with non-homogeneous coin sets.

Author:

Viktoryia Patapovich

Advisors:

Jonas Stein, Michael Kölle, Maximilian-Balthasar Mansky, Claudia Linnhoff-Popien

Student Thesis | Published July 2023 | Copyright © QAR-Lab
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