Swarm Behavior Cloning

In sequential decision-making environments, the primary approaches for training agents are Reinforcement Learning (RL) and Imitation Learning (IL). Unlike RL, which relies on modeling a reward function, IL leverages expert demonstrations, where an expert policy $\pi_e$ (e.g., a human) provides the desired behavior. Formally, a dataset $D$ of state-action pairs is provided: $D = {(s, a = \pi_e(s))}$. A common technique within IL is Behavior Cloning (BC), where a policy $\pi(s) = a$ is learned through supervised learning on $D$. Further improvements can be achieved by using an ensemble of $N$ individually trained BC policies, denoted as $E = {\pi_i(s)}{1 \leq i \leq N}$. The ensemble's action $a$ for a given state $s$ is the aggregated output of the $N$ actions: $a = \frac{1}{N} \sum{i} \pi_i(s)$. This paper addresses the issue of increasing action differences -- the observation that discrepancies between the $N$ predicted actions grow in states that are underrepresented in the training data. Large action differences can result in suboptimal aggregated actions. To address this, we propose a method that fosters greater alignment among the policies while preserving the diversity of their computations. This approach reduces action differences and ensures that the ensemble retains its inherent strengths, such as robustness and varied decision-making. We evaluate our approach across eight diverse environments, demonstrating a notable decrease in action differences and significant improvements in overall performance, as measured by mean episode returns.

Finding Strong Lottery Ticket Networks with Genetic Algorithms

According to the Strong Lottery Ticket Hypothesis, every sufficiently large neural network with randomly initialized weights contains a sub-network which - still with its random weights - already performs as well for a given task as the trained super-network. We present the first approach based on a genetic algorithm to find such strong lottery ticket sub-networks without training or otherwise computing any gradient. We show that, for smaller instances of binary classification tasks, our evolutionary approach even produces smaller and better-performing lottery ticket networks than the state-of-the-art approach using gradient information.

Architectural Influence on Variational Quantum Circuits in Multi-Agent Reinforcement Learning: Evolutionary Strategies for Optimization

In recent years, Multi-Agent Reinforcement Learning (MARL) has found application in numerous areas of science and industry, such as autonomous driving, telecommunications, and global health. Nevertheless, MARL suffers from, for instance, an exponential growth of dimensions. Inherent properties of quantum mechanics help to overcome these limitations, e.g., by significantly reducing the number of trainable parameters. Previous studies have developed an approach that uses gradient-free quantum Reinforcement Learning and evolutionary optimization for variational quantum circuits (VQCs) to reduce the trainable parameters and avoid barren plateaus as well as vanishing gradients. This leads to a significantly better performance of VQCs compared to classical neural networks with a similar number of trainable parameters and a reduction in the number of parameters by more than 97 \% compared to similarly good neural networks. We extend an approach of K\"olle et al. by proposing a Gate-Based, a Layer-Based, and a Prototype-Based concept to mutate and recombine VQCs. Our results show the best performance for mutation-only strategies and the Gate-Based approach. In particular, we observe a significantly better score, higher total and own collected coins, as well as a superior own coin rate for the best agent when evaluated in the Coin Game environment.

A Study on Optimization Techniques for Variational Quantum Circuits in Reinforcement Learning

Quantum Computing aims to streamline machine learning, making it more effective with fewer trainable parameters. This reduction of parameters can speed up the learning process and reduce the use of computational resources. However, in the current phase of quantum computing development, known as the noisy intermediate-scale quantum era (NISQ), learning is difficult due to a limited number of qubits and widespread quantum noise. To overcome these challenges, researchers are focusing on variational quantum circuits (VQCs). VQCs are hybrid algorithms that merge a quantum circuit, which can be adjusted through parameters, with traditional classical optimization techniques. These circuits require only few qubits for effective learning. Recent studies have presented new ways of applying VQCs to reinforcement learning, showing promising results that warrant further exploration. This study investigates the effects of various techniques -- data re-uploading, input scaling, output scaling -- and introduces exponential learning rate decay in the quantum proximal policy optimization algorithm's actor-VQC. We assess these methods in the popular Frozen Lake and Cart Pole environments. Our focus is on their ability to reduce the number of parameters in the VQC without losing effectiveness. Our findings indicate that data re-uploading and an exponential learning rate decay significantly enhance hyperparameter stability and overall performance. While input scaling does not improve parameter efficiency, output scaling effectively manages greediness, leading to increased learning speed and robustness.

Qandle: Accelerating State Vector Simulation Using Gate-Matrix Caching and Circuit Splitting

To address the computational complexity associated with state-vector simulation for quantum circuits, we propose a combination of advanced techniques to accelerate circuit execution. Quantum gate matrix caching reduces the overhead of repeated applications of the Kronecker product when applying a gate matrix to the state vector by storing decomposed partial matrices for each gate. Circuit splitting divides the circuit into sub-circuits with fewer gates by constructing a dependency graph, enabling parallel or sequential execution on disjoint subsets of the state vector. These techniques are implemented using the PyTorch machine learning framework. We demonstrate the performance of our approach by comparing it to other PyTorch-compatible quantum state-vector simulators. Our implementation, named Qandle, is designed to seamlessly integrate with existing machine learning workflows, providing a user-friendly API and compatibility with the OpenQASM format. Qandle is an open-source project hosted on GitHub https://github.com/gstenzel/qandle and PyPI https://pypi.org/project/qandle/ .

REACT: Revealing Evolutionary Action Consequence Trajectories for Interpretable Reinforcement Learning

To enhance the interpretability of Reinforcement Learning (RL), we propose Revealing Evolutionary Action Consequence Trajectories (REACT). In contrast to the prevalent practice of validating RL models based on their optimal behavior learned during training, we posit that considering a range of edge-case trajectories provides a more comprehensive understanding of their inherent behavior. To induce such scenarios, we introduce a disturbance to the initial state, optimizing it through an evolutionary algorithm to generate a diverse population of demonstrations. To evaluate the fitness of trajectories, REACT incorporates a joint fitness function that encourages both local and global diversity in the encountered states and chosen actions. Through assessments with policies trained for varying durations in discrete and continuous environments, we demonstrate the descriptive power of REACT. Our results highlight its effectiveness in revealing nuanced aspects of RL models' behavior beyond optimal performance, thereby contributing to improved interpretability.

A Reinforcement Learning Environment for Directed Quantum Circuit Synthesis

With recent advancements in quantum computing technology, optimizing quantum circuits and ensuring reliable quantum state preparation have become increasingly vital. Traditional methods often demand extensive expertise and manual calculations, posing challenges as quantum circuits grow in qubit- and gate-count. Therefore, harnessing machine learning techniques to handle the growing variety of gate-to-qubit combinations is a promising approach. In this work, we introduce a comprehensive reinforcement learning environment for quantum circuit synthesis, where circuits are constructed utilizing gates from the the Clifford+T gate set to prepare specific target states. Our experiments focus on exploring the relationship between the depth of synthesized quantum circuits and the circuit depths used for target initialization, as well as qubit count. We organize the environment configurations into multiple evaluation levels and include a range of well-known quantum states for benchmarking purposes. We also lay baselines for evaluating the environment using Proximal Policy Optimization. By applying the trained agents to benchmark tests, we demonstrated their ability to reliably design minimal quantum circuits for a selection of 2-qubit Bell states.

Quantum Advantage Actor-Critic for Reinforcement Learning

Quantum computing offers efficient encapsulation of high-dimensional states. In this work, we propose a novel quantum reinforcement learning approach that combines the Advantage Actor-Critic algorithm with variational quantum circuits by substituting parts of the classical components. This approach addresses reinforcement learning's scalability concerns while maintaining high performance. We empirically test multiple quantum Advantage Actor-Critic configurations with the well known Cart Pole environment to evaluate our approach in control tasks with continuous state spaces. Our results indicate that the hybrid strategy of using either a quantum actor or quantum critic with classical post-processing yields a substantial performance increase compared to pure classical and pure quantum variants with similar parameter counts. They further reveal the limits of current quantum approaches due to the hardware constraints of noisy intermediate-scale quantum computers, suggesting further research to scale hybrid approaches for larger and more complex control tasks.

Challenges for Reinforcement Learning in Quantum Computing

Quantum computing (QC) in the current NISQ-era is still limited. To gain early insights and advantages, hybrid applications are widely considered mitigating those shortcomings. Hybrid quantum machine learning (QML) comprises both the application of QC to improve machine learning (ML), and the application of ML to improve QC architectures. This work considers the latter, focusing on leveraging reinforcement learning (RL) to improve current QC approaches. We therefore introduce various generic challenges arising from quantum architecture search and quantum circuit optimization that RL algorithms need to solve to provide benefits for more complex applications and combinations of those. Building upon these challenges we propose a concrete framework, formalized as a Markov decision process, to enable to learn policies that are capable of controlling a universal set of quantum gates. Furthermore, we provide benchmark results to assess shortcomings and strengths of current state-of-the-art algorithms.

Improving Parameter Training for VQEs by Sequential Hamiltonian Assembly

A central challenge in quantum machine learning is the design and training of parameterized quantum circuits (PQCs). Similar to deep learning, vanishing gradients pose immense problems in the trainability of PQCs, which have been shown to arise from a multitude of sources. One such cause are non-local loss functions, that demand the measurement of a large subset of involved qubits. To facilitate the parameter training for quantum applications using global loss functions, we propose a Sequential Hamiltonian Assembly, which iteratively approximates the loss function using local components. Aiming for a prove of principle, we evaluate our approach using Graph Coloring problem with a Varational Quantum Eigensolver (VQE). Simulation results show, that our approach outperforms conventional parameter training by 29.99% and the empirical state of the art, Layerwise Learning, by 5.12% in the mean accuracy. This paves the way towards locality-aware learning techniques, allowing to evade vanishing gradients for a large class of practically relevant problems.