We apply a hybrid evolutionary algorithm to minimize the depth of circuits in quantum computing. More specifically, we evaluate two different variants of the algorithm. In the first approach, we combine the evolutionary algorithm with an optimization subroutine to optimize the parameters of the rotation gates present in the quantum circuit. In the second, the algorithm solely relies on evolutionary operations (i.e., mutations and crossover). We approach the problem from two sides: (1) constructing circuits from the ground up by starting with random initializations and (2) initializing individuals with a target circuit in order to optimize it further according to the fitness function. We run experiments on random circuits with 4 and 6 qubits varying in circuit depth. Our results show that the proposed methods are able to significantly reduce the depth of circuits while still retaining a high fidelity to the target state.

While exploration in single-agent reinforcement learning has been studied extensively in recent years, consid-erably less work has focused on its counterpart in multi-agent reinforcement learning. To address this issue, this work proposes a peer-incentivized reward function inspired by previous research on intrinsic curiosity and influence-based rewards. The PIMAEX reward, short for Peer-Incentivized Multi-Agent Exploration, aims to improve exploration in the multi-agent setting by encouraging agents to exert influence over each other to increase the likelihood of encountering novel states. We evaluate the PIMAEX reward in conjunction with PIMAEX-Communication, a multi-agent training algorithm that employs a communication channel for agents to influence one another. The evaluation is conducted in the Consume/Explore environment, a partially observable environment with deceptive rewards, specifically designed to challenge the exploration vs. exploitation dilemma and the credit-assignm ent problem. The results empirically demonstrate that agents using the PI-MAEX reward with PIMAEX-Communication outperform those that do not.

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 and PyPI.

Optimizing the architecture of variational quantum circuits (VQCs) is crucial for advancing quantum computing (QC) towards practical applications. Current methods range from static ansatz design and evolutionary methods to machine learned VQC optimization, but are either slow, sample inefficient or require infeasible circuit depth to realize advantages. Quality diversity (QD) search methods combine diversity-driven optimization with user-specified features that offer insight into the optimization quality of circuit solution candidates. However, the choice of quality measures and the representational modeling of the circuits to allow for optimization with the current state-of-the-art QD methods like covariance matrix adaptation (CMA), is currently still an open problem. In this work we introduce a directly matrix-based circuit engineering, that can be readily optimized with QD-CMA methods and evaluate heuristic circuit quality properties like expressivity and gate-diversity as quality measures. We empirically show superior circuit optimization of our QD optimization w.r.t. speed and solution score against a set of robust benchmark algorithms from the literature on a selection of NP-hard combinatorial optimization problems.

Abstract We propose discriminative reward co-training (DIRECT) as an extension to deep reinforcement learning algorithms. Building upon the concept of self-imitation learning (SIL), we introduce an imitation buffer to store beneficial trajectories generated by the policy, determined by their return. A discriminator network is trained concurrently to the policy to distinguish between trajectories generated by the current policy and beneficial trajectories generated by previous policies. The discriminator’s verdict is used to construct a reward signal for optimizing the policy. By interpolating prior experience, DIRECT is able to act as a reward surrogate, steering policy optimization toward more valuable regions of the reward landscape, thus, toward learning an optimal policy. In this article, we formally introduce the additional components, their intended purpose and parameterization, and define a unified training procedure. To reveal insights into the mechanics of the proposed architecture, we provide evaluations of the introduced hyperparameters. Further benchmark evaluations in various discrete and continuous control environments provide evidence that DIRECT is especially beneficial in environments possessing sparse rewards, hard exploration tasks, and shifting circumstances. Our results show that DIRECT outperforms state-of-the-art algorithms in those challenging scenarios by providing a surrogate reward to the policy and direct the optimization toward valuable areas.

Surrogate models are ubiquitously used in industry and academia to efficiently approximate black box functions. As state-of-the-art methods from classical machine learning frequently struggle to solve this problem accurately for the often scarce and noisy data sets in practical applications, investigating novel approaches is of great interest. Motivated by recent theoretical results indicating that quantum neural networks (QNNs) have the potential to outperform their classical analogs in the presence of scarce and noisy data, we benchmark their qualitative performance for this scenario empirically. Our contribution displays the first application-centered approach of using QNNs as surrogate models on higher dimensional, real world data. When compared to a classical artificial neural network with a similar number of parameters, our QNN demonstrates significantly better results for noisy and scarce data, and thus motivates future work to explore this potential quantum advantage. Finally, we demonstrate the performance of current NISQ hardware experimentally and estimate the gate fidelities necessary to replicate our simulation results.

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.

Abstract Peer incentivization (PI) is a recent approach where all agents learn to reward or penalize each other in a distributed fashion, which often leads to emergent cooperation. Current PI mechanisms implicitly assume a flawless communication channel in order to exchange rewards. These rewards are directly incorporated into the learning process without any chance to respond with feedback. Furthermore, most PI approaches rely on global information, which limits scalability and applicability to real-world scenarios where only local information is accessible. In this paper, we propose Mutual Acknowledgment Token Exchange (MATE), a PI approach defined by a two-phase communication protocol to exchange acknowledgment tokens as incentives to shape individual rewards mutually. All agents condition their token transmissions on the locally estimated quality of their own situations based on environmental rewards and received tokens. MATE is completely decentralized and only requires local communication and information. We evaluate MATE in three social dilemma domains. Our results show that MATE is able to achieve and maintain significantly higher levels of cooperation than previous PI approaches. In addition, we evaluate the robustness of MATE in more realistic scenarios, where agents can deviate from the protocol and communication failures can occur. We also evaluate the sensitivity of MATE w.r.t. the choice of token values.

Applying new computing paradigms like quantum computing to the field of machine learning has recently gained attention.However, as high-dimensional real-world applications are not yet feasible to be solved using purely quantum hardware, hybrid methods using both classical and quantum machine learning paradigms have been proposed.For instance, transfer learning methods have been shown to be successfully applicable to hybrid image classification tasks.Nevertheless, beneficial circuit architectures still need to be explored.Therefore, tracing the impact of the chosen circuit architecture and parameterization is crucial for the development of beneficially applicable hybrid methods.However, current methods include processes where both parts are trained concurrently, therefore not allowing for a strict separability of classical and quantum impact.Thus, those architectures might produce models that yield a superior prediction accuracy whilst employing the least possible quantum impact.To tackle this issue, we propose Sequential Quantum Enhanced Training (SE-QUENT) an improved architecture and training process for the traceable application of quantum computing methods to hybrid machine learning.Furthermore, we provide formal evidence for the disadvantage of current methods and preliminary experimental results as a proof-of-concept for the applicability of SEQUENT.

Stochastic partial observability poses a major challenge for decentralized coordination in multi-agent reinforcement learning but is largely neglected in state-of-the-art research due to a strong focus on state-based centralized training for decentralized execution (CTDE) and benchmarks that lack sufficient stochasticity like StarCraft Multi-Agent Challenge (SMAC). In this paper, we propose Attention-based Embeddings of Recurrence In multi-Agent Learning (AERIAL) to approximate value functions under stochastic partial observability. AERIAL replaces the true state with a learned representation of multi-agent recurrence, considering more accurate information about decentralized agent decisions than state-based CTDE. We then introduce MessySMAC, a modified version of SMAC with stochastic observations and higher variance in initial states, to provide a more general and configurable benchmark regarding stochastic partial observability. We evaluate AERIAL in Dec-Tiger as well as in a variety of SMAC and MessySMAC maps, and compare the results with state-based CTDE. Furthermore, we evaluate the robustness of AERIAL and state-based CTDE against various stochasticity configurations in MessySMAC.

The safe application of reinforcement learning (RL) requires generalization from limited training data to unseen scenarios. Yet, fulfilling tasks under changing circumstances is a key challenge in RL. Current state-of-the-art approaches for generalization apply data augmentation techniques to increase the diversity of training data. Even though this prevents overfitting to the training environment(s), it hinders policy optimization. Crafting a suitable observation, only containing crucial information, has been shown to be a challenging task itself. To improve data efficiency and generalization capabilities, we propose Compact Reshaped Observation Processing (CROP) to reduce the state information used for policy optimization. By providing only relevant information, overfitting to a specific training layout is precluded and generalization to unseen environments is improved. We formulate three CROPs that can be applied to fully observable observation- and action-spaces and provide methodical foundation. We empirically show the improvements of CROP in a distributionally shifted safety gridworld. We furthermore provide benchmark comparisons to full observability and data-augmentation in two different-sized procedurally generated mazes.

Reinforcement learning has driven impressive advances in machine learning. Simultaneously, quantum-enhanced machine learning algorithms using quantum annealing underlie heavy developments. Recently, a multi-agent reinforcement learning (MARL) architecture combining both paradigms has been proposed. This novel algorithm, which utilizes Quantum Boltzmann Machines (QBMs) for Q-value approximation has outperformed regular deep reinforcement learning in terms of time-steps needed to converge. However, this algorithm was restricted to single-agent and small 2x2 multi-agent grid domains. In this work, we propose an extension to the original concept in order to solve more challenging problems. Similar to classic DQNs, we add an experience replay buffer and use different networks for approximating the target and policy values. The experimental results show that learning becomes more stable and enables agents to find optimal policies in grid-domains with higher complexity. Additionally, we assess how parameter sharing influences the agents behavior in multi-agent domains. Quantum sampling proves to be a promising method for reinforcement learning tasks, but is currently limited by the QPU size and therefore by the size of the input and Boltzmann machine.

Value function factorization (VFF) is a popular approach to cooperative multi-agent reinforcement learning in order to learn local value functions from global rewards. However, state-of-the-art VFF is limited to a handful of agents in most domains. We hypothesize that this is due to the flat factorization scheme, where the VFF operator becomes a performance bottleneck with an increasing number of agents. Therefore, we propose VFF with variable agent sub-teams (VAST). VAST approximates a factorization for sub-teams which can be defined in an arbitrary way and vary over time, e.g., to adapt to different situations. The sub-team values are then linearly decomposed for all sub-team members. Thus, VAST can learn on a more focused and compact input representation of the original VFF operator. We evaluate VAST in three multi-agent domains and show that VAST can significantly outperform state-of-the-art VFF, when the number of agents is sufficiently large.