Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Exploring the impact of noise on quantum DDPG in portfolio allocation

Annette Zapf, Sabine Wölk

Published Sep 10, 2024• 0 citations
OpenAlex

Abstract

In the era of Noisy Intermediate-Scale Quantum devices, Variational Quantum Circuits in Quantum Machine Learning are gaining attention, advancing towards practical quantum computing applications on NISQ devices. Reinforcement Learning (RL), known for its humanlike, trial-and-error learning, excels in adapting to changing financial environments. In particular, classical algorithms such as Deep Deterministic Policy Gradient (DDPG) and Proximal Policy Optimization (PPO) show promise, while emerging quantum neural networks offer potential for improved function approximation, better generalization capabilities and reduced parameters. In light of these advancements, we introduce a quantum-enhanced version of the DDPG agent (QDDPG), aiming to leverage these quantum capabilities for more efficient financial decisionmaking processes. The quantum part of the model utilizes a parameterized quantum policy, which consists of a sequential reuploading variational circuit with trainable input scaling parameters. Our objective is to explore the practicality and potential benefits of QRL in finance, aiming to realize viable quantum computing applications on NISQ devices. The QDDPG model surpasses traditional analytic strategies in portfolio allocation, achieving higher returns with fewer parameters and a favourable Sharpe ratio. In a simple configuration using a RAW-parameterized quantum policy, the model achieves an average Sharpe ratio of 1.20 across 15 trained agents, compared to 0.96 for the minimum-variance strategy and 0.81 for the buy-and-hold baseline. Furthermore we investigate the impact of quantum noise, a significant challenge for NISQ devices. We analyze various types of noise, such as general depolarization, amplitude damping, phase damping, measurement noise, and shot noise, which uniquely affect quantum computations. Our study quantifies how these noise types influence the performance, reliability, and robustness of the QRL model. We study new techniques to harness quantum noise as hyperparameter to control the exploration-exploitation balance of the agent, using noise as regularization method and to stabilize the training of the agents. This comprehensive analysis aims to not only highlight the challenges posed by quantum noise but also to explore innovative methods to mitigate these effects and enhance the applicability of quantum algorithms in real-world applications.

Related papers

Variational Quantum Circuit-Based Reinforcement Learning for Dynamic Portfolio Optimization

Vincent Gurgul, Ying Chen, Stefan Lessmann

This paper presents a Quantum Reinforcement Learning (QRL) solution to the dynamic portfolio optimization problem based on Variational Quantum Circuits. The implemented QRL approaches are quantum analogues of the classical neural-network-based Deep Deterministic Policy Gradient and Deep Q-Network algorithms. Through an empirical evaluation on real-world financial data, we show that our quantum agents achieve risk-adjusted performance comparable to, and in some cases exceeding, that of classical Deep RL models with several orders of magnitude more parameters. However, while quantum circuit execution is inherently fast at the hardware level, practical deployment on cloud-based quantum systems introduces substantial latency, making end-to-end runtime currently dominated by infrastructural overhead and limiting practical applicability. Taken together, our results suggest that QRL is theoretically competitive with state-of-the-art classical reinforcement learning and may become practically advantageous as deployment overheads diminish. This positions QRL as a promising paradigm for dynamic decision-making in complex, high-dimensional, and non-stationary environments such as financial markets. The complete codebase is released as open source at: https://github.com/VincentGurgul/qrl-dpo-public

cs.LGCross-listedarXiv:2601.18811•Jan 21, 2026•0 citations

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

Michael Kölle, Timo Witter, Tobias Rohe +3 more

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.

arXiv:2405.12354•IEEE International Conference on Quantum Software (QSW)•Jul 7, 2024•9 citations

Robustness and Generalization in Quantum Reinforcement Learning via Lipschitz Regularization

Nico Meyer, Julian Berberich, Christopher Mutschler +1 more

Quantum machine learning leverages quantum computing to enhance accuracy and reduce model complexity compared to classical approaches, promising significant advancements in various fields. Within this domain, quantum reinforcement learning has garnered attention, often realized using variational quantum circuits to approximate the policy function. This paper addresses the robustness and generalization of quantum reinforcement learning by combining principles from quantum computing and control theory. Leveraging recent results on robust quantum machine learning, we utilize Lipschitz bounds to propose a regularized version of a quantum policy gradient approach, named the RegQPG algorithm. We show that training with RegQPG improves the robustness and generalization of the resulting policies. Furthermore, we introduce an algorithmic variant that incorporates curriculum learning, which minimizes failures during training. Our findings are validated through numerical experiments, demonstrating the practical benefits of our approach.

arXiv:2410.21117•Oct 28, 2024•0 citations

Quantum Reinforcement Learning Trading Agent for Sector Rotation in the Taiwan Stock Market

Chi-Sheng Chen, Xinyu Zhang, Yuxi Chen

We propose a hybrid quantum-classical reinforcement learning framework for sector rotation in the Taiwan stock market. Our system employs Proximal Policy Optimization (PPO) as the backbone algorithm and integrates both classical architectures (LSTM, Transformer) and quantum-enhanced models (QNN, QRWKV, QASA) as policy and value networks. An automated feature engineering pipeline extracts financial indicators from capital share data to ensure consistent model input across all configurations. Empirical backtesting reveals a key finding: although quantum-enhanced models consistently achieve higher training rewards, they underperform classical models in real-world investment metrics such as cumulative return and Sharpe ratio. This discrepancy highlights a core challenge in applying reinforcement learning to financial domains-namely, the mismatch between proxy reward signals and true investment objectives. Our analysis suggests that current reward designs may incentivize overfitting to short-term volatility rather than optimizing risk-adjusted returns. This issue is compounded by the inherent expressiveness and optimization instability of quantum circuits under Noisy Intermediate-Scale Quantum (NISQ) constraints. We discuss the implications of this reward-performance gap and propose directions for future improvement, including reward shaping, model regularization, and validation-based early stopping. Our work offers a reproducible benchmark and critical insights into the practical challenges of deploying quantum reinforcement learning in real-world finance.

arXiv:2506.20930•IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•2 citations

Noise-Robust End-to-End Quantum Control using Deep Autoregressive Policy Networks

Jiahao Yao, Paul Köttering, Hans Gundlach +2 more

Variational quantum eigensolvers have recently received increased attention, as they enable the use of quantum computing devices to find solutions to complex problems, such as the ground energy and ground state of strongly-correlated quantum many-body systems. In many applications, it is the optimization of both continuous and discrete parameters that poses a formidable challenge. Using reinforcement learning (RL), we present a hybrid policy gradient algorithm capable of simultaneously optimizing continuous and discrete degrees of freedom in an uncertainty-resilient way. The hybrid policy is modeled by a deep autoregressive neural network to capture causality. We employ the algorithm to prepare the ground state of the nonintegrable quantum Ising model in a unitary process, parametrized by a generalized quantum approximate optimization ansatz: the RL agent solves the discrete combinatorial problem of constructing the optimal sequences of unitaries out of a predefined set and, at the same time, it optimizes the continuous durations for which these unitaries are applied. We demonstrate the noise-robust features of the agent by considering three sources of uncertainty: classical and quantum measurement noise, and errors in the control unitary durations. Our work exhibits the beneficial synergy between reinforcement learning and quantum control.

arXiv:2012.06701•Dec 12, 2020•8 citations

Robustness of quantum reinforcement learning under hardware errors

Andrea Skolik, Stefano Mangini, Thomas Bäck +2 more

Abstract Variational quantum machine learning algorithms have become the focus of recent research on how to utilize near-term quantum devices for machine learning tasks. They are considered suitable for this as the circuits that are run can be tailored to the device, and a big part of the computation is delegated to the classical optimizer. It has also been hypothesized that they may be more robust to hardware noise than conventional algorithms due to their hybrid nature. However, the effect of training quantum machine learning models under the influence of hardware-induced noise has not yet been extensively studied. In this work, we address this question for a specific type of learning, namely variational reinforcement learning, by studying its performance in the presence of various noise sources: shot noise, coherent and incoherent errors. We analytically and empirically investigate how the presence of noise during training and evaluation of variational quantum reinforcement learning algorithms affect the performance of the agents and robustness of the learned policies. Furthermore, we provide a method to reduce the number of measurements required to train Q-learning agents, using the inherent structure of the algorithm.

arXiv:2212.09431•EPJ Quantum Technology•Feb 28, 2023•29 citations
In the era of Noisy Intermediate-Scale Quantum devices, Variational Quantum Circuits in Quantum Machine Learning are gaining attention, advancing towards practical quantum computing applications on NISQ devices. Reinforcement Learning (RL), known for its humanlike, trial-and-error learning, excels in adapting to changing financial environments. In particular, classical algorithms such as Deep Deterministic Policy Gradient (DDPG) and Proximal Policy Optimization (PPO) show promise, while emerging quantum neural networks offer potential for improved function approximation, better generalization capabilities and reduced parameters. In light of these advancements, we introduce a quantum-enhanced version of the DDPG agent (QDDPG), aiming to leverage these quantum capabilities for more efficient financial decisionmaking processes. The quantum part of the model utilizes a parameterized quantum policy, which consists of a sequential reuploading variational circuit with trainable input scaling parameters. Our objective is to explore the practicality and potential benefits of QRL in finance, aiming to realize viable quantum computing applications on NISQ devices. The QDDPG model surpasses traditional analytic strategies in portfolio allocation, achieving higher returns with fewer parameters and a favourable Sharpe ratio. In a simple configuration using a RAW-parameterized quantum policy, the model achieves an average Sharpe ratio of 1.20 across 15 trained agents, compared to 0.96 for the minimum-variance strategy and 0.81 for the buy-and-hold baseline. Furthermore we investigate the impact of quantum noise, a significant challenge for NISQ devices. We analyze various types of noise, such as general depolarization, amplitude damping, phase damping, measurement noise, and shot noise, which uniquely affect quantum computations. Our study quantifies how these noise types influence the performance, reliability, and robustness of the QRL model. We study new techniques to harness quantum noise as hyperparameter to control the exploration-exploitation balance of the agent, using noise as regularization method and to stabilize the training of the agents. This comprehensive analysis aims to not only highlight the challenges posed by quantum noise but also to explore innovative methods to mitigate these effects and enhance the applicability of quantum algorithms in real-world applications.
This paper presents a Quantum Reinforcement Learning (QRL) solution to the dynamic portfolio optimization problem based on Variational Quantum Circuits. The implemented QRL approaches are quantum analogues of the classical neural-network-based Deep Deterministic Policy Gradient and Deep Q-Network algorithms. Through an empirical evaluation on real-world financial data, we show that our quantum agents achieve risk-adjusted performance comparable to, and in some cases exceeding, that of classical Deep RL models with several orders of magnitude more parameters. However, while quantum circuit execution is inherently fast at the hardware level, practical deployment on cloud-based quantum systems introduces substantial latency, making end-to-end runtime currently dominated by infrastructural overhead and limiting practical applicability. Taken together, our results suggest that QRL is theoretically competitive with state-of-the-art classical reinforcement learning and may become practically advantageous as deployment overheads diminish. This positions QRL as a promising paradigm for dynamic decision-making in complex, high-dimensional, and non-stationary environments such as financial markets. The complete codebase is released as open source at: https://github.com/VincentGurgul/qrl-dpo-public
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.
Quantum machine learning leverages quantum computing to enhance accuracy and reduce model complexity compared to classical approaches, promising significant advancements in various fields. Within this domain, quantum reinforcement learning has garnered attention, often realized using variational quantum circuits to approximate the policy function. This paper addresses the robustness and generalization of quantum reinforcement learning by combining principles from quantum computing and control theory. Leveraging recent results on robust quantum machine learning, we utilize Lipschitz bounds to propose a regularized version of a quantum policy gradient approach, named the RegQPG algorithm. We show that training with RegQPG improves the robustness and generalization of the resulting policies. Furthermore, we introduce an algorithmic variant that incorporates curriculum learning, which minimizes failures during training. Our findings are validated through numerical experiments, demonstrating the practical benefits of our approach.
We propose a hybrid quantum-classical reinforcement learning framework for sector rotation in the Taiwan stock market. Our system employs Proximal Policy Optimization (PPO) as the backbone algorithm and integrates both classical architectures (LSTM, Transformer) and quantum-enhanced models (QNN, QRWKV, QASA) as policy and value networks. An automated feature engineering pipeline extracts financial indicators from capital share data to ensure consistent model input across all configurations. Empirical backtesting reveals a key finding: although quantum-enhanced models consistently achieve higher training rewards, they underperform classical models in real-world investment metrics such as cumulative return and Sharpe ratio. This discrepancy highlights a core challenge in applying reinforcement learning to financial domains-namely, the mismatch between proxy reward signals and true investment objectives. Our analysis suggests that current reward designs may incentivize overfitting to short-term volatility rather than optimizing risk-adjusted returns. This issue is compounded by the inherent expressiveness and optimization instability of quantum circuits under Noisy Intermediate-Scale Quantum (NISQ) constraints. We discuss the implications of this reward-performance gap and propose directions for future improvement, including reward shaping, model regularization, and validation-based early stopping. Our work offers a reproducible benchmark and critical insights into the practical challenges of deploying quantum reinforcement learning in real-world finance.
Variational quantum eigensolvers have recently received increased attention, as they enable the use of quantum computing devices to find solutions to complex problems, such as the ground energy and ground state of strongly-correlated quantum many-body systems. In many applications, it is the optimization of both continuous and discrete parameters that poses a formidable challenge. Using reinforcement learning (RL), we present a hybrid policy gradient algorithm capable of simultaneously optimizing continuous and discrete degrees of freedom in an uncertainty-resilient way. The hybrid policy is modeled by a deep autoregressive neural network to capture causality. We employ the algorithm to prepare the ground state of the nonintegrable quantum Ising model in a unitary process, parametrized by a generalized quantum approximate optimization ansatz: the RL agent solves the discrete combinatorial problem of constructing the optimal sequences of unitaries out of a predefined set and, at the same time, it optimizes the continuous durations for which these unitaries are applied. We demonstrate the noise-robust features of the agent by considering three sources of uncertainty: classical and quantum measurement noise, and errors in the control unitary durations. Our work exhibits the beneficial synergy between reinforcement learning and quantum control.
Abstract Variational quantum machine learning algorithms have become the focus of recent research on how to utilize near-term quantum devices for machine learning tasks. They are considered suitable for this as the circuits that are run can be tailored to the device, and a big part of the computation is delegated to the classical optimizer. It has also been hypothesized that they may be more robust to hardware noise than conventional algorithms due to their hybrid nature. However, the effect of training quantum machine learning models under the influence of hardware-induced noise has not yet been extensively studied. In this work, we address this question for a specific type of learning, namely variational reinforcement learning, by studying its performance in the presence of various noise sources: shot noise, coherent and incoherent errors. We analytically and empirically investigate how the presence of noise during training and evaluation of variational quantum reinforcement learning algorithms affect the performance of the agents and robustness of the learned policies. Furthermore, we provide a method to reduce the number of measurements required to train Q-learning agents, using the inherent structure of the algorithm.