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American Journal of Modern Physics

Light as a Quantum Agent: Bridging Path Integrals and Reinforcement Learning

Bhushan Bhoja Poojary

Published Sep 9, 2025• 1 citation
Publisher

Abstract

We propose a novel and interdisciplinary conceptual framework that bridges Feynman’s path integral formulation of quantum mechanics with reinforcement learning (RL) in artificial intelligence. In the path integral approach, a quantum system does not follow a single predetermined trajectory but instead explores all possible paths simultaneously, assigning each a complex amplitude weighted by eiS/h, where S represents the classical action. Constructive and destructive interference across these paths acts as a natural filter, amplifying trajectories of stationary action and suppressing suboptimal ones, thereby leaving paths of least action as the observable outcomes. We argue this process is strongly analogous to a quantum agent evaluating an entire policy space in superposition, where interference effectively encodes a reward mechanism that eliminates non-optimal policies. This perspective not only deepens our understanding of light’s propagation in complex refractive media but also inspires the design of quantum-inspired Reinforcement learning architectures capable of leveraging the intrinsic parallelism of quantum mechanics. Furthermore, the advent of quantum computing, with its inherent properties of superposition, entanglement, and quantum interference, provides a tangible pathway for implementing such algorithms in practice. To illustrate this paradigm, we propose a toy model wherein policies are encoded as quantum states, rewards are mapped to phase shifts, and measurement collapses the superposed state into an optimal policy. The implications of this framework extend beyond algorithmic innovation, offering insights into the possibility that nature itself operates as a quantum learning system, with physical laws emerging from a process akin to reinforcement learning.

DOI
10.11648/j.ajmp.20251405.11

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We propose a novel and interdisciplinary conceptual framework that bridges Feynman’s path integral formulation of quantum mechanics with reinforcement learning (RL) in artificial intelligence. In the path integral approach, a quantum system does not follow a single predetermined trajectory but instead explores all possible paths simultaneously, assigning each a complex amplitude weighted by eiS/h, where S represents the classical action. Constructive and destructive interference across these paths acts as a natural filter, amplifying trajectories of stationary action and suppressing suboptimal ones, thereby leaving paths of least action as the observable outcomes. We argue this process is strongly analogous to a quantum agent evaluating an entire policy space in superposition, where interference effectively encodes a reward mechanism that eliminates non-optimal policies. This perspective not only deepens our understanding of light’s propagation in complex refractive media but also inspires the design of quantum-inspired Reinforcement learning architectures capable of leveraging the intrinsic parallelism of quantum mechanics. Furthermore, the advent of quantum computing, with its inherent properties of superposition, entanglement, and quantum interference, provides a tangible pathway for implementing such algorithms in practice. To illustrate this paradigm, we propose a toy model wherein policies are encoded as quantum states, rewards are mapped to phase shifts, and measurement collapses the superposed state into an optimal policy. The implications of this framework extend beyond algorithmic innovation, offering insights into the possibility that nature itself operates as a quantum learning system, with physical laws emerging from a process akin to reinforcement learning.
This paper investigates the application of quantum-inspired algorithms to the field of reinforcement learning (RL). Traditional RL methods often struggle with exploration challenges and can be computationally expensive, particularly in complex environments. We propose a novel RL algorithm that leverages concepts from quantum mechanics, specifically superposition and entanglement, to address these limitations. The core idea is to represent states, actions, and rewards using quantum-inspired representations, allowing the agent to explore the environment more efficiently and potentially converge to optimal policies faster. This work presents a detailed formulation of the algorithm, including the mathematical framework and key considerations for implementation. The potential benefits of this approach, including improved exploration and reduced computational complexity, are discussed. The algorithm is designed to iteratively refine its policy based on simulated quantum measurements, aiming to minimize the expected return. The exploration strategy is guided by the inherent probabilistic nature of quantum states, leading to a more diverse and potentially faster learning process. Further research is warranted to fully explore the capabilities and limitations of this approach across various RL benchmark problems.
This paper investigates the potential of quantum-inspired algorithms to improve reinforcement learning (RL) policy optimization. Traditional RL methods often struggle with slow convergence and exploration challenges, particularly in complex environments. We propose a novel approach that draws inspiration from quantum mechanics, specifically superposition and entanglement, to address these limitations. Our algorithms aim to exploit superposition to simultaneously evaluate multiple action possibilities and utilize entanglement to model correlations between states, thereby accelerating the learning process. We present a framework for incorporating these concepts into RL, focusing on algorithmic design rather than a direct quantum simulation. The theoretical analysis suggests that our approach could significantly enhance exploration efficiency and, consequently, policy convergence rates. This work represents a direct application of quantum-inspired ideas to RL policy optimization, offering a potentially transformative pathway for developing more efficient and robust RL agents.
This paper investigates the potential of utilizing quantum walks to enhance the optimization of reinforcement learning (RL) policies. Traditional RL algorithms often struggle with exploring complex state spaces efficiently, leading to slow learning rates and suboptimal solutions. We propose a novel approach that leverages the inherent properties of quantum walks – superposition and interference – to accelerate the learning process. Specifically, we represent the RL environment as a graph and perform a quantum walk on this graph. The walk's quantum superposition allows for simultaneous exploration of multiple actions, drastically reducing the time required to converge to an optimal policy. We outline the theoretical framework, detailing the mathematical formulation of the quantum walk and its interaction with the RL environment. The core contribution lies in demonstrating how quantum walk's ability to explore multiple states concurrently can provide a significant advantage over classical approaches in optimizing RL policies. We present a conceptual model and a set of equations describing the process, highlighting the key elements for implementation. The results, while theoretical, demonstrate the feasibility and potential impact of this hybrid quantum-classical approach for tackling complex RL problems.
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Reinforcement learning (RL) faces significant challenges when dealing with environments characterized by delayed rewards and sparse feedback. Traditional RL algorithms often struggle to efficiently learn optimal policies in such scenarios due to the difficulty in associating actions with their eventual consequences. This research proposes a novel approach to RL leveraging quantum-inspired concepts – superposition and entanglement – to improve exploration and exploitation within the state space. The core idea involves designing a neural network architecture where nodes exist in a superposition of states, allowing the agent to concurrently evaluate multiple actions. Furthermore, entangled node interactions are implemented to facilitate the rapid and efficient transfer of information across the network, effectively addressing the problem of delayed rewards. We demonstrate, theoretically and through a conceptual framework, the potential benefits of this approach, highlighting its capacity to improve learning speed and robustness in complex RL environments. The network architecture is defined as follows: Let N=(n1,n2,...,nK)N = (n_1, n_2, ..., n_K)N=(n1​,n2​,...,nK​) represent the neural network, where nin_ini​ denotes the i-th node. Each node nin_ini​ is associated with a state vector si=(si1,si2,...,sid)s_i = (s_{i1}, s_{i2}, ..., s_{id})si​=(si1​,si2​,...,sid​) and an associated potential ViV_iVi​. The superposition state of node nin_ini​ is denoted as ∣ni⟩=αi∣0⟩+βi∣1⟩|n_i\rangle = \alpha_i |0\rangle + \beta_i |1\rangle∣ni​⟩=αi​∣0⟩+βi​∣1⟩, where αi\alpha_iαi​ and βi\beta_iβi​ are complex amplitudes. Entanglement is represented by a correlation function C(ni,nj)C(n_i, n_j)C(ni​,nj​) which quantifies the degree of interconnectedness between nodes nin_ini​ and njn_jnj​. The learning process involves updating the node potentials based on the expected future reward, considering the superposition state and entanglement interactions. The central focus is on the theoretical framework and the design principles, rather than a fully realized experimental implementation.
This paper introduces a quantum framework for addressing reinforcement learning (RL) tasks, grounded in the quantum principles and leveraging a fully quantum model of the classical Markov decision process. By employing quantum concepts and a quantum search algorithm, this work presents the implementation and optimization of the agent-environment interactions entirely within the quantum domain, eliminating reliance on classical computations. Key contributions include the quantum-based state transitions, return calculation, and trajectory search mechanism that utilize quantum principles to demonstrate the realization of RL processes through quantum phenomena. The implementation emphasizes the fundamental role of quantum superposition in enhancing computational efficiency for RL tasks. Results demonstrate the capacity of a quantum model to achieve quantum enhancement in RL, highlighting the potential of fully quantum implementations in decision-making tasks. This work not only underscores the applicability of quantum computing in machine learning but also contributes to the field of quantum reinforcement learning by offering a robust framework for understanding and exploiting quantum computing in RL systems.