Entangled N-photon states for fair and optimal social decision making

Conflict-free joint decision by lag and zero-lag synchronization in laser network

With the end of Moore's Law and the increasing demand for computing, photonic accelerators are garnering considerable attention. This is due to the physical characteristics of light, such as high bandwidth and multiplicity, and the various synchronization phenomena that emerge in the realm of laser physics. These factors come into play as computer performance approaches its limits. In this study, we explore the application of a laser network, acting as a photonic accelerator, to the competitive multi-armed bandit problem. In this context, conflict avoidance is key to maximizing environmental rewards. We experimentally demonstrate cooperative decision-making using zero-lag and lag synchronization within a network of four semiconductor lasers. Lag synchronization of chaos realizes effective decision-making and zero-lag synchronization is responsible for the realization of the collision avoidance function. We experimentally verified a low collision rate and high reward in a fundamental 2-player, 2-slot scenario, and showed the scalability of this system. This system architecture opens up new possibilities for intelligent functionalities in laser dynamics.

Decision making for large-scale multi-armed bandit problems using bias control of chaotic temporal waveforms in semiconductor lasers

Decision making using photonic technologies has been intensively researched for solving the multi-armed bandit problem, which is fundamental to reinforcement learning. However, these technologies are yet to be extended to large-scale multi-armed bandit problems. In this study, we conduct a numerical investigation of decision making to solve large-scale multi-armed bandit problems by controlling the biases of chaotic temporal waveforms generated in semiconductor lasers with optical feedback. We generate chaotic temporal waveforms using the semiconductor lasers, and each waveform is assigned to a slot machine (or choice) in the multi-armed bandit problem. The biases in the amplitudes of the chaotic waveforms are adjusted based on rewards using the tug-of-war method. Subsequently, the slot machine that yields the maximum-amplitude chaotic temporal waveform with bias is selected. The scaling properties of the correct decision-making process are examined by increasing the number of slot machines to 1024, and the scaling exponent of the power-law distribution is 0.97. We demonstrate that the proposed method outperforms existing software algorithms in terms of the scaling exponent. This result paves the way for photonic decision making in large-scale multi-armed bandit problems using photonic accelerators.

Conflict-free collective stochastic decision making by orbital angular momentum of photons through quantum interference

In recent cross-disciplinary studies involving both optics and computing, single-photon-based decision-making has been demonstrated by utilizing the wave-particle duality of light to solve multi-armed bandit problems. Furthermore, entangled-photon-based decision-making has managed to solve a competitive multi-armed bandit problem in such a way that conflicts of decisions among players are avoided while ensuring equality. However, as these studies are based on the polarization of light, the number of available choices is limited to two, corresponding to two orthogonal polarization states. Here we propose a scalable principle to solve competitive decision-making situations by using the orbital angular momentum of photons based on its high dimensionality, which theoretically allows an unlimited number of arms. Moreover, by extending the Hong-Ou-Mandel effect to more than two states, we theoretically establish an experimental configuration able to generate multi-photon states with orbital angular momentum and conditions that provide conflict-free selections at every turn. We numerically examine total rewards regarding three-armed bandit problems, for which the proposed strategy accomplishes almost the theoretical maximum, which is greater than a conventional mixed strategy intending to realize Nash equilibrium. This is thanks to the quantum interference effect that achieves no-conflict selections, even in the exploring phase to find the best arms.

Entangled and correlated photon mixed strategy for social decision making

Collective decision making is important for maximizing total benefits while preserving equality among individuals in the competitive multi-armed bandit (CMAB) problem, wherein multiple players try to gain higher rewards from multiple slot machines. The CMAB problem represents an essential aspect of applications such as resource management in social infrastructure. In a previous study, we theoretically and experimentally demonstrated that entangled photons can physically resolve the difficulty of the CMAB problem. This decision-making strategy completely avoids decision conflicts while ensuring equality. However, decision conflicts can sometimes be beneficial if they yield greater rewards than non-conflicting decisions, indicating that greedy actions may provide positive effects depending on the given environment. In this study, we demonstrate a mixed strategy of entangled- and correlated-photon-based decision-making so that total rewards can be enhanced when compared to the entangled-photon-only decision strategy. We show that an optimal mixture of entangled- and correlated-photon-based strategies exists depending on the dynamics of the reward environment as well as the difficulty of the given problem. This study paves the way for utilizing both quantum and classical aspects of photons in a mixed manner for decision making and provides yet another example of the supremacy of mixed strategies known in game theory, especially in evolutionary game theory.