Quantum AIXI: Universal Intelligence via Quantum Information

AIXI is a widely studied model of artificial general intelligence (AGI) based upon principles of induction and reinforcement learning. However, AIXI is fundamentally classical in nature - as are the environments in which it is modelled. Given the universe is quantum mechanical in nature and the exponential overhead required to simulate quantum mechanical systems classically, the question arises as to whether there are quantum mechanical analogues of AIXI. To address this question, we extend the framework to quantum information and present Quantum AIXI (QAIXI). We introduce a model of quantum agent/environment interaction based upon quantum and classical registers and channels, showing how quantum AIXI agents may take both classical and quantum actions. We formulate the key components of AIXI in quantum information terms, extending previous research on quantum Kolmogorov complexity and a QAIXI value function. We discuss conditions and limitations upon quantum Solomonoff induction and show how contextuality fundamentally affects QAIXI models.