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arXiv:2608.19779

An Irreducible Quantum Advantage in Aligning World Models with Reality

Josep Lumbreras, Hailan Ma, Jayne Thompson, Mile Gu

quant-phcs.AIcs.LGSubmitted Aug 20, 2026• Announced Aug 21, 2026• 0 citations
v1 · Aug 20, 2026v2 · Oct 2, 2026
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Abstract

World models provide digital simulacra of the true world, allowing agents to be trained and tested before costly real-world deployment. At each time step, they receive an action and generate an observation and reward matching the statistics of the true world. In complex environments where present outcomes depend on events far in the past, this requires memory. One might expect that, by increasing memory, we can always build a model accurately enough to align the optimal agent policies of the real and virtual worlds. We show that this is false for classical world models, even when the true world itself is classical. We construct true worlds for which every finite classical model fails along the same possible trajectory: it either loses the ability to distinguish actions when the true world clearly prefers one, or repeatedly assigns the highest expected reward to suboptimal actions. Its expected-reward estimates also retain a nonvanishing average error. In contrast, each such true world admits a quantum world model using a single qutrit that reproduces it exactly: its reward estimates and preferred actions always match those of the true world, ensuring that the optimal policies of the real and virtual worlds remain perfectly aligned.

Comments
31 pages, 4 figures

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World models provide digital simulacra of the true world, allowing agents to be trained and tested before costly real-world deployment. At each time step, they receive an action and generate an observation and reward matching the statistics of the true world. In complex environments where present outcomes depend on events far in the past, this requires memory. One might expect that, by increasing memory, we can always build a model accurately enough to align the optimal agent policies of the real and virtual worlds. We show that this is false for classical world models, even when the true world itself is classical. We construct true worlds for which every finite classical model fails along the same possible trajectory: it either loses the ability to distinguish actions when the true world clearly prefers one, or repeatedly assigns the highest expected reward to suboptimal actions. Its expected-reward estimates also retain a nonvanishing average error. In contrast, each such true world admits a quantum world model using a single qutrit that reproduces it exactly: its reward estimates and preferred actions always match those of the true world, ensuring that the optimal policies of the real and virtual worlds remain perfectly aligned.
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Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an optimal policy for a γγγ-discounted Markov decision process (MDP). For such an MDP, we design quantum algorithms that approximate an optimal policy (π∗π^*π∗), the optimal value function (v∗v^*v∗), and the optimal QQQ-function (q∗q^*q∗), assuming the algorithms can access samples from the environment in quantum superposition. This assumption is justified whenever there exists a simulator for the environment; for example, if the environment is a video game or some other program. Our quantum algorithms, inspired by value iteration, achieve quadratic speedups over the best-possible classical sample complexities in the approximation accuracy (εεε) and two main parameters of the MDP: the effective time horizon (11−γ\frac{1}{1-γ}1−γ1​) and the size of the action space (AAA). Moreover, we show that our quantum algorithm for computing q∗q^*q∗ is optimal by proving a matching quantum lower bound.
Whether winning blackjack or navigating busy streets, achieving desired outcomes requires agents to execute adaptive strategies, strategies where actions depend contextually on past events. In complexity science, this motivates memory as an operational quantifier of complexity: given two strategies, the more complex one demands the agent to track more about the past. Here, we show that conclusions about complexity fundamentally depend on whether agents can process and store quantum information. Thus, while classical agents might find Strategy A more complex to execute than Strategy B, quantum agents can reach the opposite conclusion. We derive sufficient conditions for such contradictory conclusions and illustrate the phenomenon across multiple scenarios. As a byproduct, our results yield an information-theoretic lower bound on the minimal memory required by any agent - classical or quantum - to execute a given strategy.
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