quant-phAug 20, 2026

An Irreducible Quantum Advantage in Aligning World Models with Reality

Authors: Josep Lumbreras, Hailan Ma, Jayne Thompson, Mile Gu

Organizations: Centre for Quantum Technologies, Nanyang Technological University, Singapore · Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore · College of Computing and Data Science, Nanyang Technological University, Singapore

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

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.

Figures & tables

Figure 1: Classical and quantum world models . The true world represents reality (a). At each time step, it receives an action ata_{t} and returns an outcome yt+1y_{t+1} that consists of an observation and reward. A world model reproduces this input–output behavior through recurrent internal dynamics, updating its memory from one simulated step to the next. In a classical world model (b), a classical register with a finite number of bits carries the memory, and it evolves under classical stochastic updates. In a quantum world model (c), the memory is encoded in a finite number of qubits and evolves through quantum operations.
Figure 2: The resettable FRDN clock world. The displayed signs illustrate a representative payoff regime: Wait offers a reward +RW+R_{W} if the clock advances but risks a failure cost −CW-C_{W} ; Maintain accepts the known cost −CM-C_{M} of an immediate reset; and Probe also resets, with reward +RP+R_{P} or cost −CP-C_{P} determined by whether the clock would have advanced. The diagram thus contrasts risky continuation under Wait, a certain outcome under Maintain, and an outcome-dependent bet under Probe, creating a nontrivial decision problem.
Figure 3: Conditional Tick probabilities. Probability of one additional Tick after h←t\overleftarrow{h}_{t} for λ=0.4\lambda=0.4 and α=π/2\alpha=\pi/\sqrt{2} . The gray curve is the true-world probability, which the qutrit world model reproduces exactly. The colored curves show the predictions of the fitted classical models with memory dimensions N=5N=5 (blue), N=50N=50 (orange), and N=500N=500 (green). Increasing NN allows the model to reproduce the nonrepeating dependence on the clock age over a larger initial range. At later ages, the predictions approach the finite limiting behavior imposed by finite classical memory.
Figure 4: Cumulative wrong-action fraction under the reward setting in Appendix B.4 . Blue, orange, and green correspond to N=5N=5 (blue), N=50N=50 (orange), and N=500N=500 (green), respectively. The qutrit world model has zero wrong actions for every TT ; its curve coincides with the horizontal axis and is omitted for clarity.
Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Conditional Tick probabilities of different models at system dimension N=100N=100 . Probability of one additional Tick after h←t\overleftarrow{h}_{t} for λ=0.4\lambda=0.4 and α=π/2\alpha=\pi/\sqrt{2} .
Figure 6: Cumulative gaps in predicted conditional probabilities for models of different sizes. (a) Age counter, (b) Rational phase cycle model, and (c) fitted HMM. The red dashed line corresponds to the asymptotic bound κFRDN\kappa_{FRDN} defined in Eq.( 152 ). Please refer to Appendix B.3 ) for detailed information.
Figure 7: Cumulative wrong-action fraction for models of different sizes. (a) Age-counter model, (b) Rational phase cycle model, and (c) fitted HMM.
Figure 8: Mean decision loss of different models with different sizes. (a) Age-counter model, (b) Rational phase cycle model, and (c) fitted HMM.
More in this topic

World Models

World models represent and predict how environments change, helping agents plan, act, and reason about possible futures.

See all 366 papers

Explore similar work

CardsList

  1. Quantum-Structured World Models (QSWMs) for Predictive Latent Dynamics

    Aug 5, 2026Hailong Jiang, Emran Hossain, Feng Yu +3Latent Dynamics ModelingQuantum-Inspired ML

    Youngstown State University, Youngstown, OH, USA · Kent State University · George Washington University

  2. Quantum-JEPA: Quantum Born Priors for Latent-Action JEPA World Models

    Oct 20, 2026Zhiyuan Liu, Sicheng Liu, Haiyu WuQuantum Circuit Born MachinesAction-Conditioned World Models

    Qinous Technology Co., Ltd., Beijing, China · Tsinghua University, Beijing, China · University of Notre Dame, Notre Dame, IN, USA

  3. Q-Learning With World Models

    Aug 17, 2026Perry Dong, Yueru Jia, Chelsea Finn +1RL for RoboticsModel-Based RL

    Stanford University · Peking University