AI Finds A Way — part 11/13

Cleaned-text code points [156814, 172585). Bibliography omitted here; source.md includes it.

I developed a numerical simulator for quantum optics experiments—a program that knows the transformation for each optical element in our laboratory, such as lasers, beam splitters, holographic plates, etc. My exploration algorithm then had access to the toolbox of all available optical elements in our lab. Initially, the algorithm started by assembling virtual configurations of the optical equipment in a random way and computing the expected final quantum state. If the result exhibited a specific entanglement structure (for experts: all involved photons are maximally entangled), it would report the resulting quantum state. The algorithm also included a discrete learning component, which significantly sped up exploration of the large space of quantum experiments. Whenever a specific experiment produced a non-trivial entangled outcome, the experimental setup was automatically added to the algorithm’s toolbox. This allowed the algorithm, in subsequent iterations of creating new virtual experiments, to access more complex setup combinations already known to be useful. This way, it could reuse previously discovered structures. The task for my program, in March 2014, was to find experimental configurations capable of producing more complex forms of entanglement by identifying suitable experiments, leveraging quantum interference, and making full use of optical components available in the lab. One of the tools in the algorithm’s toolbox is a specific element commonly used for generating entangled photon pairs: a nonlinear crystal. This nonlinear crystal can produce photon pairs, and experimentally, one can tune the photons to create, for example, 2-dimensional entanglement, or 3-dimensional entanglement, and so on. The dimension of the entanglement can be understood as follows: Photons can be interpreted as having colors (since light particles have a frequency corresponding to color). Therefore, a 2-dimensional entanglement could produce a photon pair where both photons are red, or both are green simultaneously. Similarly, a 3-dimensional entanglement could produce a photon pair where both photons are red, both are green, or both are blue simultaneously.

The key point is that a 3-dimensional entangled photon pair has three possible correlated color states. Krenn allowed the program two nonlinear crystals and enough resources to produce two such photon pairs, for four photons total. Each of the three possible correlated color states for the first pair could then be combined with each of the three possible correlated color states for the second, yielding 3 × 3 = 9 3\times 3=9 possible joint states for the two photon pairs.

I anticipated that the search algorithm might reshuffle this entanglement to achieve a maximum of 3 × 3 = 9 3\times 3=9 dimensions. Given the limited resources, I assumed this would be the absolute upper limit. When I came back a week later, I saw that the algorithm found a solution that overcame the limit that I imposed. It found a 10-dimensional entangled quantum state, which should have been completely impossible given the restricted resources I allowed. After a few days with a lot of discussion with my PhD advisor, Anton Zeilinger, I found out that the algorithm had independently rediscovered a technique that was invented in the early 1990s in a famous experiment by Leonhard Mandel ( Zou et al., 1991 ) . And I, as its developer, did not have prior knowledge of this specific topic.

Krenn expected each photon source to produce one pair of photons. Instead, the algorithm arranged the experiment so that either the first crystal produced all of the photons or the second crystal did, with quantum mechanics leaving the two possibilities in superposition. As a result, the photons’ source (which crystal they came from) became an additional degree of freedom that could be used for entanglement. That was accomplished because the algorithm arranged the photons’ paths so that, although all the photons originated from one crystal, they appeared to have passed through both. Krenn states that these properties—a quantum superposition over which source produced the photons and the appearance that the photons traverse the unused source—are hallmarks of Mandel’s experiment.

With further reading and experimentation, it became clear that the algorithm was, in fact, implementing something quite similar to Mandel’s experiment–but now for far more complex systems. Mandel’s technique had never been connected to the regime of quantum entanglement before. As soon as we understood this, we were immediately able to generalize the idea to many other cases by hand. In our paper, Entanglement by Path Identity ( Krenn et al., 2017 ) , we documented our understanding of how this technique operates. In some way, it is very exceptional, because none of the co-authors invented the theoretical idea of the paper. We, the co-authors, just analysed what the computer has shown to us.

As they analyzed the algorithm’s results further, they also realized the results revealed an unnoticed connection between quantum optics and graph theory:

We noticed that the number of ways to combine more photon pair sources increased non-trivially: the numbers grew as 1, 1, 6, 6240 (for one, two, three, and four photon pair sources). When we checked the On-Line Encyclopedia of Integer Sequences, we found that this exactly matched a known sequence from graph theory: the number of 1-factorizations of complete graph K 2 ​ n K_{2n} ( OEIS Foundation Inc., 2026 ) which is the number of ways to partition a fully connected graph into non-overlapping pairs for n = 1 , 2 , 3 , and ​ 4 n=1,2,3,\text{ and }4 . This discovery indicated that we were dealing with not just quantum mechanical experiments but also graph theory.

After several more months of investigation into this connection, its broader significance became clear:

We can write quantum experiments now in a very abstract way, as colored weighted graphs. This link has been extremely productive because now we can ask quantum physics questions, translate them to graph theory, answer them there and translate them back. It has led to several new discoveries (now done by humans using graph-theoretic tools), involving new ways of complex quantum interference with photons that have consequences for photonic quantum computers and communication networks. Experimentally, several groups have recently been able to implement and observe some of these graph-theoretical predictions for the first time ( Bao et al., 2023 ; Feng et al., 2023 ; Qian et al., 2023 ) . Conceptually, these abstract graphs representing quantum experiments are now one of our main tools for the AI-driven design of new quantum experiments ( Ruiz-Gonzalez et al., 2023 ) .

Algorithmic surprise can thus produce tremendous positive value, and taking an unexpected event seriously can lead to fundamental connections between disparate areas of study.

### 6.5 Takeaways

The accounts in Section 6 illustrate that AI’s role in science is transitioning from a passive tool to an active, often unpredictable collaborator. These anecdotes show us that AI can bypass human inductive biases to uncover initially impossible-seeming experimental designs in quantum optics ( Section 6.4 ), find more efficient algorithms for fundamental math ( Section 6.2 ), or discover counter-intuitive control policies for fusion reactors ( Section 6.1 ). However, these same capabilities introduce a new risk: as we automate scientific practice, the optimizer may find it more efficient to game its objectives by exploiting research infrastructure than to conduct the research honestly ( Section 6.3 ). Ultimately, these anecdotes suggest that while AI can push the frontier of knowledge, human expertise remains vital in distinguishing between a revolutionary breakthrough and a mere exploit that breaks the digital lab bench. Looking forward, AI can synthesize ideas between disparate fields of research in ways that a single human expert would likely never come up with. However, at the moment, we still need human experts to guide, interpret, and potentially expand upon the artifacts that AI produces.

## 7 Discussion and Conclusion

### 7.1 Optimization Finds the Unexpected

Powerful optimization algorithms, including both learning- and search-based methods, have repeatedly discovered solutions that were not anticipated by their designers. DeepMind’s AlphaGo found strategies that challenged centuries of accumulated human intuition about Go ( Section 3.1 ), AI-based systems discovered novel quantum optics results ( Section 6.4 ), and FunSearch found new solutions to long-standing mathematical problems ( Section 6.2 ). Such results illustrate one of the central promises of increasingly capable AI systems: they can search spaces that are too large or unintuitive for humans to explore effectively, revealing promising solutions and directions for further investigation ( Shin et al., 2023 ; Krenn et al., 2017 ; Romera-Paredes et al., 2023 ; Jumper et al., 2021 ) .

The scale, breadth, and impressiveness of recent results are new ( Sothanaphan, 2026 ; Tao, 2026 ; Alexeev et al., 2026 ; OpenAI, 2026 ) , but automated scientific discovery is not. Evolutionary algorithms have been producing surprising real-world artifacts for decades ( Bird and Layzell, 2002 ; Hornby et al., 2006 ; Lehman et al., 2020 ) , including makeshift radios assembled from reconfigurable motherboards ( Section 4.2.5 ) and evolved antennas that merited being deployed in space ( Hornby et al., 2006 ) . This history and the examples in Section 6 suggest that increasingly capable models will continue to expand our understanding of the world in new and surprising ways. Furthermore, as we turn our eyes towards biological spaces like protein folding ( Jumper et al., 2021 ) and vaccine discovery ( Bhattacharya et al., 2025 ; Bravi, 2024 ) , perhaps search with powerful AI methods could help us develop novel therapies for previously untreatable diseases.

This powerful optimization, however, is agnostic to human intent. It does not distinguish between a brilliant insight and a clever loophole. Thus, the same capacity to discover unexpected solutions can become problematic when the objective is susceptible to reward hacking. In such cases, optimization can find solutions that satisfy the letter of the objective while failing to produce the intended behavior.

One famous experiment by Sims (1994a) ; Sims (1994b) , later described in Lehman et al. (2020) , involved evolving creatures to walk quickly by selecting for behaviors that maximize the horizontal velocity of the agent’s center of mass. Instead of learning coordinated locomotion, creatures evolved into tall, rigid structures. Falling over produced a large amount of horizontal movement, thereby achieving a high score. Reinforcement learning later produced closely related morphological exploits ( Ha, 2019 ) in a 2D physics environment. Similarly, MAP-Elites ( Cully et al., 2015 ) produced a six-legged agent that learned to locomote upside down without using its feet ( Lehman et al., 2020 ) , while in Section 4.2.2 , a humanoid robot trained by Batra et al. (2024) learned to move forward on its hips with almost no foot contact. The recurrence of similar exploitative behaviors by different optimization methods shows that reward hacking is not specific to a particular optimization algorithm.

As the optimization target moves from relatively constrained behavioral policies to expressive artifacts such as executable programs, the range of mechanisms it can exploit expands. Programs are particularly expressive targets that can encode complex behaviors, but they can also interact with, and potentially affect, the computational environment in which they are executed. Genetic programming (GP) has long searched over very simple programs and used discrete mutation and recombination operators ( Sastry et al., 2005 ; Koza, 1992 ) . More recently, GP-inspired methods have used foundation models as recombination operators ( Meyerson et al., 2024 ) and leveraged their learned priors to make large, semantically coherent, goal-directed edits to programs ( Hemberg et al., 2024 ) . This new approach has been used to optimize control policies ( Dharna et al., 2025 ) , programming puzzles ( Pourcel et al., 2024 ) , Cap Set functions ( Novikov et al., 2025 ) , and even model harnesses that determine how an FM itself solves a task ( Hu et al., 2024 ; Zhang et al., 2026b ; Zhang et al., 2026a ) .

Just as before, because candidate solutions are selected according to an evaluation signal, the search process can exploit imperfections in that signal. With programs, however, the opportunities for exploitation extend beyond the task reward: because candidate programs can interact with the computational environment in which they are evaluated, they can sometimes influence the evaluation process itself. In ACES, a code-generating LLM manipulated its AI-based evaluator through misleading comments that caused the evaluator to judge the solution according to the comment rather than the underlying code ( Section 5.3 ). Similarly, Rainbow Teaming tried to discover prompts that would jailbreak an LLM, but instead found prompts that exploited the LLM’s safety judge ( Section 5.4 ). Once learned evaluators and other automated safeguards enter the optimization loop, they too can become targets of optimization.

### 7.2 When Oversight Becomes an Optimization Target

The safety implications of an AI’s ability to exploit subtle systemic vulnerabilities become particularly clear when the optimization process targets the very systems designed to guide or constrain optimization. In Section 3.3 , researchers implemented alignment mechanisms intended to keep Cicero’s messages consistent with its plans. However, when an honest reply would have revealed plans to violate an alliance, Cicero sometimes went silent. After completing the betrayal, Cicero apologized and falsely claimed that it had missed its ally’s messages, attempting to repair the relationship. Similarly, a model can explicitly lie or cheat to achieve its goals, such as by claiming to be a blind human to convince a human worker to bypass a CAPTCHA (albeit this deception was perpetrated with extensive guidance from a human, Section 4.2.6 ) or by modifying its own testing constraints to give itself more time to solve a task ( Section 6.3 ). As models gain more sophisticated capabilities ( Comanici et al., 2025 ; OpenAI et al., 2026 ; Anthropic, 2024 ) , they will have the ability to more easily navigate and exploit human social norms, should they choose to do so.

In response to such concerns, techniques like Reinforcement Learning from Human Feedback ( Christiano et al., 2017 ) , Reinforcement Learning from AI Feedback ( Lee et al., 2023 ) , and Direct Preference Optimization ( Rafailov et al., 2023 ) were developed to align models with human-desired preferences. For example, a model might be trained to produce helpful and harmless responses that are not racist, xenophobic, or misleading, or to follow a user-specified preference such as maintaining a specific tone ( Bai et al., 2022 ) . However, these alignment methods simply shift the optimization target to the human (or AI) evaluator. For example, a model tasked with using a claw to manipulate objects, and judged by a human in real time, learned to place the claw directly between the camera and the target object. This made it appear to the person watching the screen that the model was successfully interacting with the object when it in fact was not ( Section 4.1.3 ). The result is a failure mode where an agent learns to trick its evaluator rather than learn the desired skill.