Flower algorithm

When learning a strategy in a game, we barely focus on what’s possible (that’d be done outside of the game), but rather learn gradually context manifolds given (more common) game interactions. With a small, but important exception —surprise. It can break local context-building symmetry, and lead to aggressive re-exploration of what’s less common.

Before a concept gets discovered, and then implemented, aggressive re-exploration feels like a short-lived cancer. Only after a while can the concept solidify.

Now, the concept of surprise reminds me of stringent conditions in non-abelian anyon creation. It’s hard to create such an environment. The complexity (more complex braiding statistics compared to Abelian) makes the conditions required for the non-Abelian existence more stringent and harder to achieve. On the other hand, perhaps certain states or behaviors in non-abelian anyon systems could be (similarly) undecidable. The combination of the two could mean that:

• there could exist configurations of anyons whose future states could be predicted or determined by any (does not have to be any; it can be a specific class, or layer) algorithm,

• there could exist a quite-general quantum algorithm for learning by drawing a line through surprises and hide-to-find concepts.

Let’s go back to surprise. A highly speculative +EV line in a game implies that a concept must be missing in the context. But since the concept is extremely hard to find, it cannot be reached by regular cancer. It also has to offer some future learning robustness — otherwise, it being a surprise would not suffice.

(Feel free to skip this insight) Certain concepts, when not present in the context, can make it close to impossible to win a game. That’s why meta concepts — I call them gems — are so important. They allow you to quickly learn higher-order concepts.

Now think non-Abelian anyons are enumeration probes. They already have distinctive signatures in terms of braiding and fusion rules, and perhaps could also provide further insight into enumerating topological orders.

Looking for topological orders involves identifying systems where the ground state degeneracy is robust against local perturbations and where excitations exhibit topologically protected properties. Non-Abelian topological orders are even trickier. That makes me think of hardness-measuring gadgets.

Imagine a very special braiding through a maze with a number of surprises where the path to the exit could only be found if one could discover some really hard to find concepts in the most efficient way (in order to deal with the surprises).

That’d be a different way of consuming information. A special way — the one that would remind growing a flower from a seed. Our default way is closer to using building blocks (or creating low-level building blocks in math, or using experiment-driven blocks in physics).

Now imagine that flower algorithm.

What if it could be informed by hardness-measuring gadgets so that it could find locally tough-to-find concepts (most likely by actively interacting with the game while preserving the global consistency and protecting the system from long-term local perturbations). Hardness-measuring gadgets could perhaps leverage the braiding and fusion rules of non-abelian anyons to create configurations that are computationally intractable or undecidable?

And now to the main point.

Problem:

Define a quantum algorithm that by using hardness-measuring gadgets (or other measures) would aggressively find deep concepts before first enumerating too many low-order concepts.

Verification:

• Could that algorithm efficiently discover topological orders?

• Could that algorithm find all prime numbers without checking their divisors?