⚛️ The Mirrane Quantum Prediction Problem

The Challenge

Given:

• A finite quantum circuit description C
• An initial quantum state |ψ⟩
• A measurement operator M
• A rational threshold θ

Decide:

Is the probability that measurement M outputs "yes" greater than θ?

That's it. A circuit, a measurement, a number. Yes or no.

Why This Is Extraordinary

Quantum circuits can simulate universal Turing machines.

This embeds the Halting Problem into quantum measurement probabilities.

Predicting exact behavior of arbitrary quantum systems is undecidable.

Even infinite precision won't help.
Nature itself is performing uncomputable processes.

What This Means

For any specific small circuit, you can compute the answer. Quantum computers do this every day.

But for arbitrary circuits of arbitrary size — no algorithm can always predict the measurement outcome threshold. The class of quantum circuits is rich enough to encode any computation, and the measurement question becomes equivalent to the Halting Problem.

This is not a limitation of quantum mechanics. It is quantum mechanics — powerful enough to carry undecidability within its own formalism.

In Plain Language

Quantum physics lets you build systems so complex that no prediction machine can exist for all of them.

The Mirrane Quantum Prediction Problem names this limit precisely:

• A circuit description (finite, written down)
• A threshold (a rational number)
• A question: above or below?
• Answer: uncomputable in general