Learning Functions Implies Difficulty with Factoring 2048-Bit RSA Moduli
Researchers have shown that efficiently predicting energy levels of quantum systems on a classical computer is at least as hard as factoring large RSA moduli, including 2048-bit keys. The result is a formal reduction: a fast classical algorithm for this prediction task would imply a fast classical factoring algorithm. This places the simulation task among problems whose classical hardness is tied to widely used cryptographic assumptions.
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What this could mean
- 0–2 yearsPlausible
This reduction could enable a new class of near-term quantum advantage experiments based on energy prediction, where the classical hardness is directly inherited from RSA factoring and the advantage claim rests only on the assumed hardness of factoring.
If experimenters can encode a 2048-bit RSA challenge into a quantum system's energy-prediction instance, then a quantum device solving that instance faster than classical computers would demonstrate advantage under a standard cryptographic assumption, while verification could use the factoring solution.
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