The Hardness of Learning Quantum Circuits and its Cryptographic Applications

We show that concrete hardness assumptions about learning or cloning the output state of a random quantum circuit can be used as the foundation for secure quantum cryptography. In particular, under these assumptions we construct secure one-way state generators (OWSGs), digital signature schemes, quantum bit commitments, and private key encryption schemes. We also discuss evidence for these hardness assumptions by analyzing the best-known quantum learning algorithms, as well as proving black-box lower bounds for cloning and learning given state preparation oracles.Our random circuit-based constructions provide concrete instantiations of quantum cryptographic primitives whose security do not depend on the existence of one-way functions. The use of random circuits in our constructions also opens the door to NISQ-friendly quantum cryptography. We discuss noise tolerant versions of our OWSG and digital signature constructions which can potentially be implementable on noisy quantum computers connected by a quantum network. On the other hand, they are still secure against noiseless quantum adversaries, raising the intriguing possibility of a useful implementation of an end-to-end cryptographic protocol on near-term quantum computers. Finally, our explorations suggest that the rich interconnections between learning theory and cryptography in classical theoretical computer science also extend to the quantum setting.

@article{fefferman2025_2504.15343,
  title={ The Hardness of Learning Quantum Circuits and its Cryptographic Applications },
  author={ Bill Fefferman and Soumik Ghosh and Makrand Sinha and Henry Yuen },
  journal={arXiv preprint arXiv:2504.15343},
  year={ 2025 }
}