The Hardness of Learning Quantum Circuits and its Cryptographic Applications

• URL: http://arxiv.org/abs/2504.15343v1
• Date: Mon, 21 Apr 2025 18:00:03 GMT
• Title: The Hardness of Learning Quantum Circuits and its Cryptographic Applications
• Authors: Bill Fefferman, Soumik Ghosh, Makrand Sinha, Henry Yuen,
• Abstract summary: 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.<n>We construct secure one-way state generators (OWSGs), digital signature schemes, quantum bit commitments, and private key encryption schemes.
• Score: 1.2116854758481395
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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