The Hardness of Learning Quantum Circuits and its Cryptographic Applications

2025-04-21

AI Summary

This work addresses the computational hardness of learning and cloning output states of random quantum circuits, proposing it as a quantum-cryptographic security foundation independent of classical one-way functions. Methodologically, it is the first to directly translate this computational unlearnability into security guarantees for multiple quantum cryptographic primitives, while designing NISQ-compatible, noise-resilient constructions that preserve security against ideal quantum adversaries even under approximate implementation. Theoretical tools include modeling of random quantum circuits, quantum black-box lower-bound analysis, complexity theory for quantum state learning/cloning, and noise-tolerant protocol design. Key contributions are: (i) constructions of information-theoretically or computationally secure quantum one-way state generators, digital signatures, quantum bit commitments, and symmetric-key encryption schemes; (ii) tight analyses and rigorous black-box lower bounds for mainstream quantum learning algorithms; and (iii) end-to-end experimental validation of feasibility on noisy quantum hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

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.

Problem

• Study hardness of learning quantum circuits for cryptography
• Construct secure quantum cryptographic primitives without one-way functions
• Explore noise-tolerant quantum cryptography for near-term devices

Innovation

• Random quantum circuits enable secure cryptography
• NISQ-friendly noise-tolerant quantum cryptographic constructions
• Learning theory and cryptography interconnected quantumly