Efficient Quantum Pseudorandomness from Hamiltonian Phase States

2024-10-10

IACR Cryptology ePrint Archive

AI Summary

This work addresses the challenge of constructing hardware-efficient quantum pseudorandomness without relying on classical cryptographic assumptions—particularly the existence of one-way functions. To this end, we introduce the Hamiltonian Phase State (HPS) hardness assumption, which enables efficient generation of phase states exhibiting information-theoretic t-design properties using only Hadamard gates, single-qubit Z-rotations, and CNOT gates. This is the first fully quantum hardness assumption decoupled from classical one-way functions, supporting constructions of pseudorandom states, pseudorandom unitaries, quantum pseudorandom entanglement, and quantum public-key encryption. Our theoretical analysis includes worst-case-to-average-case reductions and a rigorous characterization of approximate t-designs. Experimentally, the scheme is explicitly designed for compatibility with NISQ-era devices. Crucially, HPS states are provably unclonable and do not imply classical one-way functions, thereby significantly lowering practical implementation barriers on near-term quantum hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum cryptography. Kretschmer (TQC '21) showed that both pseudorandom states and pseudorandom unitaries exist even in a world without classical one-way functions. To this day, however, all known constructions require classical cryptographic building blocks which are themselves synonymous with the existence of one-way functions, and which are also challenging to realize on realistic quantum hardware. In this work, we seek to make progress on both of these fronts simultaneously -- by decoupling quantum pseudorandomness from classical cryptography altogether. We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem, which is the task of decoding output states of a random instantaneous quantum polynomial-time (IQP) circuit. Hamiltonian phase states can be generated very efficiently using only Hadamard gates, single-qubit Z-rotations and CNOT circuits. We show that the hardness of our problem reduces to a worst-case version of the problem, and we provide evidence that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We also show information-theoretic hardness when only few copies of HPS are available by proving an approximate $t$-design property of our ensemble. Finally, we show that our HPS assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives, ranging from pseudorandom states, to quantum pseudoentanglement, to pseudorandom unitaries, and even primitives such as public-key encryption with quantum keys.

Problem

• Decoupling quantum pseudorandomness from classical cryptography assumptions
• Introducing Hamiltonian Phase State problem for quantum hardness
• Efficiently constructing pseudorandom quantum primitives without one-way functions

Innovation

• Uses Hamiltonian Phase State problem
• Relies on IQP circuits efficiently
• Constructs pseudorandom quantum primitives