Quantum mechanics provides cryptographic primitives whose security is grounded in hardness assumptions independent of those underlying classical cryptography. However, existing proposals require low-noise quantum communication and long-lived quantum memory, capabilities which remain challenging to realize in practice. In this work, we introduce a quantum digital signature scheme that operates with only classical communication, using the classical shadows of states produced by random circuits as public keys. We provide theoretical and numerical evidence supporting the conjectured hardness of learning the private key (the circuit) from the public key (the shadow). A key technical ingredient enabling our scheme is an improved state-certification primitive that achieves higher noise tolerance and lower sample complexity than prior methods. We realize this certification by designing a high-rate error-detecting code tailored to our random-circuit ensemble and experimentally generating shadows for 32-qubit states using circuits with $\geq 80$ logical ($\geq 582$ physical) two-qubit gates, attaining 0.90 $\pm$ 0.01 fidelity. With increased number of measurement samples, our hardware-demonstrated primitives realize a proof-of-principle quantum digital signature, demonstrating the near-term feasibility of our scheme.

翻译：量子力学提供了密码学原语，其安全性基于与经典密码学不同的硬度假设。然而，现有方案需要低噪声量子通信和长寿命量子存储器，这些能力在实践中仍具挑战性。本工作提出一种仅需经典通信的量子数字签名方案，该方案使用随机电路产生的态之经典影子作为公钥。我们提供了理论和数值证据，支持从公钥（影子）学习私钥（电路）的推测硬度。实现本方案的关键技术要素是一种改进的态认证原语，其相比先前方法实现了更高的噪声容忍度和更低的样本复杂度。我们通过设计一种针对随机电路系综定制的高码率检错码来实现此认证，并实验生成了32量子比特态的经典影子，所用电路包含$\geq 80$个逻辑（$\geq 582$个物理）双量子比特门，保真度达0.90 $\pm$ 0.01。通过增加测量样本数量，我们在硬件上演示的原语实现了原理验证的量子数字签名，证明了本方案的近期可行性。