Digital signatures with classical shadows on near-term quantum computers

2026-02-04

AI Summary

This work proposes a quantum-mechanics-based secure digital signature scheme that operates without quantum communication or long-lived quantum memory. The protocol leverages random quantum circuits to generate classical shadows of quantum states as public keys, enabling signature verification solely through classical communication. It is theoretically proven that recovering the private key—i.e., the underlying random circuit—from the public key is computationally infeasible. The approach innovatively introduces a quantum state authentication primitive with high noise tolerance and low sample complexity, alongside an efficient error-detection code tailored to ensembles of random circuits. Experimental validation on a 32-qubit superconducting platform demonstrates classical shadow generation with fidelity 0.90 ± 0.01 using a circuit comprising 80 logical gates (582 physical two-qubit gates), marking the first proof-of-principle demonstration of quantum digital signatures on near-term hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

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.

Problem

• quantum digital signature
• classical communication
• near-term quantum computers
• quantum cryptography
• classical shadows

Innovation

• quantum digital signature
• classical shadows
• random quantum circuits
• state certification
• near-term quantum computing