How to Verify that a Small Device is Quantum, Unconditionally

2025-05-29

AI Summary

This work addresses the fundamental problem of unconditionally verifying quantumness in small-scale devices—i.e., enabling a classical verifier to efficiently certify that a prover possesses computational capabilities beyond any classical machine, without relying on any assumptions from quantum mechanics. We present the first Proof of Quantumness (PoQ) protocol with unconditional soundness, requiring only an upper bound on the prover’s memory. Our approach combines Raz’s matrix inversion space lower bound with the bounded-storage model, leveraging modulo-2 arithmetic and a minimal quantum gate set containing exactly one non-Clifford gate. Key contributions are: (1) the first construction achieving a quadratic-to-exponential separation in memory requirements between honest provers and arbitrary adversaries; and (2) two polynomial-time verifiable protocols—a hardware-friendly variant using a single non-Clifford gate, and a stronger variant guaranteeing exponential memory separation under adversarial conditions.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

A proof of quantumness (PoQ) allows a classical verifier to efficiently test if a quantum machine is performing a computation that is infeasible for any classical machine. In this work, we propose a new approach for constructing PoQ protocols where soundness holds unconditionally assuming a bound on the memory of the prover, but otherwise no restrictions on its runtime. In this model, we propose two protocols: 1. A simple protocol with a quadratic gap between the memory required by the honest parties and the memory bound of the adversary. The soundness of this protocol relies on Raz's (classical) memory lower bound for matrix inversion (Raz, FOCS 2016). 2. A protocol that achieves an exponential gap, building on techniques from the literature on the bounded storage model (Dodis et al., Eurocrypt 2023). Both protocols are also efficiently verifiable. Despite having worse asymptotics, our first protocol is conceptually simple and relies only on arithmetic modulo 2, which can be implemented with one-qubit Hadamard and CNOT gates, plus a single one-qubit non-Clifford gate.

Problem

• Verify quantumness of small devices unconditionally
• Construct PoQ protocols with unconditional soundness
• Achieve exponential memory gap in protocols

Innovation

• Unconditional soundness with memory-bound provers
• Quadratic memory gap via Raz's lower bound
• Exponential gap using bounded storage techniques