How to Verify that a Small Device is Quantum, Unconditionally

TL;DR

This paper introduces new unconditionally sound proof-of-quantumness protocols that rely on memory bounds, with one being simple and implementable with minimal quantum gates, and both offering efficient verification.

Contribution

It presents two novel PoQ protocols with unconditional soundness based on memory bounds, including a simple, practically implementable one and an exponential gap protocol.

Findings

Simple protocol relies on arithmetic modulo 2 and minimal quantum gates.

Both protocols are efficiently verifiable.

Achieves unconditionally sound PoQ based on memory assumptions.

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.