Classically-Verifiable Quantum Advantage from a Computational Bell Test

TL;DR

This paper introduces a new, efficiently classically verifiable quantum advantage protocol based on cryptographic functions and Bell's inequality, with novel constructions and implementation improvements for quantum cryptography.

Contribution

It presents a novel interactive protocol for quantum advantage that is classically verifiable, expanding TCFs, and introduces implementation innovations for quantum cryptography.

Findings

Protocol is efficiently classically verifiable

Proposes two new TCF constructions based on Diffie-Hellman and Rabin's function

Improves implementation efficiency with garbage bit removal and post-selection techniques

Abstract

We propose and analyze a novel interactive protocol for demonstrating quantum computational advantage, which is efficiently classically verifiable. Our protocol relies upon the cryptographic hardness of trapdoor claw-free functions (TCFs). Through a surprising connection to Bell's inequality, our protocol avoids the need for an adaptive hardcore bit, with essentially no increase in the quantum circuit complexity and no extra cryptographic assumptions. Crucially, this expands the set of compatible TCFs, and we propose two new constructions: one based upon the decisional Diffie-Hellman problem and the other based upon Rabin's function, $x^2 \bmod N$. We also describe two independent innovations which improve the efficiency of our protocol's implementation: (i) a scheme to discard so-called "garbage bits", thereby removing the need for reversibility in the quantum circuits, and (ii) a natural way of performing post-selection which significantly reduces the fidelity needed to demonstrate quantum advantage. These two constructions may also be of independent interest, as they may be applicable to other TCF-based quantum cryptography such as certifiable random number generation. Finally, we design several efficient circuits for $x^2 \bmod N$ and describe a blueprint for their implementation on a Rydberg-atom-based quantum computer.