Generating Hard Ising Instances With Planted Solutions Using Post-Quantum Cryptographic Protocols

TL;DR

This paper introduces a cryptographic-based method for generating challenging Ising model instances with guaranteed unique solutions, enhancing the testing of quantum devices while ensuring security against solution extraction.

Contribution

The paper presents a novel cryptographic protocol for creating hard Ising instances with planted solutions, leveraging post-quantum cryptography for security and hardness tuning.

Findings

Instances are cryptographically secure and hard to solve.

Hardness can be tuned by adjusting the private key size.

The method guarantees a unique ground state for each instance.

Abstract

In this paper we present a novel method to generate hard instances with planted solutions based on the public-private McEliece post-quantum cryptographic protocol. Unlike other planting methods rooted in the infinite-size statistical analysis, our cryptographic protocol generates instances which are all hard (in cryptographic terms), with the hardness tuned by the size of the private key, and with a guaranteed unique ground state. More importantly, because of the private-public key protocol, planted solutions cannot be easily recovered by a direct inspection of the planted instances without the knowledge of the private key used to generate them, therefore making our protocol suitable to test and evaluate quantum devices without the risk of "backdoors" being exploited.