Quantum computing devices can now perform sampling tasks which, according to complexity-theoretic and numerical evidence, are beyond the reach of classical computers. This raises the question of how one can efficiently verify that a quantum computer operating in this regime works as intended. In 2008, Shepherd and Bremner proposed a protocol in which a verifier constructs a unitary from the comparatively easy-to-implement family of so-called IQP circuits, and challenges a prover to execute it on a quantum computer. The challenge problem is designed to contain an obfuscated secret, which can be turned into a statistical test that accepts samples from a correct quantum implementation. It was conjectured that extracting the secret from the challenge problem is NP-hard, so that the ability to pass the test constitutes strong evidence that the prover possesses a quantum device and that it works as claimed. Unfortunately, about a decade later, Kahanamoku-Meyer found an efficient classical secret extraction attack. Bremner, Cheng, and Ji very recently followed up by constructing a wide-ranging generalization of the original protocol. Their IQP Stabilizer Scheme has been explicitly designed to circumvent the known weakness. They also suggested that the original construction can be made secure by adjusting the problem parameters. In this work, we develop a number of secret extraction attacks which are effective against both new approaches in a wide range of problem parameters. The important problem of finding an efficient and reliable verification protocol for sampling-based proofs of quantum supremacy thus remains open.

翻译：量子计算设备如今能够执行一些采样任务，根据复杂性理论和数值证据，这些任务超出了经典计算机的能力范围。这引发了一个问题：如何有效验证运行在此机制下的量子计算机是否按预期工作？2008年，Shepherd和Bremner提出了一种协议，其中验证者从相对易于实现的所谓IQP电路族中构造一个酉算子，并要求证明者在量子计算机上执行该算子。该挑战问题被设计为包含一个经过混淆的秘密，该秘密可转化为一项统计测试，用于接受来自正确量子实现的采样结果。当时推测，从挑战问题中提取秘密是NP难问题，因此通过测试的能力构成有力证据，表明证明者拥有量子设备且其工作符合预期。然而，大约十年后，Kahanamoku-Meyer发现了一种高效的经典秘密提取攻击。最近，Bremner、Cheng和Ji跟进构建了原始协议的一个广泛推广版本。他们的IQP稳定子方案被明确设计为规避已知的弱点。他们还建议，通过调整问题参数可以使原始构造变得安全。在本工作中，我们开发了多种秘密提取攻击，这些攻击在广泛的问题参数范围内对新旧方法均有效。因此，寻找基于采样的量子霸权证明的高效可靠验证协议这一重要问题仍然悬而未决。