发表机构
Center for Quantum Technologies (QuTe) and Department of Computer Science, Saarland University; QuEra Computing Inc.; Joint Center for Quantum Information and Computer Science, University of Maryland; Institute for Theoretical Physics, ETH Zürich; Simons Institute for the Theory of Computing, University of California at Berkeley; Wuhan University; Centre for Quantum Software and Information, University of Technology Sydney（萨尔兰大学量子技术中心与计算机科学系; QuEra计算公司; 马里兰大学量子信息与计算科学联合中心; 苏黎世联邦理工学院理论物理研究所; 加州大学伯克利分校西蒙斯计算理论研究所; 武汉大学; 悉尼科技大学量子软件与信息研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于植入独立空间的三次多项式IQP电路的模拟秘密方案，实现仅凭经典输出即可验证的量子优势，并估计可在100个逻辑量子比特上实现。
AI 中文摘要
量子优势理论中的一个核心问题是：是否存在与随机电路采样具有相似资源需求、且仅从量子计算输出的经典结果即可验证的量子优势协议。在此，我们发展了用于可验证优势的模拟秘密（simulation secrets）思想。验证者可以利用模拟秘密来评估交叉熵测试，其速度比经典对手通过该测试所需的时间更快。我们使用由具有植入独立空间的三次多项式描述的IQP电路来实例化这一思想。这些独立空间对应于一般线性群下多项式轨道中的最大独立集，并产生相应态的低秩稳定子分解。我们猜想，大的独立空间对于计算能力受限的对手是不可见的，因此他们无法利用这些空间来通过协议。第二个猜想涉及为均匀随机多项式生成通过交叉熵测试的样本的细粒度复杂性。在这些猜想下，我们的方案导致验证时间与经典对手通过协议所需时间之间存在多项式差距——两者都是指数级的。由于输出分布具有高最小熵，该方案具有生成经典可认证随机性的潜在应用。我们估计，植入多项式方案可在约$10^{-6}$的逻辑错误率下使用100个逻辑量子比特实现。
英文摘要
A central question in the theory of quantum advantage is whether there are quantum advantage protocols with similar resource requirements as random circuit sampling that are also verifiable just from the classical outputs of the quantum computation. Here, we develop the idea of simulation secrets for verifiable advantage. A verifier can use a simulation secret to evaluate a cross-entropy test faster than it would take a classical adversary to pass the test. We instantiate this idea using IQP circuits described by cubic polynomials with planted independent spaces. These correspond to the largest independent set in the orbit of a polynomial under the general linear group and yield a low-rank stabilizer decomposition of the corresponding state. We conjecture that large independent spaces are invisible to a computationally bounded adversary, and therefore they cannot exploit them to pass the protocol. A second conjecture regards the fine-grained complexity of producing samples that pass the cross-entropy test for uniformly random polynomials. Under these conjectures, our scheme results in a polynomial gap between the verification time and the time a classical adversary would need to pass the protocol---both are exponential. It has a potential application to generating classically certifiable randomness, since the output distributions have high min-entropy. We estimate that the planted polynomial scheme is implementable using 100 logical qubits at logical error rates around $10^{-6}$.
Comments44 pages, 1 figure. Comments welcome
