发表机构
QpiAI India Private Limited（QpiAI印度私人有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对云量子处理器验证难题，提出基于简并一致系综的协议，使客户端以O(n)时间评分每轮，通过秘密奇偶校验和特征值预测输出分布，实现高效经典验证并应用于随机性生成。
AI 中文摘要
租用云量子处理器的客户端难以判断其收到的比特串是否确实来自量子设备。基于随机电路采样的认证可在当前硬件上运行，但客户端对每个返回样本进行评分需要花费时间O(2^n)。我们提出了一种协议，使客户端在O(n)时间内对每轮进行评分，该协议基于简并一致系综。当一致态具有简并谱时，每个保持一致的门可分解为G_t=U_tP_tB_tU_{t-1}^†，其中块因子B_t与态对易，在纠缠每个纯分量的同时从系综中抵消。客户端持有一个秘密奇偶校验，其陪集是每一层的简并扇区，因此客户端构建电路并通过每层一次内积预测系综。秘密永不离开客户端。输入均匀随机发送，客户端在自身记账中为每轮附加该输入在隐藏态中的特征值；验证统计量（输入-输出一致性检验和加权碰撞检验）随后将服务器的样本与一致计算的非平坦输出分布进行比较。我们在理想模型中证明了完备性、客户端效率和可靠性，在该模型中编译后的电路不泄露关于秘密的任何信息，并且我们表明秘密必须保持隐藏：持有秘密的经典服务器能够通过。对于显式构造，我们证明了在具有无偏边缘分布的非乘积输入上，用于高效模拟一致计算的单量子比特对称性检验失败，并且我们测量到Cable和Browne的局部基查找器在我们测试的每一层上都会停止，传输分量达到最大施密特秩，电路不是Clifford电路，矩阵乘积欺骗器被拒绝。显式构造的可靠性以猜想形式陈述。
英文摘要
A client who rents a cloud quantum processor cannot easily tell whether the bitstrings it receives came from a quantum device. Certification by random circuit sampling runs on present hardware, but scoring each returned sample costs the client time $O(2^n)$. We give a protocol in which the client scores each round in time $O(n)$, built on degenerate concordant ensembles. When a concordant state has a degenerate spectrum, every concordance-preserving gate factorizes as $G_t=U_tP_tB_tU_{t-1}^\dagger$, and the block factor $B_t$, which commutes with the state, cancels from the ensemble while entangling each pure component. The client holds a secret parity whose cosets are the degenerate sectors of every layer, so that it builds the circuit and predicts the ensemble with one inner product per layer. The secret never leaves the client. Inputs are sent uniformly at random, and the client attaches to each round, in its own bookkeeping, the eigenvalue of that input in the hidden state; both verification statistics, an input--output agreement test and a weighted collision test, then compare the server's samples with the non-flat output distribution of the concordant computation. We prove completeness, client efficiency, and soundness in an ideal model in which the compiled circuit reveals nothing about the secret, and we show that the secret must stay hidden: a classical server that holds it passes. For the explicit construction we prove that the single-qubit symmetry test used in efficient simulations of concordant computation fails on non-product inputs with unbiased marginals, and we measure that the local-basis finder of Cable and Browne halts on every layer we tested, that the transmitted component saturates the maximal Schmidt rank, that the circuit is not Clifford, and that matrix-product spoofers are rejected. Soundness of the explicit construction is stated as a conjecture.
Comments17 pages, 2 figures
