矩阵乘积守恒量子链中的局域电荷、复位噪声与边界记忆
Localized charges, reset noise, and boundary memory in matrix-product-conserving quantum chains
- Rubin Anders Scientific, Inc.（鲁宾安德斯科学有限公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在矩阵乘积守恒量子链中构造边界可观测量，通过随机矩阵乘积收缩实现电荷局域化，并给出有限时间关联界与指数记忆窗口，辅以数值证书和IBM实验验证。
AI中文摘要：
我们在量子链中构造了边界可观测量，这些可观测量在量化时间窗口内保留记忆，其中基组态携带矩阵标签的有序守恒乘积。在标签矩阵的强不可约性和近迫性假设下，随机矩阵乘积的投影收缩将守恒电荷局域化于均匀基组态的均方根意义下。一个有限时间不等式随后将读出重叠和复位泄漏转化为关联界：对于守恒参考可观测量 $H$、读出 $F$、累积平方泄漏 $\mathcal B$ 以及归一化希尔伯特-施密特内积，有 $\langle F,\Phi(F)\rangle\ge 2\langle H,F\rangle^2/(\\|H\\|_2^2+\mathcal B)-\\|F\\|_2^2$。这里 $\Phi$ 是守恒通道和部分复位的序列。该界对每个此类电路成立，无需对其门进行平均。它产生距离噪声区域的距离上的指数记忆窗口，并对空间分布噪声和不完美守恒给出定量修正。对于十三态初等矩阵模型，精确多项式证书给出电荷与其最后 $r$ 个位点限制之间的均方根局域化误差 $e^{-r/1400}$，以及有理电荷的极限方差至少为 $1/19$。一个相关的归一化格拉姆电荷给出八位点证书，在两次边界复位轮次后保留超过一半的指定读出关联。均匀退极化施加了逆噪声率寿命上限。一个双量子比特 IBM 实验说明了通用复位不等式；它并未实现矩阵乘积链。我们提供证明、精确证书程序以及对存档实验结果的独立复述。
英文摘要：
We construct boundary observables that retain memory for a quantified time window in quantum chains whose basis configurations carry a conserved ordered product of matrix labels. Under strong-irreducibility and proximality hypotheses on the label matrices, projective contraction of random matrix products localizes a conserved charge in the root-mean-square over uniform basis configurations. A finite-time inequality then converts readout overlap and reset leakage into a correlation bound: for a conserved reference observable $H$, a readout $F$, accumulated squared leakage $\mathcal B$, and the normalized Hilbert-Schmidt inner product, $\langle F,Φ(F)\rangle\ge 2\langle H,F\rangle^2/(\|H\|_2^2+\mathcal B)-\|F\|_2^2$. Here $Φ$ is a sequence of conserving channels and partial resets. The bound holds for each such circuit, without averaging its gates. It yields an exponential memory window in the distance from the noisy region, with quantitative corrections for spatially distributed noise and imperfect conservation. For a thirteen-state elementary-matrix model, exact polynomial certificates give root-mean-square localization error $e^{-r/1400}$ between the charge and its restriction to the last $r$ sites, and limiting variance at least $1/19$ for a rational charge. A related normalized-Gram charge gives an eight-site certificate retaining more than half the specified readout correlation through two boundary-reset rounds. Uniform depolarization imposes an inverse-noise-rate lifetime ceiling. A two-qubit IBM experiment illustrates the general reset inequality; it does not realize the matrix-product chain. We provide proofs, exact certificate programs, and an independent recount of the archived experimental outcomes.
