论文标题
通过测量的随机统一回路进行自组织的误差校正
Self-Organized Error Correction in Random Unitary Circuits with Measurement
论文作者
论文摘要
当测量强度超过阈值时，随机测量已显示出在混沌单位动力学下演变的扩展量子系统中诱导相变。在此阈值之下，出现了具有亚热量法纠缠的稳态，它抵抗了测量的分离作用，这表明与量子误差校正的代码有联系。 Here we quantify these notions by identifying a universal, subleading logarithmic contribution to the volume law entanglement entropy: $S^{(2)}(A)=κL_A+\frac{3}{2}\log L_A$ which bounds the mutual information between a qudit inside region $A$ and the rest of the system.具体来说，我们发现互助信息的幂定律衰减$ i（\ {x \}：\ bar {a}）\ propto x^{ - 3/2} $，距离该地区边界的距离$ x $，这意味着在$ a内的$ a $ a $ a对$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $。我们通过将纠缠动力学映射到ISING模型的假想时间演变来获得这些结果，我们可以应用现场理论和基质 - 产物 - 状态技术。最后，利用错误纠正观点，我们假设volume-law状态是对量子错误校正代码中页面状态的编码，以获得对关键测量强度的限制$ p_ {c} $作为qudit dimension $ d $的函数。 $ p_ {c} \ log [（d^{2} -1）（{p_ {c}^{ - 1} -1}）] \ le \ log [（1-p_ {c}）d] $。绑定在$ p_c（d \ rightarrow \ infty）= 1/2 $中饱和，并提供了量子转换的合理估算值：$ p_c（d = 2）\ le 0.1893 $。
Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of measurements exceeds a threshold value. Below this threshold, a steady state with a sub-thermal volume law entanglement emerges, which is resistant to the disentangling action of measurements, suggesting a connection to quantum error-correcting codes. Here we quantify these notions by identifying a universal, subleading logarithmic contribution to the volume law entanglement entropy: $S^{(2)}(A)=κL_A+\frac{3}{2}\log L_A$ which bounds the mutual information between a qudit inside region $A$ and the rest of the system. Specifically, we find the power law decay of the mutual information $I(\{x\}:\bar{A})\propto x^{-3/2}$ with distance $x$ from the region's boundary, which implies that measuring a qudit deep inside $A$ will have negligible effect on the entanglement of $A$. We obtain these results by mapping the entanglement dynamics to the imaginary time evolution of an Ising model, to which we can apply field-theoretic and matrix-product-state techniques. Finally, exploiting the error-correction viewpoint, we assume that the volume-law state is an encoding of a Page state in a quantum error-correcting code to obtain a bound on the critical measurement strength $p_{c}$ as a function of the qudit dimension $d$: $p_{c}\log[(d^{2}-1)({p_{c}^{-1}-1})]\le \log[(1-p_{c})d]$. The bound is saturated at $p_c(d\rightarrow\infty)=1/2$ and provides a reasonable estimate for the qubit transition: $p_c(d=2) \le 0.1893$.
