论文标题
动态量子记忆如何忘记
How Dynamical Quantum Memories Forget
论文作者
论文摘要
最近的工作激励表明，纠正量纠正代码可以通过单位和测量的混合动态产生，我们研究了此类系统的长时间行为。我们证明，即使在“混合”阶段，最大混合的初始密度矩阵也会在等于希尔伯特空间尺寸的时间尺度上纯化（即，系统大小的指数为指数），尽管在中等时间内具有嘈杂的动力学，我们连接到Dyson Brownian运动。相比之下，我们表明，自由的费米昂系统（即，二次汉密尔顿人产生的单位和测量值是fermion biinears的，在系统大小的时间二次中纯化。特别是，纠缠熵的体积法阶段不能在自由费米昂系统中维持。
Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the "mixed" phase, a maximally mixed initial density matrix is purified on a time scale equal to the Hilbert space dimension (i.e., exponential in system size), albeit with noisy dynamics at intermediate times which we connect to Dyson Brownian motion. In contrast, we show that free fermion systems -- i.e., ones where the unitaries are generated by quadratic Hamiltonians and the measurements are of fermion bilinears -- purify in a time quadratic in the system size. In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.
