AI 中文总结
该研究提出新方法生成具有复杂动力学且影响矩阵可精确写出的量子电路，基于无修饰自由费米子电路构建，所得矩阵非马尔可夫，产生的关联模式类似典型多体系统，方法可按纠错方案解释。
AI 中文摘要
影响矩阵编码了扩展量子多体系统其余部分在演化过程中对局部子系统施加的作用。因此，了解影响矩阵有助于对局部动力学进行计算高效的模拟。本文提出了一种新的系统方法来生成具有复杂动力学的量子电路，其影响矩阵可以精确写出。与之前的此类框架（如双酉电路）不同，所得影响矩阵是非马尔可夫的，表现出非平凡的时间相关性。我们基于具有适当选择的相互作用项的无修饰自由费米子（匹配门）电路，明确构建了这类广泛的电路家族。我们表明，与之前的可解实例相反，这些电路产生的关联模式与典型多体系统的模式非常相似。我们的方法可以直接根据一种纠错方案来解释，其中破坏影响矩阵可解性的项起到了误差的作用。
英文摘要
Influence matrices encode the action exerted on local subsystems by the rest of an extended quantum many-body system during their evolution. Thus, knowledge of the influence matrix facilitates computationally efficient simulations of local dynamics. Here we propose a new systematic approach to generating quantum circuits with complex dynamics for which the influence matrices can be written down exactly. In contrast to previous frameworks of this kind, such as dual-unitary circuits, the resulting influence matrices are non-Markovian, exhibiting nontrivial temporal correlations. We explicitly construct a broad family of circuits of this kind, based on dressing free-fermion (matchgate) circuits with appropriately chosen interaction terms. We show that, contrary to previous solvable instances, these circuits produce patterns of correlations that closely resemble that of typical many-body systems. Our approach can be directly interpreted in terms of an error correction scheme where the terms breaking the solvability of the influence matrices play the role of errors.
