编码-解码量子电路中的蝴蝶效应
A Butterfly Effect in Encoding-Decoding Quantum Circuits
AI总结：
本文研究了含噪编码-解码量子电路中的信息置乱，利用$\mathcal{A}$-OTOC推导出解析表达式，发现热力学极限下微小噪声会引发宏观信息置乱的蝴蝶效应，且该效应可能广泛存在。
摘要：
对信息置乱的研究极大地加深了我们对多体量子系统的理解。近期的大量研究致力于理解开放系统中信息置乱与退相干之间的相互作用。延续这一脉络，我们在一个含噪的编码-解码电路模型中研究了信息置乱。具体而言，我们考虑一个包含 $L$ 个量子比特的电路，由 Haar 随机酉变换构成，随后在部分量子比特上作用噪声，最后进行逆酉变换。信息置乱使用二部分代数无时序关联子（$\mathcal{A}$-OTOC）进行测量，这使我们能够追踪广延尺寸子系统之间的信息传播。我们推导出了 $\mathcal{A}$-OTOC 的解析表达式，该表达式取决于系统尺寸和噪声强度。在热力学极限下，该系统表现出蝴蝶效应，即无穷小的噪声会引发宏观的信息置乱。我们还在放宽 Haar 随机性条件的限制下进行了数值模拟，初步结果表明该效应可能在更大范围的电路中显现。
英文摘要：
The study of information scrambling has profoundly deepened our understanding of many-body quantum systems. Much recent research has been devote to understanding the interplay between scrambling and decoherence in open systems. Continuing in this vein, we investigate scrambling in a noisy encoding-decoding circuit model. Specifically, we consider an $L$-qubit circuit consisting of a Haar-random unitary, followed by noise acting on a subset of qubits, and then by the inverse unitary. Scrambling is measured using the bipartite algebraic out-of-time-order correlator ($\mathcal{A}$-OTOC), which allows us to track information spread between extensively sized subsystems. We derive an analytic expression for the $\mathcal{A}$-OTOC that depends on system size and noise strength. In the thermodynamic limit, this system displays a \textit{butterfly effect} in which infinitesimal noise induces macroscopic information scrambling. We also perform numerical simulations while relaxing the condition of Haar-randomness, which preliminarily suggest that this effect may manifest in a larger set of circuits.
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