AI 中文总结
该研究在量子硬件上实现含Hayden--Preskill/Yoshida--Kitaev恢复映射的Deutsch类空闭合曲线解码器电路，通过Qiskit模拟和IBM硬件数据量化了解码器相关性能参数。
AI 中文摘要
Deutsch类空闭合曲线（D-CTCs）由违反时间顺序的寄存器的不动点条件描述。我们研究一种有限维电路模型，该模型将Hayden--Preskill/Yoshida--Kitaev恢复映射置于此类一致性循环内。寄存器路由构造使Deutsch映射明确：初始SWAP将输入的CTC状态移至空闲转储寄存器，加扰器和解码器作用于剩余的活动寄存器，最终SWAP将恢复的消息写回CTC寄存器。当活动分支恢复消息时，CTC寄存器上的诱导映射为替换通道σ↦ρ_M，具有唯一不动点ρ_M。我们在量子硬件上实现相关的Lloyd型后选择解码器电路，并为实验估计的映射制定经典反馈迭代。针对单量子比特实例的Qiskit模拟和IBM硬件数据，量化了解码器保真度、后选择开销、路由相关噪声以及量子几何敏感性。
英文摘要
Deutsch closed timelike curves (D-CTCs) are described by a fixed-point condition for a chronology-violating register. We study a finite-dimensional circuit model that places a Hayden--Preskill/Yoshida--Kitaev recovery map inside such a consistency loop. A register-routing construction makes the Deutsch map explicit: an initial SWAP moves the incoming CTC state to an idle dump register, the scrambler and decoder act on the remaining active registers, and a final SWAP writes the recovered message back to the CTC register. When the active branch recovers the message, the induced map on the CTC register is the replacement channel \(σ\mapsto ρ_M\), with the unique fixed point \(ρ_M\). We implement the associated Lloyd-type post-selected decoder circuits on quantum hardware and formulate a classical-feedback iteration for the experimentally estimated map. Qiskit simulations and IBM-hardware data for single-qubit instances quantify decoder fidelity, post-selection overhead, routing-dependent noise, and quantum-geometric susceptibility.
Comments16 pages, 13 figures
