AI 中文总结
研究在量子处理器上扩展Hayden–Preskill恢复方案，结合SWAP门与有限温度，通过IBM超导处理器实验验证强扰码可实现信息恢复，SWAP误差缓解方案可提升恢复效果。
AI 中文摘要
在原始Hayden–Preskill恢复方案中，注入后的 scrambler（扰码器）与初始态无关联。我们从两方面扩展该设置：使用SWAP门使scrambler与初始态产生关联，且考虑有限温度下的恢复。针对该修改后的协议，我们证明信息可成功恢复，体现为后选择概率不可忽略且条件保真度较高。我们发现后选择概率与条件保真度均与温度成正比，反映出低温下初始态纠缠度降低的特性。我们还在均匀算符扩散假设下推导了二者的晚期解析估计值，且与数值结果吻合良好，这表明强扰码对成功的信息恢复至关重要。我们在IBM超导处理器上采用含N=8个Majorana的二元稀疏SYK哈密顿量实现该协议，观察到数据保留了定性的恢复动力学，且基于SWAP的误差缓解方案可同时提升后选择概率与条件保真度。
英文摘要
In the original Hayden--Preskill recovery, the post-injection scrambler and initial state are {\it not related}. We extend this setup in two ways: by using a SWAP gate so that the scrambler and initial state are {\it related}, and by considering recovery at {\it finite} temperature. For this modified protocol, we show that the information is successfully recovered in the sense that the postselection probability is non-negligible and the conditional fidelity is large. We find that both the postselection probability and the conditional fidelity are proportional to temperature, reflecting the reduced entanglement of the initial state at lower temperatures. We also derive their late-time analytic estimates under the assumption of uniform operator spreading and show that they agree well with the numerical results. This demonstrates that strong scrambling is important for successful information recovery. Implementing the protocol on an IBM superconducting processor using a binary sparse SYK Hamiltonian with $N = 8$ Majoranas, we observe that the data retain the qualitative recovery dynamics and that a SWAP-based error-mitigation scheme improves both the postselection probability and the conditional fidelity.
Comments21 pages, 12 figures
