论文标题
基于推理的量子传感
Inference-Based Quantum Sensing
论文作者
论文摘要
在标准量子传感（QS）任务中，One旨在通过系统的测量来估计未知参数$θ$，该参数$θ$编码为$ n $ qubit的探头状态。该任务的成功取决于将参数变化与系统响应$ \ MATHCAL {r}（θ）$的变化相关的能力（即测量结果的变化）。对于简单的情况，$ \ Mathcal {r}（θ）$的形式是已知的，但是对于现实情况而言，这是不存在的，因为不存在一般的封闭式表达式。在这项工作中，我们为QS提供了基于推理的方案。我们表明，对于一般的编码单一家庭，$ \ Mathcal {r}（θ）$只能通过仅在$ 2N+1 $参数下测量系统响应来充分表征。这使我们能够推断出鉴于测得的响应的未知参数的值，并确定方案的灵敏度，从而表征其整体性能。我们表明，如果一个人用仅比例缩放为$ω（\ log^3（n）/δ^2）$的许多镜头测量系统响应，则推论误差的可能性很小。此外，提出的框架可以广泛应用，因为它对于任意探针状态和测量方案仍然有效，甚至在存在量子噪声的情况下也保持。我们还讨论了如何将结果扩展到统一家庭之外。最后，为了展示我们的方法，我们在实际量子硬件和数值模拟中实现了QS任务。
In a standard Quantum Sensing (QS) task one aims at estimating an unknown parameter $θ$, encoded into an $n$-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response $\mathcal{R}(θ)$ (i.e., changes in the measurement outcomes). For simple cases the form of $\mathcal{R}(θ)$ is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this work we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, $\mathcal{R}(θ)$ can be fully characterized by only measuring the system response at $2n+1$ parameters. This allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than $δ$, if one measures the system response with a number of shots that scales only as $Ω(\log^3(n)/δ^2)$. Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.
