发表机构
Chalmers University of Technology; University of Gothenburg（查尔姆斯理工大学; 哥德堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出选择性GHZ测量（SGM）阴影协议，通过随机子集上的GHZ基测量与补集上的计算基测量，实现高效量子态性质预测，在特定场景下优于局部Pauli和全局Clifford阴影，并给出理论界限与数值验证。
AI 中文摘要
经典阴影允许从测量数据中预测许多量子态性质，但其效率强烈依赖于底层测量系综。我们引入了选择性GHZ测量（SGM）阴影，该方法在随机选择的量子比特子集上执行Greenberger-Horne-Zeilinger（GHZ）基测量，并在其补集上执行计算基测量。相应的量子电路在实际中是可行的，其CNOT门数量随量子比特数线性扩展。这与通常难以实现的全局Clifford电路形成鲜明对比。改变子集分布允许针对具有指定X/Y支持的观测值类别调整SGM阴影协议，使我们在某些场景中能够超越局部Pauli阴影和全局Clifford阴影。我们确定了任意子集分布下的精确阴影通道及其逆，并利用离散傅里叶分析和马尔可夫半群理论的方法证明了阴影范数的显式界限。对于自然选择的子集分布，这为具有固定X/Y局部性的观测值提供了多项式扩展。多达50个量子比特的数值模拟支持了非局部观测值和长程系统所预测的改进，并通过展示子集分布如何针对Jordan-Wigner变换下的费米子模式等设置进行定制，证明了我们协议通用性的实际优势。
英文摘要
Classical shadows allow the prediction of many quantum-state properties from measurement data, but their efficiency strongly depends on the underlying measurement ensemble. We introduce selective GHZ measurement (SGM) shadows, which perform Greenberger-Horne-Zeilinger (GHZ)-basis measurements on randomly selected subsets of qubits and computational-basis measurements on their complement. The corresponding quantum circuits are practically feasible, with their number of CNOT gates scaling linearly with the number of qubits. This is in stark contrast to global Clifford circuits, which are generally difficult to implement. Varying the subset distribution allows tuning the SGM shadow protocol for different classes of observables with prescribed X/Y support, allowing us to outperform local Pauli as well as global Clifford shadows in certain scenarios. We determine the exact shadow channel and its inverse for arbitrary subset distributions and prove an explicit bound on the shadow norm using methods from discrete Fourier analysis and Markov semigroup theory. For natural choices of subset distributions, this gives a polynomial scaling for observables with fixed X/Y-locality. Numerical simulations of up to 50 qubits support the predicted improvements for nonlocal observables and long-range systems, and demonstrate the practical benefits of our protocol's generality by showing how the subset distributions can be tailored to settings such as fermionic modes under the Jordan-Wigner transformation.
Comments53 pages, 4 figures
