论文标题
费米子量子仿真的匹配阴影
Matchgate Shadows for Fermionic Quantum Simulation
论文作者
论文摘要
“经典阴影”是未知量子状态的估计量，它是由适当分布的随机测量在该状态的副本上构成的[自然物理学16，1050-1057]。在这里，我们分析了使用随机匹配电路获得的经典阴影，该电路对应于费米子高斯单位。我们证明，在连续的匹配电路组上，HAAR分布的前三刻等于仅在也是Clifford Unitaries的Matchgate电路上的离散均匀分布的时刻。因此，后者形成了“匹配3设计”。这意味着由两个集合产生的经典阴影在功能上是等效的。我们展示了如何使用这些匹配阴影来有效估计任意量子状态和费米子高斯状态之间的内部产品，以及本地费米子操作员和其他各种数量的期望值，从而超过了先前工作的能力。作为一种具体的应用，这使我们能够应用波函数约束，以控制量子 - 经典辅助尺寸量子量蒙特卡洛算法（QC-AFQMC）[nature 603，416-420]中的费用符号问题，而没有指示后的后处理成本。
"Classical shadows" are estimators of an unknown quantum state, constructed from suitably distributed random measurements on copies of that state [Nature Physics 16, 1050-1057]. Here, we analyze classical shadows obtained using random matchgate circuits, which correspond to fermionic Gaussian unitaries. We prove that the first three moments of the Haar distribution over the continuous group of matchgate circuits are equal to those of the discrete uniform distribution over only the matchgate circuits that are also Clifford unitaries; thus, the latter forms a "matchgate 3-design." This implies that the classical shadows resulting from the two ensembles are functionally equivalent. We show how one can use these matchgate shadows to efficiently estimate inner products between an arbitrary quantum state and fermionic Gaussian states, as well as the expectation values of local fermionic operators and various other quantities, thus surpassing the capabilities of prior work. As a concrete application, this enables us to apply wavefunction constraints that control the fermion sign problem in the quantum-classical auxiliary-field quantum Monte Carlo algorithm (QC-AFQMC) [Nature 603, 416-420], without the exponential post-processing cost incurred by the original approach.
