We introduce a post-processing technique for classical shadow measurement data that enhances the precision of ground state estimation through high-dimensional subspace expansion; the dimensionality is only limited by the amount of classical post-processing resources rather than by quantum resources. Crucial steps of our approach are the efficient identification of useful observables from shadow data, followed by our regularised subspace expansion that is designed to be numerically stable even when using noisy data. We analytically investigate noise propagation within our method, and upper bound the statistical fluctuations due to the limited number of snapshots in classical shadows. In numerical simulations, our method can achieve a reduction in the energy estimation errors in many cases, sometimes by more than an order of magnitude. We also demonstrate that our performance improvements are robust against both coherent errors (bad initial state) and gate noise in the state-preparation circuits. Furthermore, performance is guaranteed to be at least as good - and in many cases better - than direct energy estimation without using additional quantum resources and the approach is thus a very natural alternative for estimating ground state energies directly from classical shadow data.
Chemistry on quantum computers with virtual quantum subspace expansion
在量子计算机上模拟化学系统仅限于最小基础上的几个电子。我们通过实验证明，虚拟量子子空间展开[Phys. Rev. X 10，011004（2020）]可以实现氢和锂二聚体的完全基精度，与需要20个或更多量子位的模拟相当。我们开发了一种方法来最大限度地减少实验噪声对广义本征值问题稳定性的影响，广义本征值问题是量子算法的关键组成部分。此外，我们能够获得一个准确的势能曲线的氮二聚体在量子模拟在经典计算机上。
Optimizing Subspace Expansion in Quantum Chemistry through Operator Selection and Reference State Choice
Institute of Engineering Thermodynamics, German Aerospace Center (DLR)（德国航空航天中心工程热力学研究所）；Helmholtz Institute Ulm（乌尔姆亥姆霍兹研究所）；HQS Quantum Simulations GmbH（HQS量子模拟有限公司）；University of Ulm（乌尔姆大学）
