论文标题
Variational quantum algorithm for measurement extraction from the Navier-Stokes, Einstein, Maxwell, B-type, Lin-Tsien, Camassa-Holm, DSW, H-S, KdV-B, non-homogeneous KdV, generalized KdV, KdV, translational KdV, sKdV, B-L and Airy equations
Variational quantum algorithm for measurement extraction from the Navier-Stokes, Einstein, Maxwell, B-type, Lin-Tsien, Camassa-Holm, DSW, H-S, KdV-B, non-homogeneous KdV, generalized KdV, KdV, translational KdV, sKdV, B-L and Airy equations
论文作者
论文摘要
经典的量词混合算法最近引起了极大的关注，其特征是结合量子和经典计算方案以从感兴趣的量子电路中获取读数。 Lubasch等人在2019年论文中的最新进展通过使用新的变分量子算法（VQA），为解决方案提供了解决方案和Inviscid Burgers方程的读数，该量子算法（VQA）确定了以期望值和差异参数的叠加表达的成本函数的基础状态。在下文中，我们分析了其他计算前景，在这些计算前景中，VQA可以可靠地为其他PDE生成解决方案，这些PDE与以前经典实现的解决方案相媲美，这些解决方案具有无噪声量子模拟的特征。 To determine the range of nonlinearities that the algorithm can process for other IVPs, we study several PDEs, first beginning with the Navier-Stokes equations and progressing to other equations underlying physical phenomena ranging from electromagnetism, gravitation, and wave propagation, from simulations of the Einstein, Boussniesq-type, Lin-Tsien, Camassa-Holm, Drinfeld-Sokolov-Wilson（DSW）和Hunter-Saxton方程。为了制定优化程序，VQA经历了作为从量子电路读取的解决方案的数值近似值，在补充部分中提供了与每个PDE相对应的成本函数，此后由数百个Zgr-qft-qft Ansatzae产生的模拟产生。
Classical-quantum hybrid algorithms have recently garnered significant attention, which are characterized by combining quantum and classical computing protocols to obtain readout from quantum circuits of interest. Recent progress due to Lubasch et al in a 2019 paper provides readout for solutions to the Schrodinger and Inviscid Burgers equations, by making use of a new variational quantum algorithm (VQA) which determines the ground state of a cost function expressed with a superposition of expectation values and variational parameters. In the following, we analyze additional computational prospects in which the VQA can reliably produce solutions to other PDEs that are comparable to solutions that have been previously realized classically, which are characterized with noiseless quantum simulations. To determine the range of nonlinearities that the algorithm can process for other IVPs, we study several PDEs, first beginning with the Navier-Stokes equations and progressing to other equations underlying physical phenomena ranging from electromagnetism, gravitation, and wave propagation, from simulations of the Einstein, Boussniesq-type, Lin-Tsien, Camassa-Holm, Drinfeld-Sokolov-Wilson (DSW), and Hunter-Saxton equations. To formulate optimization routines that the VQA undergoes for numerical approximations of solutions that are obtained as readout from quantum circuits, cost functions corresponding to each PDE are provided in the supplementary section after which simulations results from hundreds of ZGR-QFT ansatzae are generated.
