论文标题
实用量子计算：使用量子方法求解波方程
Practical Quantum Computing: solving the wave equation using a quantum approach
论文作者
论文摘要
在过去的几年中，已经设计了几种试图解决部分微分方程解决问题的量子算法。在一侧，旨在通过执行一个大量子电路来编码PDE解决方案的“直接”量子算法。另一方面，通过执行几个小量子电路并获得经典优化器的利润来近似PDE的解。在这项工作中，我们提出了与“直接”量子算法之一相关联的理想硬件的成本研究（就栅极编号和执行时间而言）：在[PCS中设计的波动方程求解器之一。 Costa，S。Jordan，A。Ostrander，物理。 Rev. A 99，012323，2019]。我们表明，我们对量子波方程求解器的实现与算法的理论大O复杂性一致。我们还可以很好地详细说明实施步骤，并讨论改进的一些可能性。最后，我们的实现在实验上证明了一些PDE可以在量子计算机上求解，即使所选的直接量子算法需要错误校正后的量子芯片，而这些量子芯片却不在短期内可用。
In the last years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised. On one side, "direct" quantum algorithms that aim at encoding the solution of the PDE by executing one large quantum circuit. On the other side, variational algorithms that approximate the solution of the PDE by executing several small quantum circuits and making profit of classical optimisers. In this work we propose an experimental study of the costs (in terms of gate number and execution time on a idealised hardware created from realistic gate data) associated with one of the "direct" quantum algorithm: the wave equation solver devised in [PCS. Costa, S. Jordan, A. Ostrander, Phys. Rev. A 99, 012323, 2019]. We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. We also explain in great details the implementation steps and discuss some possibilities of improvements. Finally, our implementation proves experimentally that some PDE can be solved on a quantum computer, even if the direct quantum algorithm chosen will require error-corrected quantum chips, which are not believed to be available in the short-term.
