Budiyono Agung, Dipojono Hermawan K
Research Center for Nanoscience and Nanotechnology, Bandung Institute of Technology, Bandung, 40132, Indonesia.
Kubus Computing and Research, Juwana, Pati, 59185, Indonesia.
Sci Rep. 2020 Sep 8;10(1):14769. doi: 10.1038/s41598-020-71836-8.
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable-after the Heisenberg evolution associated with the circuits-is at most second order in momentum. The classical computational algorithm exploits a specific epistemic restriction in classical phase space which directly captures the quantum uncertainty relation, to transform the quantum circuits in the complex Hilbert space into classical albeit unconventional stochastic processes in the phase space. The resulting multidimensional integral is then evaluated using the Monte Carlo sampling method. The convergence rate of the classical sampling algorithm is determined by the variance of the classical physical quantity over the epistemically restricted phase space distribution. The work shows that for the specific class of computational schemes, Wigner negativity is not a sufficient resource for quantum speedup. It highlights the potential role of the epistemic restriction as an intuitive conceptual tool which may be used to study the boundary between quantum and classical computations.
我们设计了一种经典算法，该算法能有效地计算出一类连续变量量子电路中出现的量子期望值，其中与这些电路相关的海森堡演化之后的最终量子可观测量在动量上至多为二阶。经典计算算法利用经典相空间中的一种特定认知限制，该限制直接捕捉量子不确定性关系，将复希尔伯特空间中的量子电路转化为相空间中的经典（尽管是非传统的）随机过程。然后使用蒙特卡罗采样方法来计算由此产生的多维积分。经典采样算法的收敛速率由经典物理量在认知受限相空间分布上的方差决定。这项工作表明，对于特定类别的计算方案，维格纳负性并非量子加速的充分资源。它突出了认知限制作为一种直观概念工具的潜在作用，可用于研究量子计算与经典计算之间的边界。
