论文标题
用量子计算机公正量子蒙特卡洛算法的指数挑战
Exponential challenges in unbiasing quantum Monte Carlo algorithms with quantum computers
论文作者
论文摘要
最近，Huggins等。 al。 [Nature，603，416-420（2022）]设计了一种适用于量子计算机实现的一般投影量子蒙特卡洛方法。然而，这种混合方法依赖于子例程 - 量子计算机上局部能量估计器的计算，该计算在本质上受到计算时间的指数缩放和量子数量的影响。通过数值实验，我们表明这种指数缩放率显着地在“量子优势”点以下的系统上表现出来。对于原型横向景观模型，我们表明，与大约40吨的经典模拟竞争所需的时间资源已经是$ 10^{13} $投影测量的订单，估计在超导硬件上的运行时间为几千年。这些观察结果强烈表明，以目前的形式提出的混合方法不太可能比常规量子蒙特卡洛方法具有相当大的优势。
Recently, Huggins et. al. [Nature, 603, 416-420 (2022)] devised a general projective Quantum Monte Carlo method suitable for implementation on quantum computers. This hybrid approach, however, relies on a subroutine -the computation of the local energy estimator on the quantum computer -that is intrinsically affected by an exponential scaling of the computational time with the number of qubits. By means of numerical experiments, we show that this exponential scaling manifests prominently already on systems below the point of "quantum advantage". For the prototypical transverse-field Ising model, we show that the required time resources to compete with classical simulations on around 40 qubits are already of the order of $10^{13}$ projective measurements, with an estimated running time of a few thousand years on superconducting hardware. These observations strongly suggest that the proposed hybrid method, in its present form, is unlikely to offer a sizeable advantage over conventional quantum Monte Carlo approaches.
