To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.

翻译：为了在基于量子比特或量子比特的量子计算机上模拟玻色子，必须通过将无限维局部希尔伯特空间截断为有限维来对理论进行正则化。在实际量子应用的探索中，了解截断误差可能有多大至关重要。通常，除非拥有良好的量子计算机，否则很难估计误差。本文表明，传统经典设备上的采样方法，特别是马尔可夫链蒙特卡洛，可以利用当前可用的合理计算资源解决这一问题。作为演示，我们将此思想应用于二维晶格上的标量场理论，其规模超越了精确对角化方法所能实现的范围。该方法可用于估计玻色子理论实际量子模拟所需的资源，也可用于验证相应量子模拟结果的有效性。