The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout science, ranging from simulating quantum chemistry to discovering the thermodynamic phase diagram of quantum materials or high-density neutron stars. We present a classical algorithm that samples from a high-temperature quantum Gibbs state in a computational (product state) basis. The runtime grows polynomially with the number of particles, while error vanishes polynomially. This algorithm provides an alternative strategy to existing quantum Monte Carlo methods for overcoming the sign problem. Our result implies that measurement-based quantum computation on a Gibbs state can provide exponential speed up only at sufficiently low temperature, and further constrains what tasks can be exponentially faster on quantum computers.

翻译：模拟量子多体系统的计算复杂度通常随粒子数呈指数增长。这一巨大的计算成本阻碍了科学领域中许多重要问题的第一性原理模拟，范围涵盖从量子化学模拟到发现量子材料或高密度中子星的热力学相图。我们提出了一种经典算法，该算法能够在计算基（乘积态基）下对高温量子吉布斯态进行采样。该算法的运行时间随粒子数呈多项式增长，而误差则以多项式速度趋近于零。这一算法为现有量子蒙特卡洛方法克服符号问题提供了替代策略。我们的结果表明，基于吉布斯态的测量量子计算仅在足够低的温度下才能实现指数加速，并进一步界定了量子计算机上可实现指数加速的任务范围。