The key factor currently limiting the advancement of computational power of electronic computation is no longer the manufacturing density and speed of components, but rather their high energy consumption. While it has been widely argued that reversible computation can escape the fundamental Landauer limit of $k_B T\ln(2)$ Joules per irreversible computational step, there is disagreement around whether indefinitely reusable computation can be achieved without energy dissipation. Here we focus on the relatively simpler context of sampling problems, which take no input, so avoids modeling the energy costs of the observer perturbing the machine to change its input. Given an algorithm $A$ for generating samples from a distribution, we desire a device that can perpetually generate samples from that distribution driven entirely by Brownian motion. We show that such a device can efficiently execute algorithm $A$ in the sense that we must wait only $O(\text{time}(A)^2)$ between samples. We consider two output models: Las Vegas, which samples from the exact probability distribution every $4$ tries in expectation, and Monte Carlo, in which every try succeeds but the distribution is only approximated. We base our model on continuous-time random walks over the state space graph of a general computational machine, with a space-bounded Turing machine as one instantiation. The problem of sampling a computationally complex probability distribution with no energy dissipation informs our understanding of the energy requirements of computation, and may lead to more energy efficient randomized algorithms.

翻译：当前限制电子计算计算能力进步的关键因素已不再是元件的制造密度和速度，而是其高能耗。尽管可逆计算普遍被认为能逃脱每步不可逆计算耗散$k_B T\ln(2)$焦耳这一基础朗道尔极限，但对于是否能在无能量耗散的情况下实现无限可重复使用计算，学界仍存在分歧。本文聚焦于相对简单的采样问题场景——该类问题无需输入，从而避免了对观察者扰动机器以改变其输入所产生能量成本的建模。给定一个用于从某分布生成样本的算法$A$，我们期望构建一种完全由布朗运动驱动的设备，能永久生成该分布的样本。研究表明，此类设备能高效执行算法$A$，即我们只需等待$O(\text{time}(A)^2)$即可获得下个样本。我们考虑两种输出模型：拉斯维加斯模型（每4次尝试中期望恰好得到一次精确概率分布采样）和蒙特卡洛模型（每次尝试均成功但分布仅为近似）。我们将模型建立于通用计算设备状态空间图上的连续时间随机游走，并以空间有界图灵机作为具体实例。对计算复杂度较高的概率分布进行零能耗采样这一问题，有助于深化我们对计算能量需求的理解，并可能催生更节能的随机算法。