[论文解读] Stochastic P-bits for Probabilistic Spin Logic

Kerem Y. Çamsarı, Rafatul Faria+2 more|arXiv (Cornell University)|Oct 3, 2016

Quantum Computing Algorithms and Architecture被引用 3

一句话总结

本文提出随机p位——一种随机的三端子单元，通过形成稳健且相关的网络，实现概率自旋逻辑，从而准确执行布尔函数。关键贡献在于采用部分定向连接的双向p位混合电路设计，在32位加法和可逆性等操作中实现高精度，输出可逆向推导出所有有效输入，通过一个4位乘法器作为因数分解器得到验证。

ABSTRACT

Conventional logic and memory devices are built out of deterministic units such as transistors, or magnets with energy barriers in excess of 40-60 kT. We show that stochastic units, p-bits, can be interconnected to create robust correlations that implement Boolean functions with impressive accuracy, comparable to standard circuits. Also they are invertible, a unique property that is absent in digital circuits. When operated in the direct mode, the input is clamped, and the network provides the correct output. In the inverted mode, the output is clamped, and the network fluctuates among possible inputs consistent with that output. We present an implementation of an invertible gate to bring out the key role of a three-terminal building block to enable the construction of correlated p-bit networks. The results for this implementation agree well with those from a universal model, showing that p-bits need not be magnet-based: any three-terminal tunable random bit generator should be suitable. We present an algorithm for designing a Boltzmann machine (BM) with symmetric connections that implements a given truth table. We then show how BM Full Adders can be interconnected in a partially directed manner to implement large operations such as 32-bit addition. Hundreds of p-bits get precisely correlated such that the correct answer out of 2^33 possibilities can be extracted by looking at the mode of a number of time samples. With perfect directivity a small number of samples is enough, while for less directed connections more samples are needed, but even in the former case invertibility is largely preserved. This combination of accuracy and invertibility is enabled by the hybrid design that uses bidirectional units to construct circuits with partially directed connections. We establish this result with examples including a 4-bit multiplier which in inverted mode functions as a factorizer.

研究动机与目标

• 开发一种基于随机p位而非确定性晶体管或磁体的新类逻辑与存储器件。
• 通过实现可逆性（即输出可逆向推导出所有可能输入）来克服传统数字电路的局限性。
• 证明p位网络可实现复杂操作，如32位加法和4位乘法，且精度极高。
• 表明p位无需基于磁性材料，可为任意三端子可调随机位生成器。
• 建立一种用于实现任意真值表的对称连接玻尔兹曼机的设计算法。

提出的方法

• 基于对称连接的玻尔兹曼机，设计p位网络的通用模型，以实现任意布尔函数。
• 通过三端子基本单元实现可逆门，以支持p位网络中的双向信息流与相关性。
• 通过组合双向p位单元构建部分定向网络，在保持可逆性的同时支持大规模计算。
• 通过p位状态的时间采样，从2^33种可能状态中提取32位加法的最可能输出。
• 应用设计算法，将给定真值表映射为使用p位单元的对称连接玻尔兹曼机。
• 通过在部分定向拓扑中互连全加器，展示可扩展性，以执行大规模算术运算。

实验结果

研究问题

• RQ1 随机p位能否用于构建高精度、鲁棒的逻辑电路，使其在特定任务中优于确定性电路？
• RQ2 当连接为部分定向而非完全双向时，如何在p位网络中保持可逆性？
• RQ3 三端子可调随机位生成器在实现p位网络中的相关性与可逆性方面起什么作用？
• RQ4 p位网络在多大程度上可扩展以实现如32位加法或4位乘法等复杂操作？
• RQ5 p位能否不依赖磁性材料实现，而采用其他物理实现方式？

主要发现

• p位网络在32位加法中实现高精度，通过时间采样从2^33种可能状态中正确提取结果。
• 即使采用部分定向连接，可逆性仍被保持：当输出被固定时，网络会探索所有与之一致的输入，从而实现如因数分解等函数。
• 4位乘法器在反向模式下运行时，成功作为因数分解器，识别出所有产生给定输出的输入对。
• 物理实现结果与通用模型的预测高度一致，验证了设计方法的有效性。
• 三端子p位单元对于实现双向相关性与可逆性至关重要，是该架构的关键使能组件。
• 该方法具有通用性：任何三端子可调随机位生成器均可作为p位，而不仅限于磁性系统。