Stochastic p-bits for invertible logic

284Citations
Citations of this article
217Readers
Mendeley users who have this article in their library.

Abstract

Conventional semiconductor-based logic and nanomagnet-based memory devices are built out of stable, deterministic units such as standard metal-oxide semiconductor transistors, or nanomagnets with energy barriers in excess of ≈40-60 kT. In this paper, we show that unstable, stochastic units, which we call "p-bits," can be interconnected to create robust correlations that implement precise Boolean functions with impressive accuracy, comparable to standard digital circuits. At the same time, they are invertible, a unique property that is absent in standard 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 all possible inputs that are consistent with that output. First, we present a detailed implementation of an invertible gate to bring out the key role of a single three-terminal transistorlike building block to enable the construction of correlated p-bit networks. The results for this specific, CMOSassisted nanomagnet-based hardware implementation agree well with those from a universal model for p-bits, showing that p-bits need not be magnet based: any three-terminal tunable random bit generator should be suitable. We present a general algorithm for designing a Boltzmann machine (BM) with a symmetric connection matrix [J] (Jij = Jji) that implements a given truth table with p-bits. The [J] matrices are relatively sparse with a few unique weights for convenient hardware implementation. We then show how BM full adders can be interconnected in a partially directed manner (Jij ≠ Jji) to implement large logic operations such as 32-bit binary addition. Hundreds of stochastic p-bits get precisely correlated such that the correct answer out of 233 (≈8 × 109) possibilities can be extracted by looking at the statistical mode or majority vote of a number of time samples. With perfect directivity (Jji = 0) a small number of samples is enough, while for less directed connections more samples are needed, but even in the former case logical invertibility is largely preserved. This combination of digital accuracy and logical invertibility is enabled by the hybrid design that uses bidirectional BM units to construct circuits with partially directed interunit connections. We establish this key result with extensive examples including a 4-bit multiplier which in inverted mode functions as a factorizer.

Author supplied keywords

References Powered by Scopus

Neural networks and physical systems with emergent collective computational abilities.

13710Citations
N/AReaders
Get full text

Simulating physics with computers

5299Citations
N/AReaders
Get full text

Spin-torque switching with the giant spin hall effect of tantalum

3318Citations
N/AReaders
Get full text

Cited by Powered by Scopus

Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

1081Citations
N/AReaders
Get full text

Neuromorphic spintronics

675Citations
N/AReaders
Get full text

Opportunities and challenges for spintronics in the microelectronics industry

652Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Camsari, K. Y., Faria, R., Sutton, B. M., & Datta, S. (2017). Stochastic p-bits for invertible logic. Physical Review X, 7(3). https://doi.org/10.1103/PhysRevX.7.031014

Readers' Seniority

Tooltip

PhD / Post grad / Masters / Doc 76

57%

Professor / Associate Prof. 29

22%

Researcher 27

20%

Lecturer / Post doc 2

1%

Readers' Discipline

Tooltip

Engineering 76

59%

Physics and Astronomy 34

27%

Materials Science 14

11%

Computer Science 4

3%

Article Metrics

Tooltip
Mentions
Blog Mentions: 1
News Mentions: 4

Save time finding and organizing research with Mendeley

Sign up for free