tutorial: p-bits for probabilistic spin logic · 2020. 1. 21. · shuvro chowdhury anirudh...

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Tutorial: p-bits for Probabilistic Spin Logic Kerem Y. Camsari Postdoctoral Researcher Joint University Microelectronics Program

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Page 1: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Tutorial: p-bits for Probabilistic Spin Logic

Kerem Y. Camsari Postdoctoral Researcher

Joint University Microelectronics Program

Page 2: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Shuvro Chowdhury

Anirudh Ghantasala

Orchi HassanBrian M Sutton

Punyashloka Debashis

Supriyo DattaZhihong Chen

p-bits for Probabilistic Spin Logic (PSL)

Zeeshan Pervaiz

Ramtin Zand (UCF)

Sayeef Salahuddin (UC Berkeley)

Rafatul Faria

(1) Camsari et al., Phys. Rev. X (2017) (Computing with p-bits)

(2) Camsari et al., IEEE EDL (2017) (Stochastic MTJ-based p-bit)

(3) Camsari et al., arXiv:1810.XXXX (2018) (Quantum Annealing with p-bits)

(4) Camsari et al., arXiv:1809.04028(2018) (Review of PSL)

Ron DeMara(UCF)

BehtashBehin-Aein (GF)

Page 3: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

bits, p-bits and q-bits

digital circuits

bits

“0” or “1”Deterministic

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transistors / Stable magnets

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p-bits

Stochastic“0” or “1”

p-circuits

Unstable magnets

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Stable magnets

p-computer

SingleSpin

q-bitsSuperposition

of“0” and “1”

q-circuitsq-computer

Feynman 1982

Digital electronics .. notion of a “bit” , charge on a capacitor

Experimental data by Debashis / Chen

I will make a concrete p-bit to q-bit connection

Page 4: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Application space for p-bitsQuantum Computing

inspired

Adder Subtractor

(1) Subset Sum Problem

Multiplier Divider

(2) Prime Factorization Camsari et al., Phys. Rev. X, (2017)

DBN’s using p-bits

Zand et al., GLSVLSI (2018)

Combinatorial Optimization (e.g. TSP)

Sutton et al., Sci. Rep., (2017)

Machine Learning inspired

Quantum circuits emulated with p-bits

Camsari et al., arXiv:1810.XXXX

Bayesian Networks

Faria et al., AIP Advances (2018)

Page 5: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

�5

• How to build a p-bit?

• Quantum Computing-inspired (Reciprocal Networks)

• Machine Learning-inspired (Reciprocal and Non-reciprocal Networks)

Page 6: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

**update order of p-bits: needs to be

sequential or asynchronous

p-bit is a binary stochastic neuron

Synapse: Linear weighted sum

(2)

Basic Equations

p-bit: Stochastic binary neuron

(1)

***speed of synapse: -needs to be much faster

than p-bit

p-bit

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Need for hardware p-bits

Hardware-specificfeatures

* Hardware p-bit is a three-terminal device

so that it can be interconnected

as a transistor-like building block

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*** Update order: RBM qualification

Page 7: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

FWHM ~ 170 ps

• Circular low barrier magnets

can be fast

⌧�1 / ↵�HD<latexit sha1_base64="EereAcVbC0smNquP8AH5qpyWIlI=">AAACJnicbZDLSgMxFIYzXmu9VV26CRZBF8qMCLos6qLLCrYKnVrOpJk2NJkJyRmhDH0GX8MXcKtv4E7EnSufw/Sy8PZD4OM/53By/khLYdH3372Z2bn5hcXCUnF5ZXVtvbSx2bBpZhivs1Sm5iYCy6VIeB0FSn6jDQcVSX4d9c9H9es7bqxIkyscaN5S0E1ELBigs9ql/dDGNETIbvODYEhDbVKNKQ1B6h5QGnZBKaDV9gVtl8r+oT8W/QvBFMpkqlq79Bl2UpYpniCTYG0z8DW2cjAomOTDYphZroH1ocubDhNQ3Lby8UlDuuucDo1T416CdOx+n8hBWTtQketUgD37uzYy/6s1M4xPW7lIdIY8YZNFcSapO3qUD+0IwxnKgQNgRri/UtYDAwxdij+2RAb6HIdFF0zwO4a/0Dg6DBxfHpcrZ9OICmSb7JA9EpATUiFVUiN1wsg9eSRP5Nl78F68V+9t0jrjTWe2yA95H18qf6TI</latexit><latexit sha1_base64="EereAcVbC0smNquP8AH5qpyWIlI=">AAACJnicbZDLSgMxFIYzXmu9VV26CRZBF8qMCLos6qLLCrYKnVrOpJk2NJkJyRmhDH0GX8MXcKtv4E7EnSufw/Sy8PZD4OM/53By/khLYdH3372Z2bn5hcXCUnF5ZXVtvbSx2bBpZhivs1Sm5iYCy6VIeB0FSn6jDQcVSX4d9c9H9es7bqxIkyscaN5S0E1ELBigs9ql/dDGNETIbvODYEhDbVKNKQ1B6h5QGnZBKaDV9gVtl8r+oT8W/QvBFMpkqlq79Bl2UpYpniCTYG0z8DW2cjAomOTDYphZroH1ocubDhNQ3Lby8UlDuuucDo1T416CdOx+n8hBWTtQketUgD37uzYy/6s1M4xPW7lIdIY8YZNFcSapO3qUD+0IwxnKgQNgRri/UtYDAwxdij+2RAb6HIdFF0zwO4a/0Dg6DBxfHpcrZ9OICmSb7JA9EpATUiFVUiN1wsg9eSRP5Nl78F68V+9t0jrjTWe2yA95H18qf6TI</latexit><latexit sha1_base64="EereAcVbC0smNquP8AH5qpyWIlI=">AAACJnicbZDLSgMxFIYzXmu9VV26CRZBF8qMCLos6qLLCrYKnVrOpJk2NJkJyRmhDH0GX8MXcKtv4E7EnSufw/Sy8PZD4OM/53By/khLYdH3372Z2bn5hcXCUnF5ZXVtvbSx2bBpZhivs1Sm5iYCy6VIeB0FSn6jDQcVSX4d9c9H9es7bqxIkyscaN5S0E1ELBigs9ql/dDGNETIbvODYEhDbVKNKQ1B6h5QGnZBKaDV9gVtl8r+oT8W/QvBFMpkqlq79Bl2UpYpniCTYG0z8DW2cjAomOTDYphZroH1ocubDhNQ3Lby8UlDuuucDo1T416CdOx+n8hBWTtQketUgD37uzYy/6s1M4xPW7lIdIY8YZNFcSapO3qUD+0IwxnKgQNgRri/UtYDAwxdij+2RAb6HIdFF0zwO4a/0Dg6DBxfHpcrZ9OICmSb7JA9EpATUiFVUiN1wsg9eSRP5Nl78F68V+9t0jrjTWe2yA95H18qf6TI</latexit><latexit sha1_base64="EereAcVbC0smNquP8AH5qpyWIlI=">AAACJnicbZDLSgMxFIYzXmu9VV26CRZBF8qMCLos6qLLCrYKnVrOpJk2NJkJyRmhDH0GX8MXcKtv4E7EnSufw/Sy8PZD4OM/53By/khLYdH3372Z2bn5hcXCUnF5ZXVtvbSx2bBpZhivs1Sm5iYCy6VIeB0FSn6jDQcVSX4d9c9H9es7bqxIkyscaN5S0E1ELBigs9ql/dDGNETIbvODYEhDbVKNKQ1B6h5QGnZBKaDV9gVtl8r+oT8W/QvBFMpkqlq79Bl2UpYpniCTYG0z8DW2cjAomOTDYphZroH1ocubDhNQ3Lby8UlDuuucDo1T416CdOx+n8hBWTtQketUgD37uzYy/6s1M4xPW7lIdIY8YZNFcSapO3qUD+0IwxnKgQNgRri/UtYDAwxdij+2RAb6HIdFF0zwO4a/0Dg6DBxfHpcrZ9OICmSb7JA9EpATUiFVUiN1wsg9eSRP5Nl78F68V+9t0jrjTWe2yA95H18qf6TI</latexit>

⌧0 ⇡ ps� ns<latexit sha1_base64="EQYdcs5nFKReU8NRtBEQYFB2f8Y=">AAACGHicbZDLSgMxFIYz3q23qstugkVwo8yIoEvRjcsK9gKdoZxJMxqayYTkjFhKF76GL+BW38CduHXnC/gcpu0stPWHwMd/zuGc/LGWwqLvf3lz8wuLS8srq6W19Y3NrfL2TsNmuWG8zjKZmVYMlkuheB0FSt7ShkMaS96Me5ejevOeGysydYN9zaMUbpVIBAN0VqdcCW1CQ4S849MQtDbZA9WWHlJlaadc9Y/8segsBAVUSaFap/wddjOWp1whk2BtO/A1RgMwKJjkw1KYW66B9eCWtx0qSLmNBuNPDOm+c7o0yYx7CunY/T0xgNTafhq7zhTwzk7XRuZ/tXaOyVk0EErnyBWbLEpySTGjo0RoVxjOUPYdADPC3UrZHRhg6HL7syU20OM4LLlggukYZqFxfBQ4vj6pnl8UEa2QCtkjByQgp+ScXJEaqRNGHskzeSGv3pP35r17H5PWOa+Y2SV/5H3+AGy3nzI=</latexit><latexit sha1_base64="EQYdcs5nFKReU8NRtBEQYFB2f8Y=">AAACGHicbZDLSgMxFIYz3q23qstugkVwo8yIoEvRjcsK9gKdoZxJMxqayYTkjFhKF76GL+BW38CduHXnC/gcpu0stPWHwMd/zuGc/LGWwqLvf3lz8wuLS8srq6W19Y3NrfL2TsNmuWG8zjKZmVYMlkuheB0FSt7ShkMaS96Me5ejevOeGysydYN9zaMUbpVIBAN0VqdcCW1CQ4S849MQtDbZA9WWHlJlaadc9Y/8segsBAVUSaFap/wddjOWp1whk2BtO/A1RgMwKJjkw1KYW66B9eCWtx0qSLmNBuNPDOm+c7o0yYx7CunY/T0xgNTafhq7zhTwzk7XRuZ/tXaOyVk0EErnyBWbLEpySTGjo0RoVxjOUPYdADPC3UrZHRhg6HL7syU20OM4LLlggukYZqFxfBQ4vj6pnl8UEa2QCtkjByQgp+ScXJEaqRNGHskzeSGv3pP35r17H5PWOa+Y2SV/5H3+AGy3nzI=</latexit><latexit sha1_base64="EQYdcs5nFKReU8NRtBEQYFB2f8Y=">AAACGHicbZDLSgMxFIYz3q23qstugkVwo8yIoEvRjcsK9gKdoZxJMxqayYTkjFhKF76GL+BW38CduHXnC/gcpu0stPWHwMd/zuGc/LGWwqLvf3lz8wuLS8srq6W19Y3NrfL2TsNmuWG8zjKZmVYMlkuheB0FSt7ShkMaS96Me5ejevOeGysydYN9zaMUbpVIBAN0VqdcCW1CQ4S849MQtDbZA9WWHlJlaadc9Y/8segsBAVUSaFap/wddjOWp1whk2BtO/A1RgMwKJjkw1KYW66B9eCWtx0qSLmNBuNPDOm+c7o0yYx7CunY/T0xgNTafhq7zhTwzk7XRuZ/tXaOyVk0EErnyBWbLEpySTGjo0RoVxjOUPYdADPC3UrZHRhg6HL7syU20OM4LLlggukYZqFxfBQ4vj6pnl8UEa2QCtkjByQgp+ScXJEaqRNGHskzeSGv3pP35r17H5PWOa+Y2SV/5H3+AGy3nzI=</latexit><latexit sha1_base64="EQYdcs5nFKReU8NRtBEQYFB2f8Y=">AAACGHicbZDLSgMxFIYz3q23qstugkVwo8yIoEvRjcsK9gKdoZxJMxqayYTkjFhKF76GL+BW38CduHXnC/gcpu0stPWHwMd/zuGc/LGWwqLvf3lz8wuLS8srq6W19Y3NrfL2TsNmuWG8zjKZmVYMlkuheB0FSt7ShkMaS96Me5ejevOeGysydYN9zaMUbpVIBAN0VqdcCW1CQ4S849MQtDbZA9WWHlJlaadc9Y/8segsBAVUSaFap/wddjOWp1whk2BtO/A1RgMwKJjkw1KYW66B9eCWtx0qSLmNBuNPDOm+c7o0yYx7CunY/T0xgNTafhq7zhTwzk7XRuZ/tXaOyVk0EErnyBWbLEpySTGjo0RoVxjOUPYdADPC3UrZHRhg6HL7syU20OM4LLlggukYZqFxfBQ4vj6pnl8UEa2QCtkjByQgp+ScXJEaqRNGHskzeSGv3pP35r17H5PWOa+Y2SV/5H3+AGy3nzI=</latexit>

Low-barrier magnets (LBM) are natural p-bits

RAP > RP<latexit sha1_base64="/F0kPbip3OrcyWeyNShicDUbiNs=">AAAB+3icbZDLSsNAFIZP6q3WW6xLN4NFcFUSEXQlVTcuo9gLtCFMppN26OTCzEQsIa/ixoUibn0Rd76NkzYLbf1h4OM/53DO/H7CmVSW9W1UVlbX1jeqm7Wt7Z3dPXO/3pFxKghtk5jHoudjSTmLaFsxxWkvERSHPqddf3JT1LuPVEgWRw9qmlA3xKOIBYxgpS3PrA9kgO697MrJ0WUBTu6ZDatpzYSWwS6hAaUcz/waDGOShjRShGMp+7aVKDfDQjHCaV4bpJImmEzwiPY1Rjik0s1mt+foWDtDFMRCv0ihmft7IsOhlNPQ150hVmO5WCvM/2r9VAUXbsaiJFU0IvNFQcqRilERBBoyQYniUw2YCKZvRWSMBSZKx1XTIdiLX16GzmnTtpr23VmjdV3GUYVDOIITsOEcWnALDrSBwBM8wyu8GbnxYrwbH/PWilHOHMAfGZ8/cTmTZQ==</latexit><latexit sha1_base64="/F0kPbip3OrcyWeyNShicDUbiNs=">AAAB+3icbZDLSsNAFIZP6q3WW6xLN4NFcFUSEXQlVTcuo9gLtCFMppN26OTCzEQsIa/ixoUibn0Rd76NkzYLbf1h4OM/53DO/H7CmVSW9W1UVlbX1jeqm7Wt7Z3dPXO/3pFxKghtk5jHoudjSTmLaFsxxWkvERSHPqddf3JT1LuPVEgWRw9qmlA3xKOIBYxgpS3PrA9kgO697MrJ0WUBTu6ZDatpzYSWwS6hAaUcz/waDGOShjRShGMp+7aVKDfDQjHCaV4bpJImmEzwiPY1Rjik0s1mt+foWDtDFMRCv0ihmft7IsOhlNPQ150hVmO5WCvM/2r9VAUXbsaiJFU0IvNFQcqRilERBBoyQYniUw2YCKZvRWSMBSZKx1XTIdiLX16GzmnTtpr23VmjdV3GUYVDOIITsOEcWnALDrSBwBM8wyu8GbnxYrwbH/PWilHOHMAfGZ8/cTmTZQ==</latexit><latexit sha1_base64="/F0kPbip3OrcyWeyNShicDUbiNs=">AAAB+3icbZDLSsNAFIZP6q3WW6xLN4NFcFUSEXQlVTcuo9gLtCFMppN26OTCzEQsIa/ixoUibn0Rd76NkzYLbf1h4OM/53DO/H7CmVSW9W1UVlbX1jeqm7Wt7Z3dPXO/3pFxKghtk5jHoudjSTmLaFsxxWkvERSHPqddf3JT1LuPVEgWRw9qmlA3xKOIBYxgpS3PrA9kgO697MrJ0WUBTu6ZDatpzYSWwS6hAaUcz/waDGOShjRShGMp+7aVKDfDQjHCaV4bpJImmEzwiPY1Rjik0s1mt+foWDtDFMRCv0ihmft7IsOhlNPQ150hVmO5WCvM/2r9VAUXbsaiJFU0IvNFQcqRilERBBoyQYniUw2YCKZvRWSMBSZKx1XTIdiLX16GzmnTtpr23VmjdV3GUYVDOIITsOEcWnALDrSBwBM8wyu8GbnxYrwbH/PWilHOHMAfGZ8/cTmTZQ==</latexit><latexit sha1_base64="/F0kPbip3OrcyWeyNShicDUbiNs=">AAAB+3icbZDLSsNAFIZP6q3WW6xLN4NFcFUSEXQlVTcuo9gLtCFMppN26OTCzEQsIa/ixoUibn0Rd76NkzYLbf1h4OM/53DO/H7CmVSW9W1UVlbX1jeqm7Wt7Z3dPXO/3pFxKghtk5jHoudjSTmLaFsxxWkvERSHPqddf3JT1LuPVEgWRw9qmlA3xKOIBYxgpS3PrA9kgO697MrJ0WUBTu6ZDatpzYSWwS6hAaUcz/waDGOShjRShGMp+7aVKDfDQjHCaV4bpJImmEzwiPY1Rjik0s1mt+foWDtDFMRCv0ihmft7IsOhlNPQ150hVmO5WCvM/2r9VAUXbsaiJFU0IvNFQcqRilERBBoyQYniUw2YCKZvRWSMBSZKx1XTIdiLX16GzmnTtpr23VmjdV3GUYVDOIITsOEcWnALDrSBwBM8wyu8GbnxYrwbH/PWilHOHMAfGZ8/cTmTZQ==</latexit>

-1 +1-1 0 10

0.01

0.02

m

P

∆ = 0 kTτ ≈ ps− ns

∆ = 0 kT

Reducing anisotropy

• > PMA thickness• Circular

Reducing magnetic moment

• Low volume• Low sat. mag.

P

m-1 +1-1 0 10

0.2

0.4

0.6

MTJ Resistance

time

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� = 40� 60 kT<latexit sha1_base64="LRBvsCPbUIzJjYAe5S+iMkp/ieE=">AAACF3icbZDJSgNBEIZ7XGPcRr3ppTEIXgwzEtSLENSDxwjZIBNCT6cmadKz0F0jhBDwNXwBr/oG3sSrR1/A57CzHEziDw0ff1VR1b+fSKHRcb6tpeWV1bX1zEZ2c2t7Z9fe26/qOFUcKjyWsar7TIMUEVRQoIR6ooCFvoSa37sd1WuPoLSIozL2E2iGrBOJQHCGxmrZh54OqHcHEhm9pgWHntELh3q0V6YtO+fknbHoIrhTyJGpSi37x2vHPA0hQi6Z1g3XSbA5YAoFlzDMeqmGhPEe60DDYMRC0M3B+A9DemKcNg1iZV6EdOz+nRiwUOt+6JvOkGFXz9dG5n+1RorBVXMgoiRFiPhkUZBKijEdBULbQgFH2TfAuBLmVsq7TDGOJraZLb5iPcBh1gTjzsewCNXzvGv4oZAr3kwjypAjckxOiUsuSZHckxKpEE6eyAt5JW/Ws/VufVifk9YlazpzQGZkff0CiWOc4Q==</latexit><latexit sha1_base64="LRBvsCPbUIzJjYAe5S+iMkp/ieE=">AAACF3icbZDJSgNBEIZ7XGPcRr3ppTEIXgwzEtSLENSDxwjZIBNCT6cmadKz0F0jhBDwNXwBr/oG3sSrR1/A57CzHEziDw0ff1VR1b+fSKHRcb6tpeWV1bX1zEZ2c2t7Z9fe26/qOFUcKjyWsar7TIMUEVRQoIR6ooCFvoSa37sd1WuPoLSIozL2E2iGrBOJQHCGxmrZh54OqHcHEhm9pgWHntELh3q0V6YtO+fknbHoIrhTyJGpSi37x2vHPA0hQi6Z1g3XSbA5YAoFlzDMeqmGhPEe60DDYMRC0M3B+A9DemKcNg1iZV6EdOz+nRiwUOt+6JvOkGFXz9dG5n+1RorBVXMgoiRFiPhkUZBKijEdBULbQgFH2TfAuBLmVsq7TDGOJraZLb5iPcBh1gTjzsewCNXzvGv4oZAr3kwjypAjckxOiUsuSZHckxKpEE6eyAt5JW/Ws/VufVifk9YlazpzQGZkff0CiWOc4Q==</latexit><latexit sha1_base64="LRBvsCPbUIzJjYAe5S+iMkp/ieE=">AAACF3icbZDJSgNBEIZ7XGPcRr3ppTEIXgwzEtSLENSDxwjZIBNCT6cmadKz0F0jhBDwNXwBr/oG3sSrR1/A57CzHEziDw0ff1VR1b+fSKHRcb6tpeWV1bX1zEZ2c2t7Z9fe26/qOFUcKjyWsar7TIMUEVRQoIR6ooCFvoSa37sd1WuPoLSIozL2E2iGrBOJQHCGxmrZh54OqHcHEhm9pgWHntELh3q0V6YtO+fknbHoIrhTyJGpSi37x2vHPA0hQi6Z1g3XSbA5YAoFlzDMeqmGhPEe60DDYMRC0M3B+A9DemKcNg1iZV6EdOz+nRiwUOt+6JvOkGFXz9dG5n+1RorBVXMgoiRFiPhkUZBKijEdBULbQgFH2TfAuBLmVsq7TDGOJraZLb5iPcBh1gTjzsewCNXzvGv4oZAr3kwjypAjckxOiUsuSZHckxKpEE6eyAt5JW/Ws/VufVifk9YlazpzQGZkff0CiWOc4Q==</latexit><latexit sha1_base64="LRBvsCPbUIzJjYAe5S+iMkp/ieE=">AAACF3icbZDJSgNBEIZ7XGPcRr3ppTEIXgwzEtSLENSDxwjZIBNCT6cmadKz0F0jhBDwNXwBr/oG3sSrR1/A57CzHEziDw0ff1VR1b+fSKHRcb6tpeWV1bX1zEZ2c2t7Z9fe26/qOFUcKjyWsar7TIMUEVRQoIR6ooCFvoSa37sd1WuPoLSIozL2E2iGrBOJQHCGxmrZh54OqHcHEhm9pgWHntELh3q0V6YtO+fknbHoIrhTyJGpSi37x2vHPA0hQi6Z1g3XSbA5YAoFlzDMeqmGhPEe60DDYMRC0M3B+A9DemKcNg1iZV6EdOz+nRiwUOt+6JvOkGFXz9dG5n+1RorBVXMgoiRFiPhkUZBKijEdBULbQgFH2TfAuBLmVsq7TDGOJraZLb5iPcBh1gTjzsewCNXzvGv4oZAr3kwjypAjckxOiUsuSZHckxKpEE6eyAt5JW/Ws/VufVifk9YlazpzQGZkff0CiWOc4Q==</latexit>

Page 8: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

1T/1MTJMRAM

1� 100 K⌦<latexit sha1_base64="6RLWgeL+ChNd64+ThT+j8YiFHVA=">AAAB/nicbVDLSgMxFM3UV62vUXHlJlgEN5ZEBF0W3QgurGAf0BlKJs20oUlmSDJCGQr+ihsXirj1O9z5N6aPhbYeuHA4517uvSdKBTcWoW+vsLS8srpWXC9tbG5t7/i7ew2TZJqyOk1EolsRMUxwxeqWW8FaqWZERoI1o8H12G8+Mm14oh7sMGWhJD3FY06JdVLHPwhMDPEpRggGEN4Gd5L1COz4ZVRBE8BFgmekDGaodfyvoJvQTDJlqSDGtDFKbZgTbTkVbFQKMsNSQgekx9qOKiKZCfPJ+SN47JQujBPtSlk4UX9P5EQaM5SR65TE9s28Nxb/89qZjS/DnKs0s0zR6aI4E9AmcJwF7HLNqBVDRwjV3N0KaZ9oQq1LrORCwPMvL5LGWQWjCr4/L1evZnEUwSE4AicAgwtQBTegBuqAghw8g1fw5j15L9679zFtLXizmX3wB97nD2KIky0=</latexit><latexit sha1_base64="6RLWgeL+ChNd64+ThT+j8YiFHVA=">AAAB/nicbVDLSgMxFM3UV62vUXHlJlgEN5ZEBF0W3QgurGAf0BlKJs20oUlmSDJCGQr+ihsXirj1O9z5N6aPhbYeuHA4517uvSdKBTcWoW+vsLS8srpWXC9tbG5t7/i7ew2TZJqyOk1EolsRMUxwxeqWW8FaqWZERoI1o8H12G8+Mm14oh7sMGWhJD3FY06JdVLHPwhMDPEpRggGEN4Gd5L1COz4ZVRBE8BFgmekDGaodfyvoJvQTDJlqSDGtDFKbZgTbTkVbFQKMsNSQgekx9qOKiKZCfPJ+SN47JQujBPtSlk4UX9P5EQaM5SR65TE9s28Nxb/89qZjS/DnKs0s0zR6aI4E9AmcJwF7HLNqBVDRwjV3N0KaZ9oQq1LrORCwPMvL5LGWQWjCr4/L1evZnEUwSE4AicAgwtQBTegBuqAghw8g1fw5j15L9679zFtLXizmX3wB97nD2KIky0=</latexit><latexit sha1_base64="6RLWgeL+ChNd64+ThT+j8YiFHVA=">AAAB/nicbVDLSgMxFM3UV62vUXHlJlgEN5ZEBF0W3QgurGAf0BlKJs20oUlmSDJCGQr+ihsXirj1O9z5N6aPhbYeuHA4517uvSdKBTcWoW+vsLS8srpWXC9tbG5t7/i7ew2TZJqyOk1EolsRMUxwxeqWW8FaqWZERoI1o8H12G8+Mm14oh7sMGWhJD3FY06JdVLHPwhMDPEpRggGEN4Gd5L1COz4ZVRBE8BFgmekDGaodfyvoJvQTDJlqSDGtDFKbZgTbTkVbFQKMsNSQgekx9qOKiKZCfPJ+SN47JQujBPtSlk4UX9P5EQaM5SR65TE9s28Nxb/89qZjS/DnKs0s0zR6aI4E9AmcJwF7HLNqBVDRwjV3N0KaZ9oQq1LrORCwPMvL5LGWQWjCr4/L1evZnEUwSE4AicAgwtQBTegBuqAghw8g1fw5j15L9679zFtLXizmX3wB97nD2KIky0=</latexit><latexit sha1_base64="6RLWgeL+ChNd64+ThT+j8YiFHVA=">AAAB/nicbVDLSgMxFM3UV62vUXHlJlgEN5ZEBF0W3QgurGAf0BlKJs20oUlmSDJCGQr+ihsXirj1O9z5N6aPhbYeuHA4517uvSdKBTcWoW+vsLS8srpWXC9tbG5t7/i7ew2TZJqyOk1EolsRMUxwxeqWW8FaqWZERoI1o8H12G8+Mm14oh7sMGWhJD3FY06JdVLHPwhMDPEpRggGEN4Gd5L1COz4ZVRBE8BFgmekDGaodfyvoJvQTDJlqSDGtDFKbZgTbTkVbFQKMsNSQgekx9qOKiKZCfPJ+SN47JQujBPtSlk4UX9P5EQaM5SR65TE9s28Nxb/89qZjS/DnKs0s0zR6aI4E9AmcJwF7HLNqBVDRwjV3N0KaZ9oQq1LrORCwPMvL5LGWQWjCr4/L1evZnEUwSE4AicAgwtQBTegBuqAghw8g1fw5j15L9679zFtLXizmX3wB97nD2KIky0=</latexit>

⇠ 10 K⌦<latexit sha1_base64="YTGCVUA8y5kQ19SChCDdMaelmOc=">AAAB/3icbVA9SwNBEJ2LXzF+nQo2NotBsAp3ImgZtBEsjGA+IHeEvc1esmR379jdE0JM4V+xsVDE1r9h579xk1yhiQ8GHu/NMDMvSjnTxvO+ncLS8srqWnG9tLG5tb3j7u41dJIpQusk4YlqRVhTziStG2Y4baWKYhFx2owGVxO/+UCVZom8N8OUhgL3JIsZwcZKHfcg0EwEOka+hwKEboJbQXsYddyyV/GmQIvEz0kZctQ67lfQTUgmqDSEY63bvpeacISVYYTTcSnINE0xGeAebVsqsaA6HE3vH6Njq3RRnChb0qCp+ntihIXWQxHZToFNX897E/E/r52Z+CIcMZlmhkoyWxRnHJkETcJAXaYoMXxoCSaK2VsR6WOFibGRlWwI/vzLi6RxWvG9in93Vq5e5nEU4RCO4AR8OIcqXEMN6kDgEZ7hFd6cJ+fFeXc+Zq0FJ5/Zhz9wPn8AQleUTg==</latexit><latexit sha1_base64="YTGCVUA8y5kQ19SChCDdMaelmOc=">AAAB/3icbVA9SwNBEJ2LXzF+nQo2NotBsAp3ImgZtBEsjGA+IHeEvc1esmR379jdE0JM4V+xsVDE1r9h579xk1yhiQ8GHu/NMDMvSjnTxvO+ncLS8srqWnG9tLG5tb3j7u41dJIpQusk4YlqRVhTziStG2Y4baWKYhFx2owGVxO/+UCVZom8N8OUhgL3JIsZwcZKHfcg0EwEOka+hwKEboJbQXsYddyyV/GmQIvEz0kZctQ67lfQTUgmqDSEY63bvpeacISVYYTTcSnINE0xGeAebVsqsaA6HE3vH6Njq3RRnChb0qCp+ntihIXWQxHZToFNX897E/E/r52Z+CIcMZlmhkoyWxRnHJkETcJAXaYoMXxoCSaK2VsR6WOFibGRlWwI/vzLi6RxWvG9in93Vq5e5nEU4RCO4AR8OIcqXEMN6kDgEZ7hFd6cJ+fFeXc+Zq0FJ5/Zhz9wPn8AQleUTg==</latexit><latexit sha1_base64="YTGCVUA8y5kQ19SChCDdMaelmOc=">AAAB/3icbVA9SwNBEJ2LXzF+nQo2NotBsAp3ImgZtBEsjGA+IHeEvc1esmR379jdE0JM4V+xsVDE1r9h579xk1yhiQ8GHu/NMDMvSjnTxvO+ncLS8srqWnG9tLG5tb3j7u41dJIpQusk4YlqRVhTziStG2Y4baWKYhFx2owGVxO/+UCVZom8N8OUhgL3JIsZwcZKHfcg0EwEOka+hwKEboJbQXsYddyyV/GmQIvEz0kZctQ67lfQTUgmqDSEY63bvpeacISVYYTTcSnINE0xGeAebVsqsaA6HE3vH6Njq3RRnChb0qCp+ntihIXWQxHZToFNX897E/E/r52Z+CIcMZlmhkoyWxRnHJkETcJAXaYoMXxoCSaK2VsR6WOFibGRlWwI/vzLi6RxWvG9in93Vq5e5nEU4RCO4AR8OIcqXEMN6kDgEZ7hFd6cJ+fFeXc+Zq0FJ5/Zhz9wPn8AQleUTg==</latexit><latexit sha1_base64="YTGCVUA8y5kQ19SChCDdMaelmOc=">AAAB/3icbVA9SwNBEJ2LXzF+nQo2NotBsAp3ImgZtBEsjGA+IHeEvc1esmR379jdE0JM4V+xsVDE1r9h579xk1yhiQ8GHu/NMDMvSjnTxvO+ncLS8srqWnG9tLG5tb3j7u41dJIpQusk4YlqRVhTziStG2Y4baWKYhFx2owGVxO/+UCVZom8N8OUhgL3JIsZwcZKHfcg0EwEOka+hwKEboJbQXsYddyyV/GmQIvEz0kZctQ67lfQTUgmqDSEY63bvpeacISVYYTTcSnINE0xGeAebVsqsaA6HE3vH6Njq3RRnChb0qCp+ntihIXWQxHZToFNX897E/E/r52Z+CIcMZlmhkoyWxRnHJkETcJAXaYoMXxoCSaK2VsR6WOFibGRlWwI/vzLi6RxWvG9in93Vq5e5nEU4RCO4AR8OIcqXEMN6kDgEZ7hFd6cJ+fFeXc+Zq0FJ5/Zhz9wPn8AQleUTg==</latexit>

Hardware mapping for p-bit

time (ns)

MTJ Resistance

⇠ 10 K⌦<latexit sha1_base64="YTGCVUA8y5kQ19SChCDdMaelmOc=">AAAB/3icbVA9SwNBEJ2LXzF+nQo2NotBsAp3ImgZtBEsjGA+IHeEvc1esmR379jdE0JM4V+xsVDE1r9h579xk1yhiQ8GHu/NMDMvSjnTxvO+ncLS8srqWnG9tLG5tb3j7u41dJIpQusk4YlqRVhTziStG2Y4baWKYhFx2owGVxO/+UCVZom8N8OUhgL3JIsZwcZKHfcg0EwEOka+hwKEboJbQXsYddyyV/GmQIvEz0kZctQ67lfQTUgmqDSEY63bvpeacISVYYTTcSnINE0xGeAebVsqsaA6HE3vH6Njq3RRnChb0qCp+ntihIXWQxHZToFNX897E/E/r52Z+CIcMZlmhkoyWxRnHJkETcJAXaYoMXxoCSaK2VsR6WOFibGRlWwI/vzLi6RxWvG9in93Vq5e5nEU4RCO4AR8OIcqXEMN6kDgEZ7hFd6cJ+fFeXc+Zq0FJ5/Zhz9wPn8AQleUTg==</latexit><latexit sha1_base64="YTGCVUA8y5kQ19SChCDdMaelmOc=">AAAB/3icbVA9SwNBEJ2LXzF+nQo2NotBsAp3ImgZtBEsjGA+IHeEvc1esmR379jdE0JM4V+xsVDE1r9h579xk1yhiQ8GHu/NMDMvSjnTxvO+ncLS8srqWnG9tLG5tb3j7u41dJIpQusk4YlqRVhTziStG2Y4baWKYhFx2owGVxO/+UCVZom8N8OUhgL3JIsZwcZKHfcg0EwEOka+hwKEboJbQXsYddyyV/GmQIvEz0kZctQ67lfQTUgmqDSEY63bvpeacISVYYTTcSnINE0xGeAebVsqsaA6HE3vH6Njq3RRnChb0qCp+ntihIXWQxHZToFNX897E/E/r52Z+CIcMZlmhkoyWxRnHJkETcJAXaYoMXxoCSaK2VsR6WOFibGRlWwI/vzLi6RxWvG9in93Vq5e5nEU4RCO4AR8OIcqXEMN6kDgEZ7hFd6cJ+fFeXc+Zq0FJ5/Zhz9wPn8AQleUTg==</latexit><latexit sha1_base64="YTGCVUA8y5kQ19SChCDdMaelmOc=">AAAB/3icbVA9SwNBEJ2LXzF+nQo2NotBsAp3ImgZtBEsjGA+IHeEvc1esmR379jdE0JM4V+xsVDE1r9h579xk1yhiQ8GHu/NMDMvSjnTxvO+ncLS8srqWnG9tLG5tb3j7u41dJIpQusk4YlqRVhTziStG2Y4baWKYhFx2owGVxO/+UCVZom8N8OUhgL3JIsZwcZKHfcg0EwEOka+hwKEboJbQXsYddyyV/GmQIvEz0kZctQ67lfQTUgmqDSEY63bvpeacISVYYTTcSnINE0xGeAebVsqsaA6HE3vH6Njq3RRnChb0qCp+ntihIXWQxHZToFNX897E/E/r52Z+CIcMZlmhkoyWxRnHJkETcJAXaYoMXxoCSaK2VsR6WOFibGRlWwI/vzLi6RxWvG9in93Vq5e5nEU4RCO4AR8OIcqXEMN6kDgEZ7hFd6cJ+fFeXc+Zq0FJ5/Zhz9wPn8AQleUTg==</latexit><latexit sha1_base64="YTGCVUA8y5kQ19SChCDdMaelmOc=">AAAB/3icbVA9SwNBEJ2LXzF+nQo2NotBsAp3ImgZtBEsjGA+IHeEvc1esmR379jdE0JM4V+xsVDE1r9h579xk1yhiQ8GHu/NMDMvSjnTxvO+ncLS8srqWnG9tLG5tb3j7u41dJIpQusk4YlqRVhTziStG2Y4baWKYhFx2owGVxO/+UCVZom8N8OUhgL3JIsZwcZKHfcg0EwEOka+hwKEboJbQXsYddyyV/GmQIvEz0kZctQ67lfQTUgmqDSEY63bvpeacISVYYTTcSnINE0xGeAebVsqsaA6HE3vH6Njq3RRnChb0qCp+ntihIXWQxHZToFNX897E/E/r52Z+CIcMZlmhkoyWxRnHJkETcJAXaYoMXxoCSaK2VsR6WOFibGRlWwI/vzLi6RxWvG9in93Vq5e5nEU4RCO4AR8OIcqXEMN6kDgEZ7hFd6cJ+fFeXc+Zq0FJ5/Zhz9wPn8AQleUTg==</latexit>

1. Replace stableFree Layer with LBM

2. Add inverter to DRAIN(1 PMOS/1NMOS)

sLLG+PTM(SPICE)

LBM

Camsari et al., IEEE EDL (2017)

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✓VOUT

VDD/2

| {z }mi

⇡ sgn

r + tanh

✓VIN

V0

| {z }Ii

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Page 9: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Neu-MOS, Ohmi (1992), IEEE TED

Floating-Gate MOS

(mem)resistor

cross-bar

Camsari et al., IEEE EDL (2017)

(2)

(1)

Hassan et al., arXiv:1801.0926Capacitive

cross-bar

LLG

Cz,i

Cb,i

Ci,1

Ci,n

Vbias,i

VOUT,1

VOUT,n

Vin,i

0

+VDD/2 +VDD/2 (1)(2)

Possibilities for hardware synapse

might enable non-linear synapses, e.g.

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CMOS circuits

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->

Page 10: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Non-magnetic p-bits/p-circuits

Thresholding

mi

m1

m2

m15

Sum

En (Enable) C (Clamp)S (Select)

Weight Matrix

h

6

Activation Function(LUT) 32 bit

Comp

LFSR 32

Tunable RNG

12

+_

MU

X

x

Ji1

x

Ji2

x

JiN

hC

xmC

+_

7.75

-8.0001589

10112612131415

7.75

-8.00

+_

1 2 22 32

32

32

1234

FPGA implementation

• Demonstrated p-circuits up to ~500 p-

bits: Solved a 16 bit Subset Sum Problem

Pervaiz et al., IEEE TNNLS (2018)

Micro-controller Implementation

VOUT

VIN

p-transistor

V

• Demonstrated invertible p-circuits up to

~50 p-bits: 4-bit Integer Factorization

Pervaiz et al., Sci. Rep. (2017)

p-bit

To appear in TNNLS

Page 11: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

�11

• How to build a p-bit?

• Quantum Computing-inspired (Reciprocal Networks)

• Machine Learning-inspired (Reciprocal and Non-reciprocal Networks)

Page 12: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

COPY

Correlated p-bits: p-circuits(Outputs)

(Inputs)G0 = 0

01 111000

01

1110

00

0.25

time

G0 > 0

01 111000

0.25

time

NOT

0.25

G0 > 0

time

01 111000

Page 13: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Correlated p-bits: p-circuits

Boltzmann Law

Truth Table

Basic equations

timeA \ B = C

[A B C] [A B C]

time

Page 14: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Invertible Boolean Logic

[A B C]

and outputs!

[A B C]

{h} used as a handle to “clamp” inputs

Page 15: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Factorization as Inverse Multiplication

FA FAFA

time (ns)<latexit sha1_base64="SQv8xsCue5IWxvzyFK9o0RKioMc=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBahXkoigh6LXjxWsB/QhLLZbtqlu5uwOymU0H/ixYMiXv0n3vw3btsctPXBwOO9GWbmRangBjzv2yltbG5t75R3K3v7B4dH7vFJ2ySZpqxFE5HobkQME1yxFnAQrJtqRmQkWCca38/9zoRpwxP1BNOUhZIMFY85JWClvusGJsbAJcMBrilziftu1at7C+B14hekigo0++5XMEhoJpkCKogxPd9LIcyJBk4Fm1WCzLCU0DEZsp6likhmwnxx+QxfWGWA40TbUoAX6u+JnEhjpjKynZLAyKx6c/E/r5dBfBvmXKUZMEWXi+JMYEjwPAY84JpREFNLCNXc3orpiGhCwYZVsSH4qy+vk/ZV3ffq/uN1tXFXxFFGZ+gc1ZCPblADPaAmaiGKJugZvaI3J3denHfnY9lacoqZU/QHzucPesmSPQ==</latexit><latexit sha1_base64="SQv8xsCue5IWxvzyFK9o0RKioMc=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBahXkoigh6LXjxWsB/QhLLZbtqlu5uwOymU0H/ixYMiXv0n3vw3btsctPXBwOO9GWbmRangBjzv2yltbG5t75R3K3v7B4dH7vFJ2ySZpqxFE5HobkQME1yxFnAQrJtqRmQkWCca38/9zoRpwxP1BNOUhZIMFY85JWClvusGJsbAJcMBrilziftu1at7C+B14hekigo0++5XMEhoJpkCKogxPd9LIcyJBk4Fm1WCzLCU0DEZsp6likhmwnxx+QxfWGWA40TbUoAX6u+JnEhjpjKynZLAyKx6c/E/r5dBfBvmXKUZMEWXi+JMYEjwPAY84JpREFNLCNXc3orpiGhCwYZVsSH4qy+vk/ZV3ffq/uN1tXFXxFFGZ+gc1ZCPblADPaAmaiGKJugZvaI3J3denHfnY9lacoqZU/QHzucPesmSPQ==</latexit><latexit sha1_base64="SQv8xsCue5IWxvzyFK9o0RKioMc=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBahXkoigh6LXjxWsB/QhLLZbtqlu5uwOymU0H/ixYMiXv0n3vw3btsctPXBwOO9GWbmRangBjzv2yltbG5t75R3K3v7B4dH7vFJ2ySZpqxFE5HobkQME1yxFnAQrJtqRmQkWCca38/9zoRpwxP1BNOUhZIMFY85JWClvusGJsbAJcMBrilziftu1at7C+B14hekigo0++5XMEhoJpkCKogxPd9LIcyJBk4Fm1WCzLCU0DEZsp6likhmwnxx+QxfWGWA40TbUoAX6u+JnEhjpjKynZLAyKx6c/E/r5dBfBvmXKUZMEWXi+JMYEjwPAY84JpREFNLCNXc3orpiGhCwYZVsSH4qy+vk/ZV3ffq/uN1tXFXxFFGZ+gc1ZCPblADPaAmaiGKJugZvaI3J3denHfnY9lacoqZU/QHzucPesmSPQ==</latexit><latexit sha1_base64="SQv8xsCue5IWxvzyFK9o0RKioMc=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBahXkoigh6LXjxWsB/QhLLZbtqlu5uwOymU0H/ixYMiXv0n3vw3btsctPXBwOO9GWbmRangBjzv2yltbG5t75R3K3v7B4dH7vFJ2ySZpqxFE5HobkQME1yxFnAQrJtqRmQkWCca38/9zoRpwxP1BNOUhZIMFY85JWClvusGJsbAJcMBrilziftu1at7C+B14hekigo0++5XMEhoJpkCKogxPd9LIcyJBk4Fm1WCzLCU0DEZsp6likhmwnxx+QxfWGWA40TbUoAX6u+JnEhjpjKynZLAyKx6c/E/r5dBfBvmXKUZMEWXi+JMYEjwPAY84JpREFNLCNXc3orpiGhCwYZVsSH4qy+vk/ZV3ffq/uN1tXFXxFFGZ+gc1ZCPblADPaAmaiGKJugZvaI3J3denHfnY9lacoqZU/QHzucPesmSPQ==</latexit>

FA FAFA

VOUT

VIN

p-transistor

V

⌘p-bit

D-Wave reference here

Page 16: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

• Searches the phase space at GHz rates

time (ns)

Combinatorial Optimization

<latexit sha1_base64="WnT/mSrkhLstUfOfXhLtnmfMn/I=">AAACLHicbVBbS8MwGE3nbc7b1EdfgkOYMEY7BH0RhkMQnya4C6ylpFm6ZUvakqTCKP1BvvhXBPHBIb76O8y2PujmgZDDOecj+Y4XMSqVaU6N3Nr6xuZWfruws7u3f1A8PGrLMBaYtHDIQtH1kCSMBqSlqGKkGwmCuMdIxxs3Zn7niQhJw+BRTSLicDQIqE8xUlpyiw1b+vC2zF2rwt1axWb9UMkK5C49h9fQ9gXCiZUmtdSWMXcTWhmlyb2+R6nOjGY5mLrFklk154CrxMpICWRousU3ux/imJNAYYak7FlmpJwECUUxI2nBjiWJEB6jAelpGiBOpJPMl03hmVb60A+FPoGCc/X3RIK4lBPu6SRHaiiXvZn4n9eLlX/lJDSIYkUCvHjIjxlUIZw1B/tUEKzYRBOEBdV/hXiIdEFK91vQJVjLK6+Sdq1qmVXr4aJUv8nqyIMTcArKwAKXoA7uQBO0AAbP4BV8gKnxYrwbn8bXIpozsplj8AfG9w9sDaaQ</latexit>

Sutton et al., Sci. Rep. (2017)

10 -1 10 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

<latexit sha1_base64="EG3r7k777RbvrJnuQA27nMLC5vs=">AAACC3icbVDLSsNAFJ3UV62vqEs3Q4vQLqyJCLoRilJwWaEvbEKZTCd16GQSZiZiCdm78VfcuFDErT/gzr9x2mahrQcuHM65l3vv8SJGpbKsbyO3tLyyupZfL2xsbm3vmLt7bRnGApMWDlkouh6ShFFOWooqRrqRICjwGOl4o6uJ37knQtKQN9U4Im6Ahpz6FCOlpb5ZdKQPG+V6BV5AxxcIJ3aa3KbQIQ9R+ah+PGpW+mbJqlpTwEViZ6QEMjT65pczCHEcEK4wQ1L2bCtSboKEopiRtODEkkQIj9CQ9DTlKCDSTaa/pPBQKwPoh0IXV3Cq/p5IUCDlOPB0Z4DUnZz3JuJ/Xi9W/rmbUB7FinA8W+THDKoQToKBAyoIVmysCcKC6lshvkM6EaXjK+gQ7PmXF0n7pGpbVfvmtFS7zOLIgwNQBGVggzNQA9egAVoAg0fwDF7Bm/FkvBjvxsesNWdkM/vgD4zPH0EqmKQ=</latexit>

• Needs sparse, quantized J

(100 city)Istanbul

… z

Page 17: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

�17

An exact mapping of q-bits to p-bits

• Trotter-Suzuki Decomposition

• Efficient for “stoquastic” Hamiltonians

J? = � 1

2�log tanh(��/n)

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Jk = J/n<latexit sha1_base64="tw1+suG6XQY6CAnJB4zsaSPuCY0=">AAACF3icbZDLSsNAFIYnXmu9Vd3pZrAIrmoigm6EohvpqoK9QBPCZHrSDp1MwsxEKCHga/gCbvUN3Ilbl76Az+H0srCtPwz8/OcczpkvSDhT2ra/raXlldW19cJGcXNre2e3tLffVHEqKTRozGPZDogCzgQ0NNMc2okEEgUcWsHgdlRvPYJULBYPepiAF5GeYCGjRJvILx26KsQ1P3MTIgnnwHN8jWtnAmPsl8p2xR4LLxpnaspoqrpf+nG7MU0jEJpyolTHsRPtZURqRjnkRTdVkBA6ID3oGCtIBMrLxn/I8YlJujiMpXlC43H6dyIjkVLDKDCdEdF9NV8bhf/VOqkOr7yMiSTVIOhkUZhyrGM8AoK7TALVfGgMoZKZWzHtGxhUG2wzWwJJBqDzogHjzGNYNM3zimNXnPuLcvVmiqiAjtAxOkUOukRVdIfqqIEoekIv6BW9Wc/Wu/VhfU5al6zpzAGakfX1Cyumnno=</latexit><latexit sha1_base64="tw1+suG6XQY6CAnJB4zsaSPuCY0=">AAACF3icbZDLSsNAFIYnXmu9Vd3pZrAIrmoigm6EohvpqoK9QBPCZHrSDp1MwsxEKCHga/gCbvUN3Ilbl76Az+H0srCtPwz8/OcczpkvSDhT2ra/raXlldW19cJGcXNre2e3tLffVHEqKTRozGPZDogCzgQ0NNMc2okEEgUcWsHgdlRvPYJULBYPepiAF5GeYCGjRJvILx26KsQ1P3MTIgnnwHN8jWtnAmPsl8p2xR4LLxpnaspoqrpf+nG7MU0jEJpyolTHsRPtZURqRjnkRTdVkBA6ID3oGCtIBMrLxn/I8YlJujiMpXlC43H6dyIjkVLDKDCdEdF9NV8bhf/VOqkOr7yMiSTVIOhkUZhyrGM8AoK7TALVfGgMoZKZWzHtGxhUG2wzWwJJBqDzogHjzGNYNM3zimNXnPuLcvVmiqiAjtAxOkUOukRVdIfqqIEoekIv6BW9Wc/Wu/VhfU5al6zpzAGakfX1Cyumnno=</latexit><latexit sha1_base64="tw1+suG6XQY6CAnJB4zsaSPuCY0=">AAACF3icbZDLSsNAFIYnXmu9Vd3pZrAIrmoigm6EohvpqoK9QBPCZHrSDp1MwsxEKCHga/gCbvUN3Ilbl76Az+H0srCtPwz8/OcczpkvSDhT2ra/raXlldW19cJGcXNre2e3tLffVHEqKTRozGPZDogCzgQ0NNMc2okEEgUcWsHgdlRvPYJULBYPepiAF5GeYCGjRJvILx26KsQ1P3MTIgnnwHN8jWtnAmPsl8p2xR4LLxpnaspoqrpf+nG7MU0jEJpyolTHsRPtZURqRjnkRTdVkBA6ID3oGCtIBMrLxn/I8YlJujiMpXlC43H6dyIjkVLDKDCdEdF9NV8bhf/VOqkOr7yMiSTVIOhkUZhyrGM8AoK7TALVfGgMoZKZWzHtGxhUG2wzWwJJBqDzogHjzGNYNM3zimNXnPuLcvVmiqiAjtAxOkUOukRVdIfqqIEoekIv6BW9Wc/Wu/VhfU5al6zpzAGakfX1Cyumnno=</latexit><latexit sha1_base64="tw1+suG6XQY6CAnJB4zsaSPuCY0=">AAACF3icbZDLSsNAFIYnXmu9Vd3pZrAIrmoigm6EohvpqoK9QBPCZHrSDp1MwsxEKCHga/gCbvUN3Ilbl76Az+H0srCtPwz8/OcczpkvSDhT2ra/raXlldW19cJGcXNre2e3tLffVHEqKTRozGPZDogCzgQ0NNMc2okEEgUcWsHgdlRvPYJULBYPepiAF5GeYCGjRJvILx26KsQ1P3MTIgnnwHN8jWtnAmPsl8p2xR4LLxpnaspoqrpf+nG7MU0jEJpyolTHsRPtZURqRjnkRTdVkBA6ID3oGCtIBMrLxn/I8YlJujiMpXlC43H6dyIjkVLDKDCdEdF9NV8bhf/VOqkOr7yMiSTVIOhkUZhyrGM8AoK7TALVfGgMoZKZWzHtGxhUG2wzWwJJBqDzogHjzGNYNM3zimNXnPuLcvVmiqiAjtAxOkUOukRVdIfqqIEoekIv6BW9Wc/Wu/VhfU5al6zpzAGakfX1Cyumnno=</latexit>

Page 18: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

�18

Quantum Annealing with p-bits

<latexit sha1_base64="oIr9EKVx61TrHcJK9LbmlIwYGsc=">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</latexit>

• “Quantum” Boltzmann Law• Replicated p-bits vs Exact

solution: Averages and correlations match

n =250 replicas

1D spin-chain with M=8 q-bits (J=+1)

<latexit sha1_base64="pjrDpgJ+6xH4I9HTiCtetRUjgx0=">AAACG3icbZDLSsNAFIYnXmu9RV0KMlgEVyUpgi6LbrqSCvYCTSyT6aQdOsmEmROhlO58DV/Arb6BO3HrwhfwOZymWdjWAwMf/zmHf84fJIJrcJxva2V1bX1js7BV3N7Z3du3Dw6bWqaKsgaVQqp2QDQTPGYN4CBYO1GMRIFgrWB4M+23HpnSXMb3MEqYH5F+zENOCRipa594OsQ1jL1EyQQkrjzcYg94xHSGXbvklJ2s8DK4OZRQXvWu/eP1JE0jFgMVROuO6yTgj4kCTgWbFL1Us4TQIemzjsGYGCd/nN0xwWdG6eFQKvNiwJn6d2NMIq1HUWAmIwIDvdibiv/1OimEV/6Yx0kKLKYzozAV2Bw8DQX3uGIUxMgAoYqbv2I6IIpQMNHNuQSKDBlMiiYYdzGGZWhWyq7hu4tS9TqPqICO0Sk6Ry66RFVUQ3XUQBQ9oRf0it6sZ+vd+rA+Z6MrVr5zhObK+voFxJOf1g==</latexit>

Comment: SPICE simulation

Comment: Size of matrix 2^N by 2^N

Page 19: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

�19

• How to build a p-bit?

• Quantum Computing-inspired (Reciprocal Networks)

• Machine Learning-inspired (Reciprocal and Non-reciprocal Networks)

Bigger outline showing previous parts

Page 20: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Inherently probabilistic circuits: Bayesian Networks

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Correlation

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Faria et al., AIP Advances (2018)

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Page 21: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Resistive synapse

SPICEsimulations

Low-power DBN: Inference with p-bits

Ramtin Zand (UCF) et al. (2018)

• Energy x Accuracy Tradeoffvia different topologies

Thresholding

mi

m1

m2

m15

Sum

En (Enable) C (Clamp)S (Select)

Weight Matrix

h

6

Activation Function(LUT) 32 bit

Comp

LFSR 32

Tunable RNG

12

+_

MU

X

x

Ji1

x

Ji2

x

JiN

hC

xmC

+_

7.75

-8.0001589

10112612131415

7.75

-8.00

+_

1 2 22 32

32

32

1234

p-bit as Neuron: Area& Energy savings compared to

a digital neuron

MRAM-based p-bit

True North reference: LFSR’s are expensiveOf course, digital neurons are more reliable and probably offer better scaling / fully thresholded.

Full SPICE could be misleading.

Energy X 1000, could it be defended?

Page 22: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Summaryp-bit as hardware building block

LLG

Cz,i

Cb,i

Ci,1

Ci,n

Vbias,i

VOUT,1

VOUT,n

Vin,i

0

+VDD/2 +VDD/2

MRAM

Present-day

Quantum Computing

OptimizationInvertible Logic Quantum Circuits

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Machine Learning

RBM, Bayesian, …

Page 23: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

T. N. Theis and P. Wong, 2016

Novel devices and circuits for “the algorithms and applicationsof the coming decades”

p-bits & p-circuits as

p-bits for PSL

Applications/Algorithms: QuantumComputing / Machine Learning

Page 24: Tutorial: p-bits for Probabilistic Spin Logic · 2020. 1. 21. · Shuvro Chowdhury Anirudh Ghantasala Brian M Sutton Orchi Hassan Punyashloka Debashis Zhihong Chen Supriyo Datta p-bits

Anirudh Ghantasala

Orchi HassanBrian Sutton

Punyashloka Debashis

Supriyo DattaZhihong Chen

p-bits for Probabilistic Spin Logic (PSL)

Zeeshan Pervaiz

Ramtin Zand (UCF)

Sayeef Salahuddin (UC Berkeley)

Rafatul Faria

(1) Camsari et al., Phys. Rev. X (2017) (Computing with p-bits)

(2) Camsari et al., IEEE EDL (2017) (Stochastic MTJ-based p-bit)

(3) Camsari et al., arXiv:1810.XXXX (2018) (Quantum Annealing with p-bits)

(4) Camsari et al., arXiv:1809.04028(2018) (Review of PSL)

Ron DeMara(UCF)

BehtashBehin-Aein (GF)

Shuvro Chowdhury