Automatic Extraction and Compensation of P-Bit Device Variations in Large Array Utilizing Boltzmann Machine Training
A Probabilistic Bit (P-Bit) device serves as the core hardware for implementing Ising computation. However, the severe intrinsic variations of stochastic P-Bit devices hinder the large-scale expansion of the P-Bit array, significantly limiting the practical usage of Ising computation. In this work,...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Micromachines |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2072-666X/16/2/133 |
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| Summary: | A Probabilistic Bit (P-Bit) device serves as the core hardware for implementing Ising computation. However, the severe intrinsic variations of stochastic P-Bit devices hinder the large-scale expansion of the P-Bit array, significantly limiting the practical usage of Ising computation. In this work, a behavioral model which attributes P-Bit variations to two parameters, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>V</mi></mrow></semantics></math></inline-formula>, is proposed. Then the weight compensation method is introduced, which can mitigate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>V</mi></mrow></semantics></math></inline-formula> of P-Bit device variations by rederiving the weight matrix, enabling them to compute as ideal identical P-Bits without the need for weights retraining. Accurately extracting the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>V</mi></mrow></semantics></math></inline-formula> simultaneously from a large P-Bit array which is prerequisite for the weight compensation method is a crucial and challenging task. To solve this obstacle, we present the novel automatic variation extraction algorithm which can extract device variations of each P-Bit in a large array based on Boltzmann machine learning. In order for the accurate extraction of variations from an extendable P-Bit array, an Ising Hamiltonian based on a 3D ferromagnetic model is constructed, achieving precise and scalable array variation extraction. The proposed Automatic Extraction and Compensation algorithm is utilized to solve both 16-city traveling salesman problem (TSP) and 21-bit integer factorization on a large P-Bit array with variation, demonstrating its accuracy, transferability, and scalability. |
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| ISSN: | 2072-666X |