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Related Experiment Video

Updated: Jun 17, 2025

Fabrication of Spatially Confined Complex Oxides

Fabrication of Spatially Confined Complex Oxides

Published on: July 1, 2013

Improved time complexity for spintronic oscillator ising machines compared to a popular classical optimization

Neha Garg¹, Sanyam Singhal², Nakul Aggarwal³

¹Department of Physics, Indian Institute of Technology Delhi, New Delhi, Delhi 110016, India.

|August 14, 2024

Summary

This summary is machine-generated.

Phase binarized oscillators (PBOs) and spintronic oscillators solve Max-Cut problems faster than traditional algorithms. Their computation time grows logarithmically with graph size, offering improved efficiency for complex optimization tasks.

Keywords:

Goemans–Williamson algorithm Ising machines Kuramoto model of oscillators Slavin’s model of spin oscillators combinatorial optimization spintronic oscillators time complexity

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Area of Science:

Computational Mathematics
Quantum Computing
Materials Science

Background:

Combinatorial optimization problems like Max-Cut are computationally intensive for large graphs.
Brute-force algorithms face exponential time complexity, while approximate methods like Goemans-Williamson (GW) have polynomial complexity.
Phase binarized oscillators (PBOs) offer a potential alternative for solving these optimization problems.

Purpose of the Study:

To empirically compare the time-to-solution (TTS) of PBOs and spintronic oscillators against the GW algorithm for the Max-Cut problem.
To analyze the scalability of these methods with increasing graph size.
To evaluate the accuracy and efficiency of spintronic oscillators for solving Max-Cut.

Main Methods:

Empirical analysis of Max-Cut problem solving on Mobius Ladder, random cubic, and Erdös Rényi graphs up to 100 nodes.
Modeling PBOs using the Kuramoto model to assess physics-agnostic time complexity.
Modeling spintronic oscillators using Slavin's model to capture GHz-frequency dynamics.
Comparison of TTS and accuracy with the Goemans-Williamson (GW) algorithm.

Main Results:

TTS for PBOs using the Kuramoto model grows logarithmically (O(log(N))) with graph size N, significantly outperforming the GW algorithm's O(N^2) growth.
Spintronic oscillators, modeled via Slavin's model, also exhibit logarithmic TTS growth (O(log(N))) with comparable accuracy to the GW algorithm.
Spintronic oscillators demonstrate improved time complexity over the GW algorithm.

Conclusions:

Spintronic oscillators offer a significant speedup for solving Max-Cut problems compared to the GW algorithm, especially for large graphs.
The logarithmic growth of TTS for spintronic oscillators suggests high scalability and efficiency.
These findings highlight the potential of spintronic oscillators for fast and accurate solutions to complex combinatorial optimization problems.