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Limits RegistryGoogle DeepMind's AlphaEvolve, an evolutionary coding agent powered by Gemini models, found an algorithm in May 2025 that multiplies 4x4 complex-valued matrices with 48 scalar multiplications, improving on the 49 from Strassen's 1969 algorithm applied recursively. This was the first improvement for this setting in 56 years.
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Google DeepMind's AlphaEvolve, an evolutionary coding agent powered by Gemini models, found an algorithm in May 2025 that multiplies 4x4 complex-valued matrices with 48 scalar multiplications, improving on the 49 from Strassen's 1969 algorithm applied recursively. This was the first improvement for this setting in 56 years.
The smallest known number of scalar multiplications in an algorithm for multiplying two 4x4 matrices over the complex numbers.
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Limits Registry. LR-ALPHAEVOLVE-4X4-COMPLEX-MULTIPLICATIONS. Fewest multiplications for 4x4 complex matrix multiplication. 2026.