SeQuant framework for symbolic and numerical tensor algebra. I. Core capabilities

Area of Science:

• Computational Physics
• Quantum Chemistry
• Data Science

Background:

• Symbolic algebra of tensors is crucial for various scientific domains.
• Existing methods for tensor network (TN) manipulation can be computationally intensive, especially with symmetries.

Purpose of the Study:

• Introduce SeQuant, an open-source library for symbolic tensor algebra.
• Enhance the efficiency of tensor expression simplification and numerical evaluation.

Main Methods:

• Developed a graph-theoretic tensor network (TN) canonicalizer.
• Implemented support for non-covariant TNs and parametrically dependent tensor modes.
• Integrated compiler-like components for optimization and direct numerical interpretation.

Main Results:

• Achieved faster handling of TNs with symmetries compared to group-theoretic methods.
• Enabled routine simplification of conventional tensor expressions.
• Optimized the application of Wick's theorem for canonicalizing tensor products.
• Facilitated manipulation of intermediate representations for numerical evaluation.

Conclusions:

• SeQuant offers a novel approach to symbolic tensor algebra with significant performance improvements.
• The library effectively bridges symbolic manipulation and numerical evaluation.
• Provides advanced features for complex tensor structures relevant to modern simulations and data science.