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

SeQuant is an open-source library for symbolic algebra of tensors over commutative (scalar) and non-commutative (operator) rings. The key innovation supporting most of its functionality is a graph-theoretic tensor network (TN) canonicalizer that can handle TNs with symmetries faster than their standard group-theoretic counterparts. The TN canonicalizer is used for the routine simplification of conventional tensor expressions, for optimizing the application of Wick's theorem (used to canonicalize products of tensors over operator fields), and for the manipulation of the intermediate representation leading to the numerical evaluation. Notable features of SeQuant include support for noncovariant TNs (featuring hyperedges in their graphical representation and often arising from tensor decompositions) and for tensors with modes that depend parametrically on indices of other tensor modes (such dependencies between degrees of freedom are naturally viewed as nesting of tensors, or "tensors of tensors" arising in block-wise data compressions in data science and modern quantum simulation). SeQuant blurs the line between pure symbolic manipulation/code generation and numerical evaluation by including compiler-like components to optimize and directly interpret tensor expressions using external numerical tensor algebra frameworks. The SeQuant source code is available at https://github.com/ValeevGroup/SeQuant.