SeQuant Framework for Symbolic and Numerical Tensor Algebra. I. Core Capabilities

TL;DR

SeQuant is an open-source tensor algebra library that uses a graph-theoretic canonicalizer for symbolic and numerical tensor computations, supporting symmetries, tensor networks, and parametric modes.

Contribution

It introduces a novel graph-theoretic tensor network canonicalizer that accelerates tensor expression simplification and optimization over traditional group-theoretic methods.

Findings

Faster tensor network canonicalization compared to group-theoretic methods.

Supports noncovariant tensor networks and parametric tensor modes.

Integrates symbolic manipulation with numerical evaluation for efficient tensor computations.

Abstract

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 tensor networks with symmetries faster than their standard group-theoretic counterparts. The TN canonicalizer is used for routine simplification of conventional tensor expressions, for optimizing application of Wick's theorem (used to canonicalize products of tensors over operator fields), and for manipulation of the intermediate representation leading to the numerical evaluation. Notable features of SeQuant include support for noncovariant tensor networks (which often arise 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, "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.