autotn: Automata-inspired construction of tensor-network operators from symbolic local rules

2026-07-24

AI Summary

This work addresses the cumbersome, error-prone, and irreproducible process of manually converting symbolic Hamiltonians or cost functions into matrix product operator (MPO) representations. To overcome this challenge, the authors introduce an automaton-inspired framework that automatically translates user-defined local operators and interaction rules into compact, verifiable MPOs, accommodating both diagonal and off-diagonal terms. The method integrates formal rule parsing, pattern recognition, and tensor network compression to enable automated compilation from symbolic expressions to MPOs, implemented in Python. Demonstrations on Max-Cut, long-range XX+YY+Z spin models, and quantum clock models show a substantial reduction in the engineering overhead associated with constructing and verifying MPOs, thereby enhancing reproducibility and accessibility in tensor network simulations.

Abstract

Matrix product operators (MPOs) are a standard representation for structured operators in tensor-network simulations and quantum computing applications. However, converting symbolic descriptions of Hamiltonians and cost functions into MPO representations often requires substantial manual implementation, making the process error-prone and difficult to reproduce. This paper presents autotn, an open-source Python software tool that converts symbolic operator rules into MPO representations. Users define local operators and interaction rules in a high-level format, and the software generates the corresponding MPO along with validation utilities. In doing so, the software follows an automata-inspired approach that identifies repeated patterns in the symbolic description of the operator and reuses them to build a compact tensor-network representation, avoiding the need to construct each tensor by hand. The current implementation of autotn supports both diagonal operators, commonly encountered in combinatorial optimization problems, and general local matrix operators used in quantum many-body physics. The software is demonstrated on Max-Cut cost operators, long-range XX+YY+Z spin Hamiltonians, and quantum clock models. By providing a reproducible workflow from symbolic model specification to validated MPO construction, autotn reduces the engineering effort required to develop, verify, and compare MPO constructions.

Problem

• matrix product operators
• symbolic operator rules
• tensor-network
• automata-inspired
• reproducibility

Innovation

• automata-inspired
• tensor-network operators
• matrix product operators
• symbolic rules
• automatic construction