A Tensor Network based Decision Diagram for Representation of Quantum Circuits

TL;DR

This paper introduces TDD, a tensor decision diagram data structure that offers a compact, canonical, and efficient way to represent and manipulate quantum circuits, facilitating various quantum computing tasks.

Contribution

The paper presents TDD, a novel tensor network-based decision diagram that improves quantum circuit representation and operation efficiency, enabling advanced automation tasks.

Findings

TDD provides a compact, canonical representation for quantum circuits.

Operations like addition and contraction are efficiently implemented in TDD.

Benchmark testing shows TDD's effectiveness in quantum circuit tasks.

Abstract

Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper proposes a decision diagram style data structure, called TDD (Tensor Decision Diagram), for more principled and convenient applications of tensor networks. This new data structure provides a compact and canonical representation for quantum circuits. By exploiting circuit partition, the TDD of a quantum circuit can be computed efficiently. Furthermore, we show that the operations of tensor networks essential in their applications (e.g., addition and contraction), can also be implemented efficiently in TDDs. A proof-of-concept implementation of TDDs is presented and its efficiency is evaluated on a set of benchmark quantum circuits. It is expected that TDDs will play an important role in various design automation tasks related to quantum circuits, including but not limited to equivalence checking, error detection, synthesis, simulation, and verification.