  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.
