  As state-of-the-art quantum computers are capable of running increasingly
complex algorithms, the need for automated methods to design and test potential
applications rises. Equivalence checking of quantum circuits is an important,
yet hardly automated, task in the development of the quantum software stack.
Recently, new methods have been proposed that tackle this problem from widely
different perspectives. One of them is based on the ZX-calculus, a graphical
rewriting system for quantum computing. However, the power and capability of
this equivalence checking method has barely been explored. The aim of this work
is to evaluate the ZX-calculus as a tool for equivalence checking of quantum
circuits. To this end, it is demonstrated how the ZX-calculus based approach
for equivalence checking can be expanded in order to verify the results of
compilation flows and optimizations on quantum circuits. It is also shown that
the ZX-calculus based method is not complete$\unicode{x2014}$especially for
quantum circuits with ancillary qubits. In order to properly evaluate the
proposed method, we conduct a detailed case study by comparing it to two other
state-of-the-art methods for equivalence checking: one based on path-sums and
another based on decision diagrams. The proposed methods have been integrated
into the publicly available QCEC tool (https://github.com/cda-tum/qcec) which
is part of the Munich Quantum Toolkit (MQT).
