  Quantum computing is an emerging technology in which quantum mechanical
properties are suitably utilized to perform certain compute-intensive
operations faster than classical computers. Quantum algorithms are designed as
a combination of quantum circuits that each require a large number of quantum
gates, which is a challenge considering the limited number of qubit resources
available in quantum computing systems. Our work proposes a technique to
optimize quantum arithmetic algorithms by reducing the hardware resources and
the number of qubits based on ZX calculus. We have utilised ZX calculus rewrite
rules for the optimization of fault-tolerant quantum multiplier circuits where
we are able to achieve a significant reduction in the number of ancilla bits
and T-gates as compared to the originally required numbers to achieve
fault-tolerance. Our work is the first step in the series of arithmetic circuit
optimization using graphical rewrite tools and it paves the way for advancing
the optimization of various complex quantum circuits and establishing the
potential for new applications of the same.
