Quantum Circuit Optimization of Arithmeticcircuits using ZX Calculus

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