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Quantum computing is an emerging technology in which quantum mechanicalproperties are suitably utilized to perform certain compute-intensiveoperations faster than classical computers. Quantum algorithms are designed asa combination of quantum circuits that each require a large number of quantumgates, which is a challenge considering the limited number of qubit resourcesavailable in quantum computing systems. Our work proposes a technique tooptimize quantum arithmetic algorithms by reducing the hardware resources andthe number of qubits based on ZX calculus. We have utilised ZX calculus rewriterules for the optimization of fault-tolerant quantum multiplier circuits wherewe are able to achieve a significant reduction in the number of ancilla bitsand T-gates as compared to the originally required numbers to achievefault-tolerance. Our work is the first step in the series of arithmetic circuitoptimization using graphical rewrite tools and it paves the way for advancingthe optimization of various complex quantum circuits and establishing thepotential for new applications of the same.

Quantum Circuit Optimization of Arithmetic circuits using ZX Calculus