Quantum Circuit Optimization of Arithmetic circuits using ZX Calculus

TL;DR

This paper introduces a novel method using ZX calculus to optimize quantum arithmetic circuits, significantly reducing resource requirements and paving the way for more efficient quantum computations.

Contribution

It presents the first application of ZX calculus for optimizing fault-tolerant quantum multiplier circuits, reducing ancilla bits and T-gates.

Findings

Significant reduction in ancilla bits

Fewer T-gates needed for fault-tolerance

First use of graphical rewrite tools for arithmetic circuit optimization

Abstract

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.