Optimizing Quantum Circuits Using Algebraic Expressions

Optimizing quantum circuits and reducing errors plays a crucial role in quantum circuit computation. Every quantum circuit can be represented using algebraic expressions, we propose an approach that directly derives algebraic expressions, ensuring that parallelism is maximized, that is, the number of circuit slices is minimized, and secondly, the computation required for obtaining the desired algebraic expression is reduced. This results in quantum circuits that are more efficient in space and computation time. The simplification of algebraic expressions offers methods to streamline optimized circuits, reducing the number of gates and depth. This reduction is aimed at minimizing the overall complexity of the expressions, resulting in more efficient quantum computations. In this paper, we also show through simulations that the optimized circuit will have less errors when compared to original circuits.