A symbolic calculus for a class of quantum computing circuits

TL;DR

This paper presents a symbolic calculus for analyzing certain quantum circuits with controlled gates, enabling verification and minimization without complex matrix calculations, applicable to independent subcircuits.

Contribution

A novel symbolic calculus method for evaluating quantum circuit outputs using Boolean expressions, avoiding complex matrix operations and applicable to independent subcircuits.

Findings

Enables circuit verification and minimization.

Does not require complex matrix calculations.

Applicable to independent subcircuits.

Abstract

This paper introduces a symbolic calculus to evaluate the output signals at the target line(s) of quantum computing subcircuits using controlled negations and controlled-Q gates, where Q represents the k-th root of [0 1; 1 0], the unitary matrix of NOT, and k is a power of two. The controlling signals are GF(2) expressions possibly including Boolean expressions. The method does not require operating with complex-valued matrices. The method may be used to verify the functionality and to check for possible minimization of a given quantum computing circuit using target lines. The method does not apply for a whole circuit if there are interactions among target lines. In this case the method applies for the independent subcircuits.