Decomposition of quantum gates

TL;DR

This paper introduces a recurrence-based method for decomposing n-qubit unitary gates into a sequence of single-qubit gates with minimal controls, optimizing quantum circuit design.

Contribution

It presents a new recurrence scheme for decomposing large quantum gates efficiently, with explicit formulas and comparison to previous methods.

Findings

Decomposition reduces to no more than N(N-1)/2 single-qubit gates.

Explicit formulas for k-controlled single-qubit gates are provided.

Comparison shows improvements over previous schemes.

Abstract

A recurrence scheme is presented to decompose an $n$-qubit unitary gate to the product of no more than $N(N-1)/2$ single qubit gates with small number of controls, where $N = 2^n$. Detailed description of the recurrence steps and formulas for the number of $k$-controlled single qubit gates in the decomposition are given. Comparison of the result to a previous scheme is presented, and future research directions are discussed.