Analytic Constructions of General n-Qubit Controlled Gates

TL;DR

This paper introduces two analytic methods for constructing general n-qubit controlled gates using standard quantum gates, providing explicit circuits and complexity analysis.

Contribution

It presents novel analytic expressions for simulating n-qubit controlled-U gates with explicit circuit decompositions and complexity evaluations.

Findings

Two analytic expressions for n-qubit controlled gates are derived.

Explicit quantum circuits and gate counts are provided.

Complexity of the schemes is analyzed using exponential and polynomial approaches.

Abstract

In this Letter, we present two analytic expressions that most generally simulate $n$-qubit controlled-$U$ gates with standard one-qubit gates and CNOT gates using exponential and polynomial complexity respectively. Explicit circuits and general expressions of decomposition are derived. The exact numbers of basic operations in these two schemes are given using gate counting technique.