Simplified construction of $n$-qubit controlled phase gates and physical realization

TL;DR

This paper presents a simplified method for constructing n-qubit controlled phase gates using an auxiliary level and fewer operations, with a feasible cavity QED implementation that reduces total gate time.

Contribution

It introduces a novel scheme utilizing a third level to efficiently build n-qubit phase gates without increasing auxiliary levels or operations as n grows.

Findings

Uses 2n-4 two-qutrit gates and minimal single-qutrit operations

Proposes a cavity QED implementation for physical realization

Achieves reduced total gate time compared to previous methods

Abstract

We show that with the assistance of a third level of the qubits an n-qubit phase gate can be constructed from $2n-4$ two-qutrit conditional swap gates, a single qutrit-qubit controlled phase gate, and two single-qutrit operations. Unlike previous schemes, our scheme uses the auxiliary level to "expose" some state to the qutrit-qubit controlled phase gate, instead of using it to "hide" states from the conditional dynamics. Neither the number of the additional levels nor that of single-qutrit operations needs to increase with $n$. We propose a physical implementation of the required elementary gates in cavity QED, and show that the total gate time may be greatly reduced as compared with that required in the previous methods.