Efficient construction of three- and four-qubit quantum gates by global entangling gates

TL;DR

This paper introduces optimized quantum gate circuits that significantly reduce the number of global entangling operations needed for three- and four-qubit gates, enhancing efficiency for ion and circuit QED systems.

Contribution

The authors develop nearly twice as fast circuits for Toffoli and Fredkin gates using fewer global two-qubit gates without ancillas, applicable to ion and circuit QED platforms.

Findings

Toffoli gate implemented with three global two-qubit gates

Fredkin gate implemented with four global two-qubit gates

Construction of a four-qubit phase gate with seven global two-qubit gates

Abstract

We present improved circuits for the control-control-phase (Toffoli) gate and the control-swap (Fredkin) gate using three and four global two-qubit gates, respectively. This is a nearly double speed-up compared to the conventional circuits, which require five (for Toffoli) and seven (for Fredkin) conditional two-qubit gates. We apply the same approach to construct the conditional four-qubit phase gate by seven global two-qubit gates. We also present construction of the Toffoli and the Fredkin gates with five nearest-neighbour interactions. Our constructions do not employ ancilla qubits or ancilla internal states and are particularly well suited for ion qubits and for circuit QED systems, where the entangling operations can be implemented by global addressing.