How many CNOT gates does it take to generate a three-qubit state ?

TL;DR

This paper establishes the maximum number of CNOT gates needed to transform any three-qubit pure state into another, showing that at most three are needed for preparation from a product state, and only two from the GHZ state.

Contribution

It provides tight bounds on the CNOT gate count for three-qubit state transformations, including the minimal number from the GHZ state, and discusses generalizations to other two-qubit gates.

Findings

Any three-qubit pure state can be prepared from a product state with at most three CNOT gates.

Starting from the GHZ state, only two CNOT gates are needed to reach any other three-qubit state.

Any three-qubit state can be transformed into any other with at most four CNOT gates.

Abstract

The number of two-qubit gates required to transform deterministically a three-qubit pure quantum state into another is discussed. We show that any state can be prepared from a product state using at most three CNOT gates, and that, starting from the GHZ state, only two suffice. As a consequence, any three-qubit state can be transformed into any other using at most four CNOT gates. Generalizations to other two-qubit gates are also discussed.