<p>I believe this is because of Qiskit <code>initialize</code>, and not specific to the IonQ backend. You'd likely see the same (or worse!) gate depth with any backend.</p>
<p>Qiskit <code>initialize</code> uses a very general-purpose and therefore relatively naive algorithm for state encoding. Specifically, that from <a href="https://arxiv.org/abs/quant-ph/0406176v5" rel="nofollow noreferrer">Synthesis of Quantum Logic Circuits (2004)</a>; this is mentioned <a href="https://qiskit.org/documentation/_modules/qiskit/circuit/library/data_preparation/state_preparation.html#StatePreparation" rel="nofollow noreferrer">in the source for the method</a>.</p>
<p>Specifically, they say in the paper that using the method, an arbitrary n-qubit quantum state can be prepared by a circuit containing no more than 2<sup>n+1</sup> − 2n CNOT gates. For an n of 8, like you have here, that's 496 CNOTs. which is about what you're seeing.</p>
<p>Any encoding approach that is more specifically tailored to what you're trying to do will likely work better.</p>
Reducing circuit initialization complexity
<p>I'm encoding data into a QuantumCircuit via the Initialize method for QFTs. In doing this and transpiling for IonQ backends, I'm getting rather complex circuits. Is there a way to encode this data more efficiently for IonQ backends or a method to approximate this circuit? Thanks in advance!</p>
<p><a href="https://i.stack.imgur.com/J3NLB.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/J3NLB.png" alt="Encoding a sine wave into an 8 qbit register, then transpiling for IonQ sim backend" /></a></p>