Worst of all, the subordinate party may feel pressure to continue the relationship for fear of consequences in the workplace.
For that reason, most US companies prohibit romantic relationships between a supervisor and a subordinate.
If I've changed it too much from your original question, feel free to edit it further or roll back the changes. Dating subordinates is almost always a bad idea, except when it's a great idea. Other employees may end up resentful and there will be a drop of productivity if so.
Likely you will treat her differently than the others such as giving her information that she in her current position should not have, refusing to see her performance problems, etc.
You are likely to favor that person regardless of their performance in their job. Would you want your lower level managers supervising people who are their significant others? Then you can date her, she will like you for your gentleness.