I'm afraid that this is more or less a preliminary answer with some research pointers rather than a comprehensive answer to your question. I don't have personal experience with the Swiss implementation of its obligations related to the EU freedom of movement directive, but I do have a fair amount of experience with the directive's application in the EU itself.
The first thing to note is that according to the residence permits page at www.ch.ch (a great domain name, I must say), is the list of permits that apply to EU and EFTA nationals:
- Permit L EU/EFTA (short-term residence permit)
- Permit B EU/EFTA (residence permit)
- Permit C EU/EFTA (settlement permit)
- Permit Ci EU/EFTA (residence permit with gainful employment)
- Permit G EU/EFTA (cross-border commuter permit)
They then have a link to a page with contact information for the cantonal immigration authorities. The Zürich office is on the web at https://ma.zh.ch/internet/sicherheitsdirektion/migrationsamt/de/home.html.
There (if you read German) you can find, by following two links for Einreise & Aufenthalt, a link in the right-side navigation menu for EU EFTA-Personen & Personenfreizügigkeit.
The directive applies not only to spouses and other legal family, but also to "the partner with whom the Union citizen has a durable relationship, duly attested" (Article (3)(2)(b); in German: des Lebenspartners, mit dem der Unionsbürger eine ordnungsgemäß bescheinigte dauerhafte Beziehung eingegangen ist). States are free to define this phrase, however; for example, the UK requires the partners to have at least two years of cohabitation.
I do not know how Switzerland applies this phrase, and I did not see any evidence of the word "Beziehung" on their web pages. Similarly, the federal site's English-language page on the subject does not mention that route. But if they do recognize such relationships, and if yours qualifies, that will certainly be the best way to get permission for her to move to Switzerland with you, short of entering into a registered partnership or getting married.
If she cannot qualify based on your relationship, she may be able to qualify as a self-sufficient person (back to the federal site):
Persons who are not gainfully employed (e.g. retirees and students) may remain in Switzerland if the following conditions are met:
- They have adequate financial resources to cover the cost of living in Switzerland so as to ensure that they will not become dependent on welfare benefits, and
- They have a health insurance policy that also includes accident coverage.
- Students must also show the letter confirming that they have been admitted to a recognised educational institution (confirmation of enrolment).
Stays of up to 90 days within a six-month period do not require authorisation. For longer stays, foreign nationals have to register with the cantonal migration office as a non-employed person. The corresponding EU/EFTA residence permit will remain valid for a period of five years (for students, the permit will remain valid for the duration of education and training or will remain valid for one year and be renewed at one-year intervals). These residence permits will be renewed automatically as long as the abovementioned criteria are still met.
You might be able to make a formal pledge of support in that case, but the site does not seem to indicate it as a possibility. You asked
Do I have sign Verpflichtungserklärung to get her same permit as me or any other than L for 3 months?
If she can get a permit based on your relationship, then probably not. From the family reunification factsheet (PDF):
If the main entitled person is an employee , then the right to family reunification is not contingent upon that person's financial situation.
In fact, in any event, she does not need any permit to stay for up to three months. From the free movement factsheet (PDF):
No permit is needed for stays in Switzerland lasting less than three months, either as a tourist or an economically inactive person.