Exhibit 5.1

November 4, 2011

Applied Micro Circuits Corporation

215 Moffett Park Drive

Sunnyvale, CA 94089

Re: Registration Statement on Form S-8 Concerning Applied Micro Circuits Corporation 2011 Equity Incentive Plan

Ladies and Gentlemen:

We have examined the Registration Statement on Form S-8 (the “Registration Statement”), of Applied Micro Circuits Corporation, a Delaware corporation (the “Company”), to be filed with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), in connection with the offering by the Company of up to 15,087,623 shares of the Company’s common stock, par value $0.01 per share (the “Shares”) under the Applied Micro Circuits Corporation 2011 Equity Incentive Plan (the “Plan”).

We have examined the Plan and the originals, or photostatic or certified copies, of such records of the Company and certificates of officers of the Company and of public officials and such other documents as we have deemed relevant and necessary as the basis for the opinion set forth below. In our examination, we have assumed the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies.

Based upon the foregoing examination and in reliance thereon, and subject to the qualifications, assumptions and limitations stated herein and in reliance on the statements of fact contained in the documents that we have examined, we are of the opinion that the Shares, when issued and sold in accordance with the terms of the Plan, and against payment therefor, and when the Registration Statement has become effective under the Securities Act, will be validly issued, fully paid and non-assessable.

We consent to the filing of this opinion as an exhibit to the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP