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We are acting as counsel to Rigetti Computing, Inc., a Delaware corporation (the “Company”), in connection with the issuance and sale of up to $350,000,000 of shares of common stock, par value $0.0001 per share, of the Company (the “ATM Shares”), from time to time and at various prices in an “at the market offering” pursuant to the terms of the Open Market Sale Agreement^SM, dated May 29, 2025 (the “Agreement”), by and between the Company and Jefferies LLC, as sales agent (the “Agent”). The offering of the Shares by the Company is being made pursuant to its automatic shelf registration statement on Form S-3, filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), filed on May 29, 2025 (as may be amended from time to time, the “Registration Statement”), including a base prospectus dated May 29, 2025 (the “Base Prospectus”) that forms a part thereof, and the prospectus supplement dated May 29, 2025 filed with the Commission pursuant to Rule 424(b) under the Act (the “Prospectus Supplement” and together with the Base Prospectus, the “Prospectus”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinions hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including pdfs). As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

This opinion letter is based as to matters of law solely on the Delaware General Corporation Law, as amended (the “DGCL”). We express no opinion herein as to any other statutes, rules or regulations.

Hogan Lovells US LLP is a limited liability partnership registered in the state of Delaware. “Hogan Lovells” is an international legal practice that includes Hogan Lovells US LLP and Hogan Lovells International LLP, with offices in: Alicante Amsterdam Baltimore Berlin Beijing Birmingham Boston Brussels Colorado Springs Denver Dubai Dusseldorf Frankfurt Hamburg Hanoi Ho Chi Minh City Hong Kong Houston Johannesburg London Los Angeles Luxembourg Madrid Mexico City Miami Milan Minneapolis Monterrey Munich New York Northern Virginia Paris Philadelphia Riyadh Rome San Francisco São Paulo Shanghai Silicon Valley Singapore Sydney Tokyo Warsaw Washington, D.C. For more information see www.hoganlovells.com

Rigetti Computing, Inc.

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May 29, 2025

Based upon, subject to and limited by the foregoing, we are of the opinion that assuming such issuance does not exceed the Maximum Program Amount (as defined in the Agreement), following (i) execution and delivery by the Company and Agent of the Sales Agreement, (ii) authorization by the Company’s Board of Directors (the “Board”), or authorization by a duly authorized pricing committee thereof, within the limitations established by resolutions duly adopted by the Board and duly authorized pricing committee thereof and in each case made available to us, of the terms pursuant to which the Shares may be sold pursuant to the Agreement, (iii) authorization by a person or body pursuant to an authorization granted in accordance with Section 152 of the DGCL by the Board or duly authorized pricing committee thereof, to approve issuance notices (each, an “Issuance Notice”) under the Agreement, of the terms of each Issuance Notice executed in a manner consistent with the foregoing and pursuant to which the Shares may be sold pursuant to the Agreement, (iv) the issuance of the Shares pursuant to the terms established by the Board and duly authorized pricing committee thereof and the terms of the applicable Issuance Notice and (v) receipt by the Company of the proceeds for the Shares sold pursuant to such terms and such applicable Issuance Notice, the Shares will be validly issued, fully paid and non-assessable.

This opinion letter has been prepared for use in connection with the Registration Statement and the Prospectus, and speaks as of the date hereof. We assume no obligation to advise of any changes in the foregoing subsequent to the delivery of this opinion letter.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Company’s Current Report on Form 8-K filed with the Commission on the date hereof and to the reference to this firm under the caption “Legal Matters” in the Prospectus. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Act.

Very truly yours,

/s/ HOGAN LOVELLS US LLP

HOGAN LOVELLS US LLP