Rigetti Computing (RGTI) S-8 Registration of securities for employees

Exhibit 5.1

Sarah Sellers

+1 212 479 6370

ssellers@cooley.com

June 10, 2022

Rigetti Computing, Inc.

775 Heinz Avenue

Berkeley, CA, 94710

Re:    Rigetti Computing, Inc. – Registration Statement on Form S-8

Ladies and Gentlemen:

We have acted as counsel to Rigetti Computing, Inc., a Delaware corporation (the “Company”), in connection with the filing of a Registration Statement on Form S-8 (the “Registration Statement”) with the Securities and Exchange Commission covering the offering of up to 39,757,334 shares (the “Shares”) of the Company’s common stock, par value $0.0001 per share (“Common Stock”), consisting of (a) 18,332,215 shares of Common Stock issuable pursuant to the Company’s 2022 Equity Incentive Plan (the “2022 EIP”), (b) 3,055,370 shares of Common Stock issuable pursuant to the Company’s 2022 Employee Stock Purchase Plan (together with 2022 EIP, the “2022 Plans”), (c) 18,367,696 shares of Common Stock issuable pursuant to awards granted under the Rigetti & Co, Inc. 2013 Equity Incentive Plan, as amended (the “2013 Plan”), which awards were assumed by the Company pursuant to the Agreement and Plan of Merger, dated October 6, 2021, as amended on December 23, 2021 and further amended on January 10, 2022 (as so amended, the “Merger Agreement”), by and among Supernova Partners Acquisition Company II, Ltd., a Cayman Islands exempted company, Supernova Merger Sub, Inc., a Delaware corporation, Supernova Romeo Merger Sub, LLC, a Delaware limited liability company, and Rigetti Holdings, Inc., a Delaware corporation, and (d) 2,053 shares of Common Stock issuance pursuant to option awards granted under the QxBranch, Inc. 2018 Equity Compensation Plan (the “QxBranch Plan” and, collectively, with the 2013 Plan and the 2022 Plans, the “Plans”), which awards were assumed by the Company pursuant to the Merger Agreement.

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and related prospectuses, (b) the Company’s certificate of incorporation and bylaws, each as currently in effect, (c) the Merger Agreement, (d) the Plans, and (e) originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below.

We note that the Company was initially incorporated under the laws of the Cayman Islands and was domesticated as a corporation in the State of Delaware in accordance with Section 388 of the General Corporation Law of the State of Delaware (the “Domestication”). We have assumed all matters determinable under the laws of the Cayman Islands, including without limitation that (i) immediately prior to the Domestication, the Company was duly organized, validly existing and in good standing under the laws of the Cayman Islands, (ii) the Company had full power, authority and legal right to domesticate in the State of Delaware pursuant to Section 388, (iii) the laws of the Cayman Islands permitted the Company to domesticate in the State of Delaware pursuant to Section 388, (iv) the discontinuation of the Company from the Cayman Islands was duly authorized by all necessary corporate action as provided in its governing documents and was

COOLEY LLP 55 HUDSON YARDS NEW YORK, NY 10001-2157

t: (212) 479-6000 F: (212) 479-6275 COOLEY.COM

June 10, 2022

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duly effected in accordance with Cayman Islands law, (v) any and all consents, approvals and authorizations from applicable Cayman Island governmental authorities required to authorize and permit the Company to domesticate in the State of Delaware pursuant to Section 388 were obtained, and (vi) the approval of the 2022 Plans, and the approval of the Merger Agreement pursuant to which the 2013 Plan and QxBranch Plan were assumed, in each case by the board and shareholders of the Company as a Cayman Islands exempted company prior to the Domestication were done in accordance with the applicable governing documents of the Company as a Cayman Islands exempted company and the laws of the Cayman Islands.

We have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies, the accuracy, completeness and authenticity of certificates of public officials and the due authorization, execution and delivery of all documents by all persons other than the Company where authorization, execution and delivery are prerequisites to the effectiveness thereof. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold and issued in accordance with the Plans, the Registration Statement and related prospectuses, will be validly issued, fully paid, and nonassessable (except as to shares issued pursuant to deferred payment arrangements, which will be fully paid and nonassessable when such deferred payments are made in full).

We consent to the filing of this opinion as an exhibit to the Registration Statement.

Sincerely,

COOLEY LLP

By:	/s/ Sarah Sellers
	Sarah Sellers

COOLEY LLP 55 HUDSON YARDS NEW YORK, NY 10001-2157

t: (212) 479-6000 F: (212) 479-6275 COOLEY.COM