Exhibit 5.1

Rupa Briggs

+1 212 479 6525

rbriggs@cooley.com

March 23, 2022

Rigetti Computing, Inc.

775 Heinz Avenue

Berkeley, CA, 94710

Re:    Rigetti Computing, Inc. – Registration Statement on Form S-1

Ladies and Gentlemen:

We have acted as counsel to Rigetti Computing, Inc., a Delaware corporation (the “Company”), and you have requested our opinion in connection with the filing of a Registration Statement on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission, including a related prospectus included in the Registration Statement (the “Prospectus”), covering the registration of (a) the issuance of shares of common stock, $0.0001 par value per share (“Common Stock”), of the Company upon the exercise of warrants issued or assumed by the Company, and (b) the resale of Common Stock and warrants held by certain stockholders and holders of outstanding warrants of the Company, as follows:

(i) the issuance of up to 19,354,059 shares of Common Stock as follows:

• up to 4,450,000 shares of Common Stock (the “Private Warrant Shares”) issuable upon the exercise of certain outstanding warrants (the “Private Warrants”) by the holders thereof;

• up to 8,624,972 shares of Common Stock (the “Public Warrant Shares” and, together with the Private Warrant Shares, the “Warrant Shares”) issuable upon the exercise of certain outstanding warrants (together with the Private Warrants, the “Warrants”) by the holders thereof; and

• up to 6,279,087 shares of Common Stock (the “Assumed Warrant Shares”) issuable upon the exercise of warrants initially issued by Rigetti Holdings, Inc. (“Legacy Rigetti”) and assumed by the Company and converted into warrants to purchase Common Stock (the “Assumed Warrants”) pursuant to that certain Agreement and Plan of Merger, dated October 6, 2021, as amended on December 23, 2021 and January 10, 2022, by and among by and among Supernova Partners Acquisition Company II, Ltd., Supernova Merger Sub, Inc., Supernova Romeo Merger Sub, LLC and Legacy Rigetti (the “Merger Agreement”).

(ii) the resale of up to 96,941,181 shares of Common Stock (the “Selling Stockholder Shares” as follows:

• 14,641,244 shares of Common Stock issued in connection with a private placement pursuant to subscription agreements entered into on October 6, 2021 and December 23, 2021 (the “Subscription Agreements”);

• up to 8,625,000 shares of common stock (the “Founder Shares”) originally issued in a private placement to Supernova Partners II LLC (“Supernova Sponsor”) pursuant to that certain Sponsor Agreement, dated as of October 6, 2021, by and among Supernova Sponsor, Supernova and Legacy Rigetti, as amended and modified from time to time (the “Sponsor Agreement”) in connection with the Supernova initial public offering, including 3,059,273 Founder Shares subject to vesting and forfeiture (the “Sponsor Vesting Shares”);

• up to 4,450,000 Private Warrant Shares;

• up to 2,446,716 Assumed Warrant Shares;

• up to 6,226,065 shares of Common Stock (the “Option Shares”) issuable upon exercise of outstanding options that were initially granted by Legacy Rigetti and assumed by the Company and converted into options to purchase Common Stock pursuant to the Merger Agreement;

• up to 6,288,369 shares of Common Stock (the “RSU Shares”) issuable upon the settlement of restricted stock units assumed by the Company and converted into restricted stock units with respect to Common Stock.

• 54,263,787 shares of Common Stock issued pursuant to the Merger Agreement; and

(iii) the resale of up to 4,450,000 Private Warrants (the “Resale Warrants”).

The Warrants were issued pursuant to a Warrant Agreement, dated March 1, 2021, between the Company and American Stock Transfer & Trust Company, LLC, as warrant agent (“Warrant Agreement”).

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and the Prospectus, (b) the Company’s certificate of incorporation and bylaws, each as currently in effect, (c) the Warrant Agreement, (d) the Subscription Agreements, (e) the Sponsor Agreement; (f) the Merger Agreement and (g) originals or copies certified to our satisfaction of such opinions, 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 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 due 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.

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 DGCL (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 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 issued and outstanding ordinary shares of the Company as an exempted company incorporated under the laws of the Cayman Islands immediately prior to the Domestication were validly issued, fully paid and nonassessable, and (vii) all share issuances and documents related thereto that were authorized by the Company prior to the Domestication, including those to be effected pursuant to or in connection with the Warrants, the Subscription Agreements, the Sponsor Agreement and the Merger Agreement 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.

Rupa Briggs Cooley LLP    55 Hudson Yards New York, NY    10001-2157

t: (212) 479-6000    f: (212) 479-6000    cooley.com

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware and the laws of the State of New York. 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.

With respect to the Warrants, the Warrant Shares, the Assumed Warrants and the Assumed Warrant Shares, we express no opinion to the extent that future issuances of securities of the Company, including the Warrant Shares and the Assumed Warrant Shares and/or antidilution adjustments to outstanding securities of the Company, including the Warrants and the Assumed Warrants, may cause the number of Warrant Shares issuable upon exercise of the Warrants or the number of Assumed Warrant Shares issuable upon exercise of the Assumed Warrants to be greater than the number of shares of Common Stock that then remain authorized but unissued. Further, we have assumed the exercise prices of the Warrants and the Assumed Warrants will not be adjusted to an amount below the par value per share of Common Stock.

With regard to our opinion concerning the Resale Warrants constituting valid and binding obligations of the Company:

(i) Our opinion is subject to, and may be limited by, (a) applicable bankruptcy, reorganization, insolvency, moratorium, fraudulent conveyance, debtor and creditor, and similar laws which relate to or affect creditors’ rights generally, and (b) general principles of equity (including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing) regardless of whether considered in a proceeding in equity or at law.

(ii) Our opinion is subject to the qualification that the availability of specific performance, an injunction or other equitable remedies is subject to the discretion of the court before which the request is brought.

(iii) We express no opinion as to any provision of the Warrants that: (a) provides for liquidated damages, buy-in damages, monetary penalties, prepayment or make-whole payments or other economic remedies to the extent such provisions may constitute unlawful penalties, (b) relates to advance waivers of claims, defenses, rights granted by law, or notice, opportunity for hearing, evidentiary requirements, statutes of limitations, trial by jury, or procedural rights, (c) restricts non-written modifications and waivers, (d) provides for the payment of legal and other professional fees where such payment is contrary to law or public policy, (e) relates to exclusivity, election or accumulation of rights or remedies, (f) authorizes or validated conclusive or discretionary determinations, or (g) provides that provisions of the Warrants are severable to the extent an essential part of the agreed exchange is determined to be invalid and unenforceable.

(iv) We express no opinion as to whether a state court outside of the State of New York or a federal court of the United States would give effect to the choice of New York law provided for in the Warrants.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that:

1. The Warrant Shares and the Assumed Warrant Shares, when issued and paid for upon exercise of the Warrants or the Assumed Warrants, as applicable, in accordance with the terms of the Warrants or the Assumed Warrants, as applicable, will be validly issued, fully paid and nonassessable.

2. The Resale Warrants constitute valid and binding obligations of the Company.

3. The Selling Stockholder Shares, other than any Private Warrant Shares, Sponsor Vesting Shares, Assumed Warrant Shares, Option Shares or RSU Shares included in the Selling Stockholder Shares, are validly issued, fully paid and nonassessable. Any Private Warrant Shares, Assumed Warrant Shares, Option Shares or RSU Shares included in the Selling Stockholder Shares, when issued and, if applicable, paid for in accordance with the terms of the Private Warrants, the Assumed Warrants, the Stock Options or the RSUs, will be validly issued, fully paid and nonassessable. The Sponsor Vesting Shares have been validly issued and are nonassessable and, when the conditions to vesting stated in the Sponsor Agreement have been satisfied, will be fully paid and no longer subject to forfeiture.

Rupa Briggs Cooley LLP    55 Hudson Yards New York, NY    10001-2157

t: (212) 479-6000    f: (212) 479-6000    cooley.com

Our opinion is limited to the matters stated herein and no opinion is implied or may be inferred beyond the matters expressly stated. Our opinion is based on these laws as in effect on the date hereof, and we disclaim any obligation to advise you of facts, circumstances, events or developments which hereafter may be brought to our attention and which may alter, affect or modify the opinion expressed herein.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to our firm under the caption “Legal Matters” in the Prospectus.

[signature page follows]

Rupa Briggs Cooley LLP    55 Hudson Yards New York, NY    10001-2157

t: (212) 479-6000 f: (212) 479-6000 cooley.com

Very truly yours, COOLEY LLP
By:	/s/ Rupa Briggs
	Rupa Briggs

Rupa Briggs Cooley LLP    55 Hudson Yards New York, NY    10001-2157

t: (212) 479-6000 f: (212) 479-6000 cooley.com