Exhibit 5.1

John T. McKenna

+1 650 843 5059

jmckenna@cooley.com

October 20, 2021

IonQ, Inc.

4505 Campus Drive

College Park, MD 20740

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

Ladies and Gentlemen:

We have acted as counsel to IonQ, Inc., a Delaware corporation (the “Company”), with respect to certain matters in connection with the filing by the Company of a Registration Statement on Form S-1 (the “Registration Statement”) (No. 333-260008) 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, par value of $0.0001 per share (the “Common Stock”), of the Company upon the exercise of warrants issued by the Company, and (b) the resale of Common Stock and warrants issued by the Company held by certain stockholders and holders of outstanding warrants of the Company, as follows:

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

(ii) the issuance of up to 7,500,000 shares (the “Public Warrant Shares” and, together with the Private Warrant Shares, the “Warrant Shares”) of Common Stock upon the exercise of certain outstanding warrants (the “Public Warrants” and, together with the Private Warrants, the “Warrants”) by the holders thereof;

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

(iv) the resale of up to 105,086,092 shares of Common Stock (the “Selling Stockholder Shares”) consisting of:

• 34,500,000 shares of Common Stock issued pursuant to subscription agreements entered into on March 7, 2021;

• 7,500,000 shares of Common Stock issued in a private placement in connection with the Company’s initial public offering;

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

• 50,784,890 shares of Common Stock issued pursuant to that certain Agreement and Plan of Merger, dated March 7, 2021, by and among the Company, IonQ, Inc. (“Legacy IonQ”), and IonQ Trap Acquisition Inc. (the “Business Combination Agreement”); and

Cooley LLP    3175 Hanover Street    Palo Alto, CA    94304-1130

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IonQ, Inc.

October 20, 2021

Page Two

• up to 8,301,202 shares of Common Stock (the “Legacy Warrant Shares”) issuable upon the exercise of certain warrants (the “Legacy Warrants”) initially issued by Legacy IonQ.

The Warrants were issued pursuant to a Warrant Agreement, dated November 12, 2020, between dMY Technology Group Inc. III and Continental Stock Transfer & Trust Company, 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 Business Combination Agreement, (d) the Warrant Agreement, (e) the Legacy Warrants 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 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; and 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.

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

Our opinion herein is expressed solely 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 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 Resale Warrants that: (a) provides for

Cooley LLP    3175 Hanover Street    Palo Alto, CA    94304-1130

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IonQ, Inc.

October 20, 2021

Page Three

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 Resale Warrants.

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

1. The Warrant Shares, when issued and paid for upon exercise of the Warrants in accordance with the terms of the Warrants, 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 and Legacy Warrants Shares included in the Selling Stockholder Shares, are validly issued, fully paid and non-assessable. Any Private Warrant Shares or Legacy Warrant Shares included in the Selling Stockholder Shares, when issued and paid for in accordance with the terms of the Private Warrants or Legacy Warrants, as applicable, will be validly issued, fully paid and non-assessable.

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

Sincerely,

COOLEY LLP

By:	/S/ JOHN T. MCKENNA
	John T. McKenna

Cooley LLP    3175 Hanover Street    Palo Alto, CA    94304-1130

t: (650) 843-5000    f: (650) 849-7400    cooley.com