Exhibit 5.1

	LUCOSKY BROOKMAN LLP 101 Wood Avenue South 5th Floor Woodbridge, NJ 08830 T - (732) 395-4400 F- (732) 395-4401
	111 Broadway Suite 807 New York, NY 10006 T - (212) 417-8160 F - (212) 417-8161 www. lucbro.com

October 9, 2025

Quantum Computing, Inc.

5 Marine View Plaza, Suite 214

Hoboken, NJ 07030

RE: Quantum Computing, Inc.’s Registration Statement on Form S-3ASR

Ladies and Gentlemen:

We have acted as counsel to you, Quantum Computing, Inc., a Delaware corporation, (the “Company”) in connection with the Company’s Registration Statement on Form S-3ASR filed with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”) on the date hereof (the “Registration Statement ”). The Registration Statement relates to the resale by certain selling stockholders of up to an aggregate of 37,183,937 shares (the “Shares”) of the Company’s common stock, $0.0001 par value per share (the “Common Stock”), all in accordance with those certain Securities Purchase Agreements, each dated as of October 5, 2025 (the “Purchase Agreements”), by and among the Company and the Purchasers named therein; and pursuant to that certain Placement Agency Agreement, dated October 5, 2025 (the “Placement Agency Agreement”). The Purchase Agreement, and the Placement Agency Agreement are referred to collectively herein as the “Transaction Documents”.

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

In connection with this opinion, we have examined the originals or copies certified or otherwise identified to our satisfaction of the following:

(a) the Amended and Restated Certificate of Incorporation of the Company;

(b) the Amended and Restated Bylaws of the Company;

(c) certain resolutions of the Board of Directors of the Company related to the filing of the Registration Statement, the authorization and issuance of the Shares;

(d) the Registration Statement and all exhibits thereto;

(e) the Transaction Documents; and

(f) such other records, documents and instruments as we deemed relevant and necessary for purposes of the opinion stated herein.

In addition to the foregoing, we also have relied as to matters of fact upon the representations made by the Company and its representatives and we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, and the conformity to original documents of all documents submitted to us certified or photostatic copies. 

Based upon the foregoing and in reliance thereon, and subject to the qualifications, limitations, exceptions and assumptions set forth herein, we are of the opinion that the Shares have been duly authorized by all necessary corporate action on the part of the Company under the General Corporation Law of the State of Delaware (the “DGCL”) and are validly issued, fully paid and non-assessable.

The opinion expressed herein is limited to those matters governed by the DGCL. This opinion letter is limited to the laws in effect as of the date hereof and is provided exclusively in connection with the public offering contemplated by the Registration Statement.

This opinion letter is qualified to the extent that the enforceability of any applicable agreement, document, or instrument discussed herein may be limited by or subject to bankruptcy, insolvency, fraudulent transfer or conveyance, reorganization, moratorium or other similar laws relating to or affecting creditors’ rights generally, and general equitable or public policy principles.

This opinion letter speaks only as of the date hereof and we assume no obligation to update or supplement this opinion letter if any applicable laws change after the date of this opinion letter or if we become aware after the date of this opinion letter of any facts, whether existing before or arising after the date hereof, that might change the opinions expressed above.

This opinion letter is furnished in connection with the filing of the Registration Statement and may not be relied upon for any other purpose without our prior written consent in each instance. Further, no portion of this letter may be quoted, circulated or referred to in any other document for any other purpose without our prior written consent.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference of this firm under the caption “Legal Matters” in the prospectus which is made part of the Registration Statement. In giving this consent, we do not thereby admit that we come within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Lucosky Brookman LLP

Lucosky Brookman LLP