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Revenue Recognition
 9 Months Ended
Sep. 30, 2025
Revenue Recognition  
Revenue Recognition

(11)

Revenue Recognition

The following tables depict the disaggregation of revenue according to the type of good or service and timing of transfer of goods or services for the three and nine months ended September 30, 2025 and September 30, 2024 (in thousands):

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​

​

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Three Months Ended September 30,

​

Nine Months Ended September 30,

​

​

    

2025

    

2024

    

2025

    

2024

​

Collaborative research and professional services

​

$

1,896

​

$

1,963

​

$

4,939

​

$

6,891

​

Collaborative research materials and sales of quantum computers

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​

—

​

​

343

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​

—

​

​

1,333

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Access to quantum computing systems

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​

51

​

​

72

​

​

281

​

​

292

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​

​

$

1,947

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$

2,378

​

$

5,220

​

$

8,516

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​

​

​

​

​

​

​

​

​

​

​

​

​

​

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Three Months Ended September 30,

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Nine Months Ended September 30,

​

    

2025

    

2024

    

2025

    

2024

Revenue recognized at a point in time

​

$

—

​

$

—

​

$

—

​

$

523

Revenue recognized over time

 

 

1,947

​

 

2,378

​

 

5,220

 

 

7,993

​

​

$

1,947

​

$

2,378

​

$

5,220

​

$

8,516

​

Selected condensed consolidated balance sheet line items that reflect accounts receivable, contract assets and liabilities as of September 30, 2025, December 31, 2024 and December 31, 2023 were as follows (in thousands):

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​

​

​

​

​

​

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September 30, 2025

    

December 31, 2024

    

December 31, 2023

Trade receivables

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$

777

​

$

1,498

​

$

2,650

Unbilled receivables

​

$

1,500

​

$

929

​

$

2,379

Current portion of deferred revenue

​

$

—

​

$

(113)

​

$

(343)

Deferred revenue, less current portion

​

$

(698)

​

$

(698)

​

$

—

​

Changes in deferred revenue from contracts with customers were as follows:

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​

​

​

​

​

​

​

​

​

​

Nine Months Ended September 30,

​

​

    

2025

    

2024

​

Balance at beginning of period

​

$

(811)

​

$

(343)

​

Deferral of revenue

​

​

(110)

​

​

(771)

​

Recognition of deferred revenue

​

​

223

​

​

228

​

Total deferred revenue at end of period

​

$

(698)

​

$

(886)

​

Current portion of deferred revenue

​

$

—

​

$

(886)

​

Deferred revenue, less current portion

​

$

(698)

​

$

—

​

​

Amounts recognized as revenue from beginning contract liabilities during the three and nine months ended September 30, 2025 was $0.1 million and $0.2 million, respectively. Amounts recognized as revenue from beginning contract liabilities during the three and nine months ended September 30, 2024 was an immaterial amount and $0.2 million, respectively. Remaining performance obligations represent the portion of the transaction price that has not yet been satisfied or achieved. As of September 30, 2025, the aggregate amount of the transaction price allocated to remaining performance obligations was approximately $5.5 million. The Company expects to recognize estimated revenues related to performance obligations that are unsatisfied (or partially satisfied) during the next twelve months, except for remaining performance obligations totaling $0.9 million.

The Company has not identified any costs that are incremental to the acquisition of customer contracts that would be capitalized as deferred costs on the balance sheet. Accordingly, the Company does not have any capitalized contract fulfillment costs as of September 30, 2025 or December 31, 2024.