(14) 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 years ended December 31, 2025 and December 31, 2024 (in thousands):

Year Ended December 31,

  ​ ​ ​

2025

  ​ ​ ​

2024

Collaborative research and professional services

$

6,676

$

8,044

Collaborative research materials and sales of quantum computers

2,390

Access to quantum computing systems

412

356

$

7,088

$

10,790

  ​ ​ ​

Year Ended December 31,

  ​ ​ ​

2025

  ​ ​ ​

2024

Revenue recognized at a point in time

$

$

1,579

Revenue recognized over time

 

 

7,088

 

 

9,211

$

7,088

$

10,790

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

  ​ ​ ​

December 31, 2025

  ​ ​ ​

December 31, 2024

  ​ ​ ​

December 31, 2023

Trade receivables

$

1,204

$

1,498

$

2,650

Unbilled receivables

$

1,347

$

929

$

2,379

Current portion of deferred revenue

$

(847)

$

(113)

$

(343)

Deferred revenue, less current portion

$

(698)

$

(698)

$

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

Year Ended December 31,

  ​ ​ ​

2025

  ​ ​ ​

2024

Balance at beginning of period

$

(811)

$

(343)

Deferral of revenue

(963)

(698)

Recognition of deferred revenue

229

230

Total deferred revenue at end of period

$

(1,545)

$

(811)

Current portion of deferred revenue

$

(847)

$

(113)

Deferred revenue, less current portion

$

(698)

$

(698)

Amounts recognized as revenue from beginning contract liabilities during the years ended December 31, 2025 and December 31, 2024 totaled $0.1 million 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 December 31, 2025, the aggregate amount of the transaction price allocated to remaining performance obligations was approximately $3.8 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 $0.8 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 in accordance with ASC 340-40. Accordingly, the Company did not have any capitalized contract fulfillment costs as of December 31, 2025 or December 31, 2024.

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Historical Timeline

Fiscal YearFiled
2025Mar 4, 2026Showing above
2024Mar 7, 2025
2023Mar 14, 2024
2022Mar 27, 2023

About Revenue Disclosures

Revenue disclosures under ASC 606 explain how a company identifies performance obligations, allocates transaction prices, and determines when revenue is recognized. This section is essential for understanding whether reported revenue reflects genuine economic activity or aggressive accounting choices. Analysts examine the mix of point-in-time versus over-time recognition, which directly affects revenue timing and comparability.

Key signals: rising contract liabilities (deferred revenue) suggest strong future revenue visibility, while declining contract assets may indicate slowing project milestones. Watch for variable consideration estimates — rebates, returns, and performance bonuses that require management judgment. Significant changes in disaggregated revenue by geography or product line can reveal shifting business mix before it appears in headline numbers. Compare revenue growth against contract liability growth to assess sustainability, and scrutinize any changes in the timing of recognition that coincide with earnings pressure.