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Stock-based compensation - Narrative (Details) - USD ($) |  | 9 Months Ended | 12 Months Ended |
--- | --- | --- | --- | ---
Apr. 14, 2022 | Sep. 30, 2022 | Sep. 30, 2021 | Dec. 31, 2021 | Dec. 31, 2020 | Nov. 30, 2020
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Weighted average grant date fair value, stock options granted (in usd per share) |  | $ 3.1 | $ 0.36 |  |  |
Fair value of stock options vested |  | $ 6,564,103 | $ 812,329 |  |  |
Warrants, exercise price (in usd per share) |  | $ 7.91 |  |  |  |
Warrants outstanding (in shares) |  | 17,920,898 |  |  |  |
Common shares reserved for future issuance (in shares) |  | 16,965,849 |  |  |  |
Period over which shares reserved for future issuance will increase |  | 9 years |  |  |  |
Additional shares reserved for issuance, percentage |  | 5.00% |  |  |  |
Expected dividend yield |  | 0.00% | 0.00% |  |  |
Number of common stock warrants, Granted during the period |  | 1,500,081 |  |  |  |
Share-based Payment Arrangement, Option [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Expected dividend yield |  | 0.00% |  |  |  |
Two Thousand Twenty Equity Incentive Plan [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Percentage of options vested |  |  |  | 25.00% |  |
The Two Thousand Twenty Two Plan [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Number of common stock warrants, Granted during the period |  | 1,500,081 |  |  |  |
The Two Thousand Twenty Plan [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Number of common stock warrants, Granted during the period |  | 4,341,966 |  |  |  |
DWave System [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Weighted average grant date fair value, stock options granted (in usd per share) |  |  |  | $ 1.99 | $ 0.35 |
Fair value of stock options vested |  |  |  | $ 1,733,745 | $ 1,035,000 |
Expected dividend yield |  |  |  | 0.00% | 0.00% |
Number of common stock warrants, Granted during the period |  |  |  | 4,369,866 |  |
DWave System [Member] | Two Thousand Twenty Equity Incentive Plan [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award Options Grant Outstanding Number |  |  |  | $ 16,336,134,000 | $ 12,654,807,000 |
Percentage of options vested |  |  |  | 75.00% |  |
DWave System [Member] | oneyearcliff [Member] | Two Thousand Twenty Equity Incentive Plan [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period |  |  |  | 4 years |  |
D Wave Systems Common Stock Warrants [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Warrants expired (in shares) | 617,972 |  |  |  |  |
Warrants, exercise price (in usd per share) | $ 1.75 |  |  |  |  |
Warrants outstanding (in shares) |  | 0 |  |  |  |
Preferred Stock Warrants [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Warrants, exercise price (in usd per share) |  |  |  |  |  | $ 2.16
Warrants outstanding (in shares) |  | 3,247,637 |  |  |  |
Warrants, number of shares issuable (in shares) |  | 2,889,282 |  |  |  | 3,247,637
Preferred Stock Warrants [Member] | DWave System [Member] |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |
Warrants, exercise price (in usd per share) |  |  |  |  |  | $ 1.92
Warrants outstanding (in shares) |  |  |  | 3,247,637 | 1,100,000 | 3,247,637

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