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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