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Property and equipment, net (Details) - USD ($)
$ in Thousands
 3 Months Ended 6 Months Ended
Jun. 30, 2023
Jun. 30, 2022
Jun. 30, 2023
Jun. 30, 2022
Dec. 31, 2022
Property, Plant and Equipment [Line Items]          
Total property and equipment $ 25,446   $ 25,446   $ 25,405
Less: Accumulated depreciation (23,654)   (23,654)   (23,111)
Property and equipment, net 1,792   1,792   2,294
Depreciation expense 200 $ 300 500 $ 700  
North America          
Revenues from External Customers and Long-Lived Assets [Line Items]          
Long-lived assets 10,500   10,500   11,400
Quantum computer systems          
Property, Plant and Equipment [Line Items]          
Total property and equipment 13,712   13,712   13,714
Lab equipment          
Property, Plant and Equipment [Line Items]          
Total property and equipment 6,687   6,687   6,666
Computer equipment          
Property, Plant and Equipment [Line Items]          
Total property and equipment 3,573   3,573   3,545
Leasehold improvements          
Property, Plant and Equipment [Line Items]          
Total property and equipment 1,075   1,075   1,075
Furniture and fixtures          
Property, Plant and Equipment [Line Items]          
Total property and equipment 328   328   319
Construction-in-progress          
Property, Plant and Equipment [Line Items]          
Total property and equipment $ 71   $ 71   $ 86