Tax Receivable Agreement - Narrative (Details) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Oct. 01, 2022	Oct. 01, 2022	Dec. 31, 2021
Tax Receivable Agreement [Abstract]
Cash tax savings payable to holders (as a percent)		85.00%
Cash tax savings retained (as a percent)		15.00%
Estimate of future payments	$ 34,092	$ 34,092
TRA liabilities if sufficient income to utilize tax attributes	44,396	44,396
Tax receivable agreement liabilities	32,972	$ 32,972	$ 0
Gain on reduction of TRA liability	$ 1,120

n/a

No definition available.

Name:	qtek_TaxReceivableAgreementAbstract
Namespace Prefix:	qtek_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

Tax Receivable Agreement, Gain (Loss) On Liability Decrease (Increase)

No definition available.

Name:	qtek_TaxReceivableAgreementGainLossOnLiabilityDecreaseIncrease
Namespace Prefix:	qtek_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

Carrying amount of expected future payments due under Tax receivable agreement.

No definition available.

Name:	qtek_TaxReceivableAgreementLiability
Namespace Prefix:	qtek_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

Tax Receivable Agreement Liability, Estimate Of Future Payments

No definition available.

Name:	qtek_TaxReceivableAgreementLiabilityEstimateOfFuturePayments
Namespace Prefix:	qtek_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

The amount of future payments due under Tax receivable agreement if there was sufficient income to utilize all tax attributes.

No definition available.

Name:	qtek_TaxReceivableAgreementLiabilitySufficientIncomeToUtilizeTaxAttributes
Namespace Prefix:	qtek_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

The percent of cash tax savings to be payable to holders under tax receivable agreement.

No definition available.

Name:	qtek_TaxReceivableAgreementPercentOfCashTaxSavingsPayableToHolders
Namespace Prefix:	qtek_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

The percent of cash tax savings retained under tax receivable agreement.

No definition available.

Name:	qtek_TaxReceivableAgreementPercentOfCashTaxSavingsRetained
Namespace Prefix:	qtek_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration