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abstract: 'The application and analysis of the Cut-and-Choose technique in protocols secure against quantum adversaries is not a straightforward transposition of the classical case, among other reasons due to the difficulty to use “rewinding” in the quantum realm. We introduce a Quantum Computation Cut-and-Choose (QC-CC) technique which is a generalisation of the classical Cut-and-Choose in order to build quantum protocols secure against *quantum covert adversaries*. Such adversaries can essentially deviate arbitrarily provided that their deviation is not detected with high probability. As an application of the QC-CC technique we give a protocol for securely performing a two-party quantum computation with classical input and output. As a basis we use the concept of secure delegated quantum computing [@bfk], and in particular the protocol for quantum garbled circuit computation of [@KW16] that has been proven secure against only a weak specious adversaries (defined in [@DNS10]). A unique property of these protocols is the separation between classical and quantum communications and the asymmetry between client and server, which enables us to sidestep the issues linked to quantum rewinding. This opens the possibility of applying the QC-CC technique to other quantum protocols that have this separation. In our proof of security we adapt 