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Secure multi-party quantum computation (MPQC) protocol is a versatile toolthat enables error-free distributed quantum computation to a group of $n$mutually distrustful quantum nodes even when some of the quantum nodes do notfollow the instructions of the protocol honestly. However, in case of the MPQCprotocols built on top of the quantum error correction technique, theversatility is significantly affected by the fact that one has to choose aparticular quantum error-correcting code (QECC), which immediately applies aconstraint on the number of quantum nodes $n$. Therefore, in this talk, wesuggest a modified MPQC protocol based on triorthogonal QECCs which appliessignificantly less constraint on the number of quantum nodes $n$ if compared tothe previously suggested MPQC protocol based on triply-even QECCs. Especially,the variety of available options in the region of a small number of quantumnodes $n$ becomes important in the noisy intermediate-scale quantum (NISQ) era.

An improvement on the versatility of secure multi-party quantum computation protocol: exploitation of triorthogonal quantum error-correcting codes