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

TL;DR

This paper introduces a modified secure multi-party quantum computation protocol utilizing triorthogonal quantum error-correcting codes, reducing constraints on the number of quantum nodes and enhancing versatility, especially for small-scale quantum systems.

Contribution

The paper proposes a new MPQC protocol based on triorthogonal QECCs, offering greater flexibility in the number of quantum nodes compared to previous protocols using triply-even QECCs.

Findings

Reduced constraints on the number of quantum nodes n

Enhanced versatility for small quantum systems in NISQ era

Applicable to error-free distributed quantum computation

Abstract

Secure multi-party quantum computation (MPQC) protocol is a versatile tool that enables error-free distributed quantum computation to a group of $n$ mutually distrustful quantum nodes even when some of the quantum nodes do not follow the instructions of the protocol honestly. However, in case of the MPQC protocols built on top of the quantum error correction technique, the versatility is significantly affected by the fact that one has to choose a particular quantum error-correcting code (QECC), which immediately applies a constraint on the number of quantum nodes $n$. Therefore, in this talk, we suggest a modified MPQC protocol based on triorthogonal QECCs which applies significantly less constraint on the number of quantum nodes $n$ if compared to the previously suggested MPQC protocol based on triply-even QECCs. Especially, the variety of available options in the region of a small number of quantum nodes $n$ becomes important in the noisy intermediate-scale quantum (NISQ) era.