Secure multi-party quantum computation protocol built on top of the triply-even quantum error-correcting codes

Secure multi-party quantum computation (MPQC) protocol is a cryptographic task which 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 [1]. In this talk we describe MPQC protocol which adopts unconventional triply-even Calderbank-Shor-Steane (CSS) quantum error-correcting codes (QECCs) [2-5]. Our decision allows us to avoid previously indispensable but ambiguous procedure of the “magic” state verification present in the preceding MPQC protocol built on top of the self-dual CSS QECCs [6]. Besides, since every extra qubit reduces the credibility of physical devices, our suggestion makes the MPQC protocol more accessible for the near-future technology by reducing the number of necessary qubits per quantum node from $n^2 + 4n$ to $n^2 + 3n$ [7].

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[4] K. Betsumiya and A. Munemasa, J. London Math. Soc. 86, 1-16 (2012).

[5] E. Knill, R. Laflamme, and W. Zurek, arXiv:quant-ph/9610011 (1996).

[6] V. Lipinska, J. Ribeiro, and S. Wehner, Phys. Rev. A 102, 022405 (2020).

[7] P. A. Mishchenko and K. Xagawa, arXiv:2206.04871 (2022).