Fault-Tolerant Consensus in Quantum Networks

MohammadTaghi Hajiaghayi; Dariusz R. Kowalski; Jan Olkowski

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arXiv · 2305.10618

Fault-Tolerant Consensus in Quantum Networks

MohammadTaghi Hajiaghayi·Dariusz R. Kowalski·Jan Olkowski

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Abstract

Fault-tolerant consensus is about reaching agreement on some of the input values in a limited time by non-faulty autonomous processes, despite of failures of processes or communication medium. This problem is particularly challenging and costly against an adaptive adversary with full information. Bar-Joseph and Ben-Or (PODC'98) were the first who proved an absolute lower bound $\Omega(\sqrt{n/\log n})$ on expected time complexity of consensus in any classic (i.e., randomized or deterministic) message-passing network with $n$ processes succeeding with probability $1$ against such a strong adaptive adversary crashing processes. Seminal work of Ben-Or and Hassidim (STOC'05) broke the $\Omega(\sqrt{n/\log n})$ barrier for consensus in classic (deterministic and randomized) networks by employing quantum computing. They showed an (expected) constant-time quantum algorithm for a linear number of crashes $t<n/3$. In this paper, we improve upon that seminal work by reducing the number of quantum and communication bits to an arbitrarily small polynomial, and even more, to a polylogarithmic number -- though, the latter in the cost of a slightly larger polylogarithmic time (still exponentially smaller than the time lower bound $\Omega(\sqrt{n/\log n})$ for classic computation).

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MohammadTaghi Hajiaghayi, Dariusz R. Kowalski, Jan Olkowski. 2023-05-18. Fault-Tolerant Consensus in Quantum Networks. https://arxiv.org/abs/2305.10618

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