Distributed Fast Crash-Tolerant Consensus with Nearly-Linear Quantum Communication

Authors Mohammad T. HajiAghayi, Dariusz R. Kowalski, Jan Olkowski



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Author Details

Mohammad T. HajiAghayi
  • University of Maryland, College Park, MD, USA
Dariusz R. Kowalski
  • School of Computer and Cyber Sciences, Augusta University, GA, USA
Jan Olkowski
  • University of Maryland, College Park, MD, USA

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Mohammad T. HajiAghayi, Dariusz R. Kowalski, and Jan Olkowski. Distributed Fast Crash-Tolerant Consensus with Nearly-Linear Quantum Communication. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 80:1-80:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.80

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 Ω(√{n/log n}) on expected time complexity of Consensus in any classical (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 Ω(√{n/log n}) barrier for consensus in the classical (deterministic and randomized) networks by enhancing the model with quantum channels. In such networks, quantum communication between every pair of processes participating in the protocol is also allowed. 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 Ω(√{n/log n}) for the classical computation models).

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Theory of computation → Distributed algorithms
Keywords
  • distributed algorithms
  • quantum algorithms
  • adaptive adversary
  • crash failures
  • Consensus
  • quantum common coin
  • approximate counting

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