Distributed Fast Crash-Tolerant Consensus with Nearly-Linear Quantum Communication
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).
distributed algorithms
quantum algorithms
adaptive adversary
crash failures
Consensus
quantum common coin
approximate counting
Theory of computation~Quantum computation theory
Theory of computation~Distributed algorithms
80:1-80:19
Track A: Algorithms, Complexity and Games
https://arxiv.org/abs/2305.10618
Mohammad T.
HajiAghayi
Mohammad T. HajiAghayi
University of Maryland, College Park, MD, USA
Partially supported by DARPA QuICC, ONR MURI 2024 award on Algorithms, Learning, and Game Theory, Army-Research Laboratory (ARL) grant W911NF2410052, NSF AF:Small grants 2218678, 2114269, 2347322.
Dariusz R.
Kowalski
Dariusz R. Kowalski
School of Computer and Cyber Sciences, Augusta University, GA, USA
Jan
Olkowski
Jan Olkowski
University of Maryland, College Park, MD, USA
Partially supported by DARPA QuICC, ONR MURI 2024 award on Algorithms, Learning, and Game Theory, Army-Research Laboratory (ARL) grant W911NF2410052, NSF AF:Small grants 2218678, 2114269, 2347322.
10.4230/LIPIcs.ICALP.2024.80
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Mohammad T. HajiAghayi, Dariusz R. Kowalski, and Jan Olkowski
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