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Strategies for Quantum Races

Authors Troy Lee, Maharshi Ray, Miklos Santha



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Author Details

Troy Lee
  • Centre for Quantum Software and Information, School of Software, Faculty of Engineering and Information Technology, University of Technology Sydney, Australia
Maharshi Ray
  • Centre for Quantum Technologies, National University of Singapore, Singapore
Miklos Santha
  • IRIF, Univ. Paris Diderot, CNRS, 75205 Paris, France
  • and, Centre for Quantum Technologies and MajuLab, National University of Singapore, Singapore 117543

Cite AsGet BibTex

Troy Lee, Maharshi Ray, and Miklos Santha. Strategies for Quantum Races. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 51:1-51:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ITCS.2019.51

Abstract

We initiate the study of quantum races, games where two or more quantum computers compete to solve a computational problem. While the problem of dueling algorithms has been studied for classical deterministic algorithms [Immorlica et al., 2011], the quantum case presents additional sources of uncertainty for the players. The foremost among these is that players do not know if they have solved the problem until they measure their quantum state. This question of "when to measure?" presents a very interesting strategic problem. We develop a game-theoretic model of a multiplayer quantum race, and find an approximate Nash equilibrium where all players play the same strategy. In the two-party case, we further show that this strategy is nearly optimal in terms of payoff among all symmetric Nash equilibria. A key role in our analysis of quantum races is played by a more tractable version of the game where there is no payout on a tie; for such races we completely characterize the Nash equilibria in the two-party case. One application of our results is to the stability of the Bitcoin protocol when mining is done by quantum computers. Bitcoin mining is a race to solve a computational search problem, with the winner gaining the right to create a new block. Our results inform the strategies that eventual quantum miners should use, and also indicate that the collision probability - the probability that two miners find a new block at the same time - would not be too high in the case of quantum miners. Such collisions are undesirable as they lead to forking of the Bitcoin blockchain.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • Game theory
  • Bitcoin mining
  • Quantum computing
  • Convex optimization

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References

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