How Quantum Computers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation

The feasibility of computationally superior quantum computers is one of the most exciting and clear-cut scientific questions of our time. The question touches on fundamental issues regarding probability, physics, and computability, as well as on exciting problems in experimental physics, engineering, computer science, and mathematics. We propose three related directions towards a negative answer. The first is a conjecture about physical realizations of quantum codes, the second has to do with correlations in stochastic physical systems, and the third proposes a model for quantum evolutions when noise accumulates. The paper is dedicated to the memory of Itamar Pitowsky.Comment: 16 page

Three Puzzles on Mathematics, Computation, and Games

In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure

Voluntary Commitments Lead to Efficiency

Consider an agent (manager,artist, etc.) who has imperfect private information about his productivity. At the beginning of his career (period 1, “short run”), the agent chooses among publicly observable actions that generate imperfect signals of his productivity. The actions can be ranked according to the informativeness of the signals they generate. The market observes the agent’s action and the signal generated by it, and pays a wage equal to his expected productivity. In period 2 (the “long run”), the agent chooses between a constant payoff and a wage proportional to his true productivity, and the game ends. We show that in any equilibrium where not all types of the agent choose the same action, the average productivity of an agent choosing a less informative action is greater. However, the types choosing that action are not uniformly higher. In particular, we derive conditions for the existence of a tripartite equilibrium where low and high types pool on a less informative action while medium (on average, lower) types choose to send a more informative signal.signalling, career concerns

Structural Robustness of Large Games

This short survey discusses recent findings on the robustness of Nash equilibria of strategic games with many semianonymous players. It describes the notion of structural robustness and its general consequences, as well as implications to particular games, such as ones played on the web and market games.Nash Equilibrium,ex-post Nash, anonymous games, market games, rational expectations, structural robustness, information proofness, web games