Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with what we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required.
There are other pseudo-telepathy games that are related to the magic square game. Ad 'an Cabello's game @cite_31 @cite_26 does not resembles the magic square game on first approach. However, closer analysis reveals that the two games are totally equivalent!
@cite_31 @cite_26
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(2016) introduced the notion of a pseudo-count, derived from a density model, to generalize count-based exploration to non-tabular reinforcement learning. This pseudo-count was used to generate an exploration bonus for a DQN agent and combined with a mixed Monte Carlo update was sufficient to achieve state of the art on the Atari 2600 game Montezuma's Revenge. We consider two questions left open by their work: First, how important is the quality of the density model for exploration? Second, what role does the Monte Carlo update play in exploration? We answer the first question by demonstrating the use of PixelCNN, an advanced neural density model for images, to supply a pseudo-count. In particular, we examine the intrinsic difficulties in adapting 's approach when assumptions about the model are violated. The result is a more practical and general algorithm requiring no special apparatus. We combine PixelCNN pseudo-counts with different agent architectures to dramatically improve the state of the art on several hard Atari games. One surprising finding is that the mixed Monte Carlo update is a powerful facilitator of exploration in the sparsest of settings, including Montezuma's Revenge. Bell inequality violations correspond to behavior of entangled quantum systems that cannot be simulated classically. We give two new two-player games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work.The first game is based on the Hidden Matching problem of quantum communication complexity, introduced by Bar-Yossef, Jayram, and Kerenidis. This game can be won with probability 1 by a quantum strategy using a maximally entangled state with local dimension n (e.g., log n EPR-pairs), while we show that the winning probability of any classical strategy differs from 1 2 by at most O(log(n) sqrt(n)).The second game is based on the integrality gap for Unique Games by Khot and Vishnoi and the quantum rounding procedure of Kempe, Regev, and Toner. Here n-dimensional entanglement allows to win the game with probability 1 (log n)^2, while the best winning probability without entanglement is 1 n. This near-linear ratio ( Bell inequality violation'') is near-optimal, both in terms of the local dimension of the entangled state, and in terms of the number of possible outputs of the two players. We study the connection between pebble games and complexity. First, we derive complexity results using pebble games. It is shown that three pebble games used for studying computational complexity are equivalent: namely, the two-person pebble game of Dymond-Tompa, the two-person pebble game of Raz-McKenzie, and the one-person reversible pebble game of Bennett have the same pebble costs over any directed acyclic graph. The three pebble games have been used for studying parallel complexity and for proving lower bounds under restricted settings, and we show one more such lower bound on circuit-depth. Second, the pebble costs are applied to proof complexity. Concerning a family of unsatisfiable CNFs called pebbling contradictions, the pebble cost in any of the pebble games controls the scaling of some parameters of resolution refutations. Namely, the pebble cost controls the minimum depth of resolution refutations and the minimum size of tree-like resolution refutations. Finally, we study the space complexity of computing the pebble costs and of computing the minimum depth of resolution refutations. It is PSPACE-complete to compute the pebble cost in any of the three pebble games, and to compute the minimum depth of resolution refutations. Pseudo-random number generation on the Atari 2600 was commonly accomplished using a Linear Feedback Shift Register (LFSR). One drawback was that the initial seed for the LFSR had to be hard-coded into the ROM. To overcome this constraint, programmers sampled from the LFSR once per frame, including title and end screens. Since a human player will have some random amount of delay between seeing the title screen and starting to play, the LFSR state was effectively randomized at the beginning of the game despite the hard-coded seed. Other games used the player’s actions as a source of randomness. Notable pseudo-random games include Adventure in which a bat randomly steals and hides items around the game world and River Raid which used randomness to make enemy movements less predictable. Relying on the player to provide a source of randomness is not sufficient for computer controlled agents which are capable of memorizing and repeating pre-determined sequences of actions. Ideally, the games themselves would provide stochasticity generated from an external source such as the CPU clock. In practice, this was not an option presented by the hardware. Atari games are deterministic given a fixed policy leading to a set sequence of actions. This article discusses different approaches for adding stochasticity to Atari games and examines how effective each approach is at derailing an agent known to memorize action sequences. Additionally it is the authors’ hope that this article will spark discussion in the community over the following questions: