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Register a new userSudoQ -- a quantum variant of the popular game
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We introduce SudoQ, a quantum version of the classical game Sudoku. Allowing the entries of the grid to be (non-commutative) projections instead of integers, the solution set of SudoQ puzzles can be much larger than in the classical (commutative) setting. We introduce and analyze a randomized algorithm for computing solutions of SudoQ puzzles. Finally, we state two important conjectures relating the quantum and the classical solutions of SudoQ puzzles, corroborated by analytical and numerical evidence.
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We introduce a quantum version of the Game of Life and we use it to study the emergence of complexity in a quantum world. We show that the quantum evolution displays signatures of complex behaviour similar to the classical one, however a regime exists, where the quantum Game of Life creates more complexity, in terms of diversity, with respect to the corresponding classical reversible one.
The Systematic Normal Form (SysNF) is a canonical form of lattices introduced in [Eldar,Shor 16], in which the basis entries satisfy a certain co-primality condition. Using a smooth analysis of lattices by SysNF lattices we design a quantum algorithm that can efficiently solve the following variant of the bounded-distance-decoding problem: given a lattice L, a vector v, and numbers b = {lambda}_1(L)/n^{17}, a = {lambda}_1(L)/n^{13} decide if vs distance from L is in the range [a/2, a] or at most b, where {lambda}_1(L) is the length of Ls shortest non-zero vector. Improving these parameters to a = b = {lambda}_1(L)/sqrt{n} would invalidate one of the security assumptions of the Learning-with-Errors (LWE) cryptosystem against quantum attacks.
The aim of this note is to give a short and popular review of the ideas which led to my model of magnetic monopoles (hep-ph/9708394) and my prediction of the second kind of electromagnetic radiation. I will also point out the many and far-reaching consequences if these magnetic photon rays would be confirmed.
We investigate the quantum dynamics of a spin chain that implements a quantum analog of Conways game of life. We solve the time-dependent Schrodinger equation starting with initial separable states and analyse the evolution of quantum correlations across the lattice. We report examples of evolutions leading to all-entangled chains and/or to time oscillating entangling structures and characterize them by means of entanglement and network measures. The quantum patterns result to be quite different from the classical ones, even in the dynamics of local observables. A peculiar instance is a structure behaving as the quantum analog of a blinker, but that has no classical counterpart.
Nonlocal game as a novel witness of the nonlocality of entanglement is of fundamental importance in various fields. The known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks of single entanglement. Our goal in this paper is to propose a unified method for constructing cooperating games in network scenarios. We first propose an efficient method to construct numerous multipartite games from any graphs. The main idea is the graph representation of entanglement-based quantum networks. We further specify these graphic games with quantum advantages by providing a simple sufficient and necessary condition. The graphic games imply the first linear testing of the nonlocality of general quantum networks consisting of EPR states. It also allows generating new instances going beyond well-known CHSH games. Our result has interesting applications in quantum networks, Bell theory, computational complexity, and theoretical computer science.
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