Related papers: Fast optimization algorithms and the cosmological …
The standard cosmological model, now strongly constrained by direct observation at early epochs, is very successful in describing the structure of the evolved universe on large and intermediate scales. Unfortunately, serious contradictions…
The Cosmological Constant Problem is re-examined from an effective field theory perspective. While the connection between gravity and particle physics has not been experimentally probed in the quantum regime, it is severely constrained by…
We suggest a novel picture of the quantum Universe -- its creation is described by the {\em density matrix} defined by the Euclidean path integral. This yields an ensemble of universes -- a cosmological landscape -- in a mixed state which…
Computational modeling is widely used to study how humans and organizations search and solve problems in fields such as economics, management, cultural evolution, and computer science. We argue that current computational modeling research…
Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a…
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…
We consider a recent proposal to solve the cosmological constant problem within the context of brane world scenarios with infinite volume extra dimensions. In such theories bulk can be supersymmetric even if brane supersymmetry is…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only…
The traditional "explanation" for the observed acceleration of the universe is the existence of a positive cosmological constant. However, this can hardly be a truly convincing explanation, as an expanding universe is not expected to have a…
The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number $\kappa$ and the allowable error $\epsilon$ [PRX Quantum…
Spacetime geometry is treated as a fluctuating, stochastic quantum system allowing an effective quantum gravity solution to the cosmological constant problem. A Focker-Planck equation for the probability density of spacetime metric…
We prove lower bounds on the complexity of finding $\epsilon$-stationary points (points $x$ such that $\|\nabla f(x)\| \le \epsilon$) of smooth, high-dimensional, and potentially non-convex functions $f$. We consider oracle-based complexity…
Although the cosmological constant has primarily cosmological consequences, its smallness poses one of the basic problems in particle physics. Various attempts have been made to explain this mystery, but no satisfactory solution has been…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
Quantum algorithm can find target item in a database faster than any classical. One can trade accuracy for speed and find a part of the database (a block) containing the target item even faster: this is partial search. One can think of…
We consider global optimization problems, where the feasible region $\X$ is a compact subset of $\mathbb{R}^d$ with $d \geq 10$. For these problems, we demonstrate the following. First: the actual convergence of global random search…
A finite and unitary nonlocal formulation of quantum gravity is applied to the cosmological constant problem. The entire functions in momentum space at the graviton-standard model particle loop vertices generate an exponential suppression…
Within the holographic cosmology paradigm, specifically the model of McFadden and Skenderis, but more generally than that, the cosmological constant is found to naturally flow from a large value, to a small value, which can even be as low…
Several mathematical problems can be modeled as a search in a database. An example is the problem of finding the minimum of a function. Quantum algorithms for solving this problem have been proposed and all of them use the quantum search…