Related papers: High Performance Algorithms for Quantum Gravity an…
The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…
Quantum-mechanical phenomena are playing an increasing role in information processing, as transistor sizes approach the nanometer level, and quantum circuits and data encoding methods appear in the securest forms of communication.…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
Simulating non-wetting fluid invasion in volumetric images of porous materials is of broad interest in applications as diverse as electrochemical devices and CO2 sequestration. Among available methods, image-based algorithms offer much…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
Given black-box access to the input and output systems, we develop the first efficient quantum causal order discovery algorithm with polynomial query complexity with respect to the number of systems. We model the causal order with quantum…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
We present a general method to convert algorithms into faster algorithms for almost-regular input instances. Informally, an almost-regular input is an input in which the maximum degree is larger than the average degree by at most a constant…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
Coordination of dynamical routes can alleviate traffic congestion and is essential for the coming era of autonomous self-driving cars. However, dynamical route coordination is difficult and many existing routing protocols are either static…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional non-convex variational parameter landscape. To simplify this optimization, we can reduce the search space using problem…
In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables…