Related papers: Physical complexity and black hole quantum compute…
We explain that black holes are the most efficient capacitors of quantum information. It is thereby expected that all sufficiently advanced civilizations ultimately employ black holes in their quantum computers. The accompanying Hawking…
After reviewing the relation of entropy to information, I derive the entropy bound as applied to bounded weakly gravitating systems, and review the bound's applications to cosmology as well as its extensions to higher dimensions. I then…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Quantum information can provide a lens for characterizing the operational implications of spacetime physics. A well-known result in this area is that quantum entanglement is degraded in the vicinity of a black hole. This result treats the…
It is currently not possible to quantify the resources needed to perform a computation. As a consequence, it is not possible to reliably evaluate the hardware resources needed for the application of algorithms or the running of programs.…
We clarify the confusion, misunderstanding and misconception that the physical finiteness of the universe, if the universe is indeed finite, would rule out all hypercomputation, the kind of computation that exceeds the Turing computability,…
Over the last few decades, developments in the physical limits of computing and quantum computing have increasingly taught us that it can be helpful to think about physics itself in computational terms. For example, work over the last…
This thesis deals with the problematics of the scalability of fault-tolerant quantum computing. This question is studied under the angle of estimating the resources needed to set up such computers. What we call a resource is, in principle,…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
One of the predominant challenges when engineering future quantum information processors is that large quantum systems are notoriously hard to maintain and control accurately. It is therefore of immediate practical relevance to investigate…
The anticipated applications of quantum computers span across science and industry, ranging from quantum chemistry and many-body physics to optimization, finance, and machine learning. Proposed quantum solutions in these areas typically…
Future quantum computers are anticipated to be able to perform simulations of quantum many-body systems and quantum field theories that lie beyond the capabilities of classical computation. This will lead to new insights and predictions for…
The emergence of a complex, large-scale organisation of cosmic matter into the Cosmic Web is a beautiful exemplification of how complexity can be produced by simple initial conditions and simple physical laws. In the epoch of Big Data in…
While several paths have emerged in microelectronics and computing as follow-ons to Turing architectures, and have been implemented using essentially silicon circuits, very little beyond Moore research has considered: (1) first biological…
Merely by existing, all physical systems register information. And by evolving dynamically in time, they transform and process that information. The laws of physics determine the amount of information that a physical system can register…
Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…
Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_…
There are inherent limits in classical computation for it to serve as an adequate model of human cognition. In particular, non-commutativity, while ubiquitous in physics and psychology, cannot be sufficiently handled. We propose that we…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…