Related papers: Physical complexity and black hole quantum compute…
Computers are physical systems: what they can and cannot do is dictated by the laws of physics. In particular, the speed with which a physical device can process information is limited by its energy and the amount of information that it can…
More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be…
It is not known what the limitations are on using quantum computation to speed up classical computation. An example would be the power to speed up PSPACE-complete computations. It is also not known what the limitations are on the duration…
The physical limits to computation have been under active scrutiny over the past decade or two, as theoretical investigations of the possible impact of quantum mechanical processes on computing have begun to make contact with realizable…
By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with…
Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find that…
Accounting for resources is the central issue in computational efficiency. We point out physical constraints implicit in information readout that have been overlooked in classical computing. The basic particle-counting mode of read-out sets…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
Computational problems can be classified according to their algorithmic complexity, which is defined based on how the resources needed to solve the problem, e.g. the execution time, scale with the problem size. Many problems in…
We continue our analysis of volume and energy measures that are appropriate for quantifying inductive inference systems. We extend logical depth and conceptual jump size measures in AIT to stochastic problems, and physical measures that…
We investigate if physical laws can impose limit on computational time and speed of a quantum computer built from elementary particles. We show that the product of the speed and the running time of a quantum computer is limited by the type…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
This paper reviews connections between physics and computation, and explores their implications. The main topics are computational "hardness" of physical systems, computational status of fundamental theories, quantum computation, and the…
Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on $n$ qubits which cannot be implemented inside of black holes with entropy less than…
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…
The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems.…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…