相关论文: Engines of Parsimony: Part I; Limits on Computatio…
In Part I of this series, the limits on the sustained performance of large reversible computers were investigated and found to scale as $\sqrt{AV}$ where $A$ is the convex bounding surface area of the system and $V$ its internal volume,…
This paper concludes a three-Part series on the limits the laws of physics place on the sustained performance of reversible computers. Part I concerned aggregate performance in terms of computational operations per unit time, but neglected…
A computer, in order to perform a given computation, requires a certain amount of space (memory) and a certain amount of time (runtime). This leaves certain computations beyond reach due to technological limits on processing speed and…
If the 20th century was known for the computational revolution, what will the 21st be known for? Perhaps the recent strides in the nascent fields of molecular programming and biological computation will help bring about the 'Coming Era of…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an…
An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the…
The upper limit on what is computable in our universe is unknown, but widely believed to be set by the Turing machine -- with a function being physically computable if and only if it is Turing-computable. I show how this apparently mild…
It is now well established that there is no lower bound for the energy dissipated during a computation. The relevance of the zero-energy limit is unclear, however, because it entails computations that are unreliable or infinitely slow, or…
The key factor currently limiting the advancement of computational power of electronic computation is no longer the manufacturing density and speed of components, but rather their high energy consumption. While it has been widely argued…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
We investigate the service-rate region (SRR) of distributed storage systems that employ linear codes. We focus on systems where each server stores one code symbol, and a user recovers a data symbol by accessing any of its recovery groups,…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
In this paper we prove a theorem that provides an upper bound for the density of packings of congruent copies of a given convex body in $\mathbb{R}^n$; this theorem is a generalization of the linear programming bound for sphere packings. We…
We prove two-sided bounds on the expected values of several geometric functionals of the convex hull of Brownian motion in $\mathbb{R}^n$ and their inverse processes. This extends some recent results of McRedmond and Xu (2017),…
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…
Conventional computing has many sources of heat dissipation, but one of these--the Landauer limit--poses a fundamental lower bound of 1 bit of entropy per bit erased. 'Reversible Computing' avoids this source of dissipation, but is…
Motivated by studies of ultimate speed of computers, we examine the question of minimum time of orthogonalization in a simple anharmonic oscillator and find an upper bound on the rate of computations. Furthermore, we investigate the growth…
We describe an algorithm for solving an important geometric problem arising in computer-aided manufacturing. When cutting away a region from a solid piece of material -- such as steel, wood, ceramics, or plastic -- using a rough tool in a…
We study the maximum speed of quantum computation and how it is affected by limitations on physical resources. We show how the resulting concepts generalize to a broader class of physical models of computation within dynamical systems and…