Related papers: Ancient Computers
The original Pascaline was a mechanical calculator able to sum and subtract integers. It encodes information in the angles of mechanical wheels and through a set of gears, and aided by gravity, could perform the calculations. Here, we show…
Recent astonishing experiments with quantum computers have demonstrated unambiguously the existence of a quantum multiverse, where calculations of mind-boggling complexity are effortlessly computed in just a few minutes. Here, we…
Pebble games are popular models for analyzing time-space trade-offs. In particular, the reversible pebble game is often applied in quantum algorithms like Grover's search to efficiently simulate classical computation on inputs in…
Quantum computers (QCs), which work based on the law of quantum mechanics, are expected to be faster than classical computers in several computational tasks such as prime factoring and simulation of quantum many-body systems. In the last…
The primordial model of quantum computation was introduced over thirty years ago and the first quantum algorithms have appeared for over twenty years. Yet the exact architectures for quantum computer seem foreign to an undergraduate student…
The Fibonacci numbers are familiar to all of us. They appear unexpectedly often in mathematics, so much there is an entire journal and a sequence of conferences dedicated to their study. However, there is also another sequence of numbers…
Quantum computing has the potential to provide exponential performance benefits in processing over classical computing. It utilizes quantum mechanics phenomena (such as superposition, entanglement, and interference) to solve a computational…
The challenge of programming classical computers to play traditional, competitive games against human players has helped to advance classical hardware and software. Quantum computers have the potential to play games in a unique way:…
The Fibonacci numbers are a sequence of integers in which every number after the first two, 0 and 1, is the sum of the two preceding numbers. These numbers are well known and algorithms to compute them are so easy that they are often used…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
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…
Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…
Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi. Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals.…
Today's PCs can directly manipulate numbers not longer than 64 bits because the size of the CPU registers and the data-path are limited. Consequently, arithmetic operations such as addition, can only be performed on numbers of that length.…
The Achilles heel of classic analog computers was the complex, error prone, and time consuming process of programming. This typically involved manually patching hundreds or even thousands of connections between individual computing elements…
We propose a novel physical realization of a quantum computer. The qubits are electric dipole moments of ultracold diatomic molecules, oriented along or against an external electric field. Individual molecules are held in a 1-D trap array,…
The quantum computer is supposed to process information by applying unitary transformations to the complex amplitudes defining the state of N qubits. A useful machine needing N=1000 or more, the number of continuous parameters describing…
Quantum computers are believed to bring computational advantages in simulating quantum many body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems…
Negative and complex numbers are so familiar in modern mathematics, physics, and engineering that it is easy to forget how uncertain their status once was. They did not become established through a single route. This article follows four…