ua nt - p h / 99 08 04 3 v 1 1 3 A ug 1 99 9 Ultimate physical limits to computation

Computers are physical systems: what they can and cannot do is dictated by the laws of physics (1-23). In particular, the speed with which a physical device can process information is limited by its energy (24-27), and the amount of information that it can process is limited by the number of degrees of freedom it possesses (1-2). The way in which it processes information is determined by the forces of nature that the computer has at its disposal. This paper explores the fundamental physical limits of computation as determined by the speed of light c, the quantum scale ¯ h and the gravitational constant G. As an example, quantitative bounds are put to the computational power of an 'ultimate laptop' with a mass of one kilogram confined to a volume of one liter. Over the past half century, the amount of information that computers are capable of processing and the rate at which they process it has doubled every two years, a phenomenon known as Moore's law. A variety of technologies — most recently, integrated circuits — have enabled this exponential increase in information processing power. There is no particular reason why Moore's law should continue to hold, other than human ingenuity. Moore's law is a phenomenological law whose continued accuracy depends upon the uncertaintly of future technological development, not a law of nature. At some point, Moore's law must break down. The question is, When? Extrapolation of current exponential improvements over two more decades would result in computers that process information at the scale of individual atoms. Although an Avogadro scale computer that can act on 10 23 bits at a speed of 10 15 cycles per second might seem implausible, prototype quantum computers that store and process information on individual atoms have already been demonstrated. There is nothing in the laws of physics that forbids the construction of an Avogadro-scale computer.