Ultimate physical limits to computation

@article{Lloyd2000UltimatePL,
  title={Ultimate physical limits to computation},
  author={Seth Lloyd},
  journal={Nature},
  year={2000},
  volume={406},
  pages={1047-1054}
}
  • S. Lloyd
  • Published 13 August 1999
  • Physics, Medicine
  • Nature
Computers are physical systems: the laws of physics dictate what they can and cannot do. 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 process is limited by the number of degrees of freedom it possesses. Here I explore the physical limits of computation as determined by the speed of light c, the quantum scale ℏ and the gravitational constant G. As an example, I put quantitative bounds to the… Expand

Figures and Topics from this paper

The physical limits of computing
  • M. Frank
  • Computer Science
  • Computing in Science & Engineering
  • 2002
TLDR
The author reviews the fundamental technology-independent limits of computing and concludes that novel physically motivated computing paradigms can help in certain ways, but even they remain subject to some basic limits. Expand
Physical limits of computation and emergence of life
TLDR
Computability from the quantum measurement framework is discussed, which indicates that effective quantum computation is possible via the maintenance of a long-living cold decoherence-free internal state, which is achieved by applying error-correction commands to it and by screening it from thermal fluctuations. Expand
The ultimate physical limits to reversibility
We argue that if, in order to reverse an object's dynamics, we need to be able to keep track of it with enough precision, then there is an upper bound on the size of the object whose dynamics we canExpand
Realistic limits to computation I. Physical limits
The ultimate limits of computation have been determined in the hypothesis that computation is a physical process occurring in a medium immersed in a thermal reservoir at assigned (room) temperatureExpand
Physical limits on information processing
We derive a fundamental upper bound on the rate at which a device can process information (i.e., the number of logical operations per unit time), arising from quantum mechanics and generalExpand
Quantum Limit on Computational Time and Speed
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 aExpand
Applications of Finsler Geometry to Speed Limits to Quantum Information Processing
TLDR
Some relevant parts of the theory of Finsler metrics on Lie groups and homogeneous spaces such as the special unitary groups and complex projective spaces are reviewed and it is shown how these constructions can be applied to analysing the limit to the speed of quantum information processing operations in constrained quantum systems with finite dimensional Hilbert spaces of states. Expand
Numerical Analysis of Quantum Speed Limits: Controlled Quantum Spin Chain Systems with Constrained Control Functions
TLDR
A numerical search approach is used to discover specific optimal control schemes for two coupled spins controlled in two scenarios: (i) a single control field influencing each spin separately; (ii) two orthogonal control fields influencing eachspin. Expand
The Geometry of Speed Limiting Resources in Physical Models of Computation
TLDR
A family of quantum speed limit results in resource-constrained quantum systems with pure states and a finite dimensional state space are derived by using a geometric method based on right invariant action functionals on SU(N), showing that constant Hamiltonians are time optimal for these constraints. Expand
On the Interpretation of Energy as the Rate of Quantum Computation
  • M. Frank
  • Physics, Computer Science
  • Quantum Inf. Process.
  • 2005
TLDR
This paper explores the precise nature of the connection between the energy of a quantum system and the difficulty of any specific quantum or classical computational operation, and calculates its difficulty, defined as the minimum effort required to perform that operation on a worst-case input state. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 177 REFERENCES
The physical nature of information
Information is inevitably tied to a physical representation and therefore to restrictions and possibilities related to the laws of physics and the parts available in the universe. Quantum mechanicalExpand
The maximum speed of dynamical evolution
Abstract We discuss the problem of counting the maximum number of distinct states that an isolated physical system can pass through in a given period of time — its maximum speed of dynamicalExpand
The thermodynamics of computation—a review
Computers may be thought of as engines for transforming free energy into waste heat and mathematical work. Existing electronic computers dissipate energy vastly in excess of the mean thermalExpand
Complexity as thermodynamic depth
Abstract A measure of complexity for the macroscopic states of physical systems is defined. Called depth, the measure is universal: it applies to all physical systems. The form of the measure isExpand
Classical and quantum limitations on energy consumption in computation
Fundamental limitations on the energy dissipated during one elementary logical operation are discussed. A model of a real physical device (parametric quantron) based on the Josephson effect inExpand
Entropy content and information flow in systems with limited energy
Physical systems of finite size and limited total energy E have limited entropy content S (alternatively, limited information-storing capacity). We demonstrate the validity of our previouslyExpand
Quantum-mechanical computers and uncomputability.
  • Lloyd
  • Physics, Medicine
  • Physical review letters
  • 1993
The time evolution operator for any quantum-mechanical computer is diagonalizable, but to obtain the diagonal decomposition of a program state of the computer is as hard as actually performing theExpand
Physical limitations of rate, depth, and minimum energy in information processing
The effect of the quantum nature of matter on the maximum informationprocesssing potentialities is considered. It is shown that the degeneracy of the energy levels of a physicalExpand
Information is physical
Thermodynamics arose in the 19th century out of the attempt to understand the performance limits of steam engines in a way that would anticipate all further inventions. Claude Shannon, after WorldExpand
Efficient Simulation of Quantum Systems by Quantum Computers
TLDR
It is shown that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer and ultimately the simulation of quantum field theory might be possible on large quantum computers. Expand
...
1
2
3
4
5
...