Related papers: Ultimate physical limits to computation
It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than $c=a/\tau$, $a$ and $\tau$ being the minimum space and time distances…
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 can reverse - even using all the available…
The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources.…
Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
A quantum computer has now solved a specialized problem believed to be intractable for supercomputers, suggesting that quantum processors may soon outperform supercomputers on scientifically important problems. But flaws in each quantum…
Coherence is the most fundamental quantum resource in quantum information processing. How fast a physical system gets coherence or decoherence is a critical ingredient. We present an attainable quantum speed limit based on the variation of…
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 dynamical evolution. Previous analyses have given bounds in terms of…
The amount of heat generated by computers is rapidly becoming one of the main problems for developing new generations of information technology. The thermodynamics of computation sets the ultimate physical bounds on heat generation. A lower…
Many people think of analog computing as a historic dead-end in computing. In fact, nothing could be further from the truth as analog computing - together with quantum computing - has the potential to bring computing to new levels with…
Do physical laws limit the speed of "all data processing systems, manmade as well as biological"? This question proposed and positively answered by H. J. Bremermann in 1962, should be corrected to make it compatible with Einstein's theory…
The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this, we derive exact quantum speed limits for…
Quantum mechanics imposes fundamental constraints known as quantum speed limits (QSLs) on the information processing speed of all quantum systems. Every QSL known to date comes from the restriction imposed on the evolution time between two…
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…
We clarify the confusion, misunderstanding and misconception that the physical finiteness of the universe, if the universe is indeed finite, would rule out all hypercomputation, the kind of computation that exceeds the Turing computability,…
Framing computation as the transformation of metastable memories, we explore its fundamental thermodynamic limits. The true power of information follows from a novel decomposition of nonequilibrium free energy derived here, which provides a…
As revealed by discussions of principle on energy dissipation by computers, logic imposes constraints on physical systems designed for a logical function. We define a notion of logical dissipation for a finite automaton. We discuss the…
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…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
The relationship between brains and computers is often taken to be merely metaphorical. However, genuine computational systems can be implemented in virtually any media; thus, one can take seriously the view that brains literally compute.…