The fundamental limit on the rate of quantum dynamics: the unified bound is tight

The question of how fast a quantum state can evolve has attracted a considerable attention in connection with quantum measurement, metrology, and information processing. Since only orthogonal states can be unambiguously distinguished, a transition from a state to an orthogonal one can be taken as the elementary step of a computational process. Therefore, such a transition can be interpreted as the operation of "flipping a qubit", and the number of orthogonal states visited by the system per unit time can be viewed as the maximum rate of operation. A lower bound on the orthogonalization time, based on the energy spread DeltaE, was found by Mandelstam and Tamm. Another bound, based on the average energy E, was established by Margolus and Levitin. The bounds coincide, and can be exactly attained by certain initial states if DeltaE=E; however, the problem remained open of what the situation is otherwise. Here we consider the unified bound that takes into account both DeltaE and E. We prove that there exist no initial states that saturate the bound if DeltaE is not equal to E. However, the bound remains tight: for any given values of DeltaE and E, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit value. The relation between the largest energy level, the average energy, and the orthogonalization time is also discussed. These results establish the fundamental quantum limit on the rate of operation of any information-processing system.Comment: 4 pages 1 PS figure Late

Thermodynamic cost of reversible computing

Since reversible computing requires preservation of all information throughout the entire computational process, this implies that all errors that appear as a result of the interaction of the information-carrying system with uncontrolled degrees of freedom must be corrected. But this can only be done at the expense of an increase in the entropy of the environment corresponding to the dissipation, in the form of heat, of the ``noisy'' part of the system's energy. This paper gives an expression of that energy in terms of the effective noise temperature, and analyzes the relationship between the energy dissipation rate and the rate of computation. Finally, a generalized Clausius principle based on the concept of effective temperature is presented.Comment: 5 pages; added two paragraphs and fixed a number of typo

Computer interconnection networks with virtual cut-through routing

This paper considers a model of a toroidal computer interconnection network with the virtual cut-through routing. The interrelationships between network parameters, load and performance are analyzed. An exact analytical expression for the saturation point and expressions for the latency as a function of the message generation rate under the mean field theory approximation have been obtained. The theoretical results have been corroborated with the results of simulation experiments for various values of network parameters. The network behavior has been found not depending on the torus linear dimensions provided that they are at least twice as large as the message path length. The saturation point has been found to be inversely proportional to the message length in good agreement with the analytical results. A good agreement with Little’s theorem has been found if the network remains in the steady state during the experiment.Accepted manuscrip

An analytical model for virtual cut-through routing

An analytical model of a network with 2-dim torus topology and virtual cut-through routing has been considered in order to find out and analyze certain relationships between network parameters, load and performance. An exact expression for the saturation point (message generation rate at which network saturates) and expressions for the latency as a function of the message generation rate under the assumptions of the “mean field” theory have been obtained. It has been found that the saturation point is inversely proportional to the message length and to the distance between the source and destination. The theoretical results are in a good agreement with small-scale simulation experiments.Accepted manuscrip