Quasiclassical computation

Abstract

The chemical kinetic description of time evolution where the phase is random but the states are discrete is discussed as a basis for a computational approach. This proposed scheme uses numbers in the entire range of 0 to 1 to represent Boolean propositions. In the implementation by chemical kinetics these numbers are the mole fractions of different species. Vibrational relaxation in a mixture of HCl and DCI is the physical system that is used to illustrate the approach. Energy exchange in such a mixture corresponds to two strongly coupled two-level systems. A search problem, previously discussed in the quantum computing literature, is solved as an example. The solution requires the same number of function evaluations as in the quantal case. The action of the oracle is described in detail.T he basic element of current logic devices is a switch. It is either on or off. This corresponds to the two possible values, say 0 and 1 or true and false, of a Boolean variable. The values of physical observables are not usually either 0 or 1. A molecule is not easily made to act as a switch. On the other hand, molecules exhibit a rich dynamical behavior that we would like to take advantage of so as to perform logic operations.In this article we focus on what is, to us, a rather common characteristic of molecules. It is that molecules can be classified into discrete alternatives. The simplest such distinction is the very idea of a chemical species. The operational definition of a molecule is made possible by the (relative) stability of the entities we know as atoms and by the atoms combining into molecules in simple and definite proportions. Thereby a molecule can be identified to be, say, HCl and not HBr or any other diatomic one. A finer but still operationally fully viable resolution is that molecules of a given chemical species can be identified to occupy definite quantum states (or groups of states). Except for special circumstances it is typical of molecules that the quantum mechanical phase of its states is random. So the different states of molecules act as discrete and mutually exclusive classical alternatives. This state of affairs is what we mean by quasiclassical. We want to perform logic operations by taking advantage of the probabilities of occupancy of the different quantum states that are resolvable in an experiment. By the end of this article we intend to show, by an explicit example, that this is possible.To implement our program we need input from several directions. In this introduction we review the different ideas that we intend to invoke. Then we describe a solution of a particular problem with special reference to what is the logic problem that we claim to solve, what is the physical system that is used, and how we set up the interface between them.We do not use the phase of the quantum mechanical state because we propose to operate under conditions where this phase is random. Starting with the work of Deutsch (1, 2), there is an extensive current literature emphasizing the critical computational advant...

Ultrafast vibrational spectroscopy and relaxation in polyatomic molecules: Potential for molecular parallel computing

“…This is dictated by the physics, in this case by the relaxation being purely unimolecular. For bimolecular processes, e.g., [15] the machine will usually not be linear. Another comment about the physics is that it is possible to incorporate the pump action in the definition of the matrix B as discussed in the appendix.…”

“…On the other hand, it does make essential use of the discrete energy spectrum of molecules. We sometimes call it 'quasiclassical' [15] and as we discuss, it is a massively parallel machine.…”

Logic Gates and Circuits

“…Examples include systems based on stimulation with magnetic [29] and electric [30] fields, optical transitions and high Rydberg states [31], two-photon processes [27,32], oscillating reactions [33], quantum interference effects [34], reaction kinetics [35], and circular [36] and electrical linear [30] dichroism readout. Examples include systems based on stimulation with magnetic [29] and electric [30] fields, optical transitions and high Rydberg states [31], two-photon processes [27,32], oscillating reactions [33], quantum interference effects [34], reaction kinetics [35], and circular [36] and electrical linear [30] dichroism readout.…”

Continuous variables logic via coupled automata using a DNAzyme cascade with feedback

“…The theoretical idea that enables continuous logic is, as we suggested before, 30 the use of the Cox point of view 31 – 33 of probability theory as propositional logic. 34 In the simple Boolean approach a proposition is either true or false so the logic is two-valued.…”