Programming Complex Systems

Details Programming Complex Systems Programming Complex Systems

1997-10-15

arxiv.org/abs/quant-ph/9710035v1

Physics

Quantum Physics

8 pages, LaTeX2e. This paper combines and enhances quant-ph/9612052 and quant-ph/9702057 with an eye towards complex systems.

Scientific paper

Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental properties of complex systems. This formal language allows the expression of quantumized algorithms, which are extensions of randomized algorithms in that probabilities can be negative, and events can cancel out. An illustration of the power of quantumized algorithms is the ability to efficiently solve the satisfiability problem, something that many believe is beyond the capability of classical computers. This paper proves that the lambda-q calculus is not only capable of solving satisfiability but can also simulate such complex systems as quantum computers. Since satisfiability is believed to be beyond the capabilities of quantum computers, the lambda-q calculus may be strictly stronger.

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