Wolfgang Polak

An introduction to quantum computing for non-physicists

Richard Feynmans observation that certain quantum mechanical effects cannot be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used these quantum effects. This speculation proved justified when Peter Shor described a polynomial time quantum algorithm for factoring intergers. In quantum systems, the computational space increases exponentially with the size of the system, which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new nontraditional programming techniques. The aim of this paper is to guide computer scientists through the barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to exploiting the power of quantum parallelism are explained. We conclude with a discussion of quantum error correction.

The evolution of technology within a simple computer model

Technology—the collection of devices and methods available to human society—evolves by constructing new devices and methods from ones that previously exist, and in turn offering these as possible components—building blocks—for the construction of further new devices and elements. The collective of technology in this way forms a network of elements where novel elements are created from existing ones and where more complicated elements evolve from simpler ones. We model this evolution within a simple artificial system on the computer. The elements in our system are logic circuits. New elements are formed by combination from simpler existing elements (circuits), and if a novel combination satisfies one of a set of needs, it is retained as a building block for further combination. We study the properties of the resulting build out. We find that our artificial system can create complicated technologies (circuits), but only by first creating simpler ones as building blocks. Our results mirror Lenski et al.s: that complex features can be created in biological evolution only if simpler functions are first favored and act as stepping stones. We also find evidence that the resulting collection of technologies exists at self-organized criticality.

Tools for Quantum Algorithms

We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of the phase adjustments to block matrix transformations. These operations generalize those used in proposed quantum search algorithms.