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Richard Phillips
Wolfram Science Group
Boston, USA

Registered: Oct 2003
Posts: 46

Papers on Quantum Cellular Automata and complicated dynamics

Here are two recent papers by the same authors in the NKS bibliography:

Weinstein, Y. S. and C. Stephen Hellberg.
Simulating Complex Quantum Dynamics

http://arxiv.org/PS_cache/quant-ph/pdf/0402/0402157.pdf

Abstract: We demonstrate scalable quantum algorithms that realize pseudo-random operators that reproduce statistical properties of the three universal classes of random matrices: unitary, symmetric, and symplectic. These algorithms can be used to simulate and study characteristics of many complex quantum systems and processes which are well described by random matrices, such as the nuclear level spacings of large atoms and chaotic scattering. Modified versions of the algorithms are introduced for quantum cellular automata.

and the second:

Weinstein, Y. S. and C. S. Hellberg.
Quantum Cellular Automata Pseudo-Random Maps

http://arxiv.org/PS_cache/quant-ph/pdf/0401/0401040.pdf

Abstract: Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in which all qubits of a species evolve in parallel. We show that, in spite of its inherent constraints, a QCA system can be used to study complex quantum dynamics. To this aim, we demonstrate scalable operations on a QCA system that fulfill statistical criteria of randomness and explore which criteria of randomness can be fulfilled by operators from various QCA architectures. Other means of realizing random operators with only a few independent operators are also discussed.

Some comments:

Both papers (particularly the second) discuss quantum cellular automata, and can be seen as arguing that despite their simple structure compared to more traditional quantum gate based approaches, they are just as powerful a framework for quantum information processing, and can efficiently simulate complex quantum processes described traditionally by random unitary operators.
Evidence from computer experiments is provided in both.

The papers bring to mind the following comment in NKS (although the papers don't explicitely mention this):

"I suspect, however, that in fact the most important source of randomness in most cases will instead be the phenomenon of intrinsic randomness generation that I first discovered in systems like the rule 30 cellular automaton...."

Reference: http://www.wolframscience.com/nksonline/page-1062b-text

Perhaps further work in both directions would be useful.

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