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Quantum Cellular Automata

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  • First Online:
Cellular Automata

Part of the book series: Encyclopedia of Complexity and Systems Science Series ((ECSSS))

  • Originally published in
  • R. A. Meyers (ed.), Encyclopedia of Complexity and Systems Science, © Springer Science+Business Media New York 2013

Glossary

BQP complexity class:

Bounded error, quantum probabilistic, the class of decision problems solvable by a quantum computer in polynomial time with an error probability of at most one third.

Configuration:

The state of all cells at a given point in time.

Hadamard gate:

The one-qubit unitary gate \( U=\frac{1}{\sqrt{2}}\left(\begin{array}{ll}1& 1\\ {}1& -1\end{array}\right) \)

Heisenberg picture:

Time evolution is represented by observables (elements of an operator algebra) evolving in time according to a unitary operator acting on them.

Neighborhood:

All cells with respect to a given cell that can affect this cell’s state at the next time step. A neighborhood always contains a finite number of cells.

Pauli operator:

The three Pauli operators are \( {\sigma}_x=\left(\begin{array}{cc}0& 1\\ {}1& 0\end{array}\right),{\sigma}_y=\left(\begin{array}{cc}0& -i\\ {}i& 0\end{array}\right),{\sigma}_z=\left(\begin{array}{cc}1& 0\\ {}0& -1\end{array}\right) \)

Phase gate:
...

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Bristol, Bristol, UK

    Karoline Wiesner

Authors
  1. Karoline Wiesner
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Correspondence to Karoline Wiesner .

Editor information

Editors and Affiliations

  1. Unconventional Computing Centre, University of the West of England, Bristol, UK

    Andrew Adamatzky

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Wiesner, K. (2018). Quantum Cellular Automata. In: Adamatzky, A. (eds) Cellular Automata. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8700-9_426

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