Local Unitary Quantum Cellular Automata
arXiv:0709.0006 · doi:10.1103/PhysRevA.76.032320
Abstract
In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. It is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains and others. Some results that show the benefits of basing the model on local unitary operators are shown: universality, strong connections to the circuit model, simple implementation on quantum hardware, and a wealth of applications.
To appear in Physical Review A
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- What is a quantum computer, and how do we build one?
- When is a Quantum Cellular Automaton (QCA) a Quantum Lattice Gas Automaton (QLGA)?
- A comparative study of universal quantum computing models: towards a physical unification
- Quantum cellular automata for quantum error correction and density classification
- A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton
- Intrinsically universal n-dimensional quantum cellular automata
- Cellular Automata as a Model of Physical Systems
- Entanglement dynamics and ergodicity breaking in a quantum cellular automaton
- A Quantum Cellular Automata architecture with nearest neighbor interactions using one quantum gate type
- Quantum Algorithm of Evolutionary Analysis of 1D Cellular Automata