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An overview of Quantum Cellular Automata
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Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates information at a bounded speed) and translation-invariant (it acts everywhere the same). Quantum cellular automata provide a model/architecture for distributed quantum computation. More generally, they encompass most of discrete-space discrete-time quantum theory. We give an overview of their theory, with particular focus on structure results; computability and universality results; and quantum simulation results.
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Cited by 3 Pith papers
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Causal Decompositions of 1D Quantum Cellular Automata
For N > 4r, every 1D quantum cellular automaton of causality radius r is exactly a routed unitary circuit of nearest-neighbour interactions, and translation-invariant automata get translation-invariant circuits.
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Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations
Gravitational topological responses are shown to appear as the projective phase (ST)^3=Y in gauging/stacking relations, corresponding on the lattice to nontrivial QCAs implementable via finite-depth circuits, measurem...
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Crystalline Spectral Form Factors
Strong level repulsion produces damped crystalline oscillations of the spectral form factor, with a Debye-Waller suppression, a new plateau time scale t* ≈ t_H sqrt(β/4), and predictable derivative singularities.
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