Quantum error correction (QEC) and fault-tolerant quantum computation represent one of
the most vital theoretical aspects of quantum information processing. It was well known from …

This article surveys some theoretical aspects of cellular automata CA research. In particular,
we discuss classical and new results on reversibility, conservation laws, limit sets …

We study two families of error-correcting codes defined in terms of very sparse matrices."
MN"(MacKay-Neal (1995)) codes are recently invented, and" Gallager codes" were first …

We analyze surface codes, the topological quantum error-correcting codes introduced by
Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of …

The discovery of quantum error correction has greatly improved the long-term prospects for
quantum computing technology. Encoded quantum information can be protected from errors …

We prove a new version of the quantum threshold theorem that applies to concatenation of a
quantum code that corrects only one error, and we use this theorem to derive a rigorous …

Cellular automata are simple models of computation which exhibit fascinatingly complex
behavior. They have captured the attention of several generations of researchers, leading to …

This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at
St. John's College in Santa Fe under the auspices of the Santa Fe Institute. The …

The spontaneous breaking of time-translation symmetry in periodically driven quantum
systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits …

We review cellular automata as a modeling formalism and discuss how it can be used for
modeling (spatial) ecological processes. The implications of this modeling paradigm for …