Related papers: The Group Structure of Quantum Cellular Automata
We study locality preserving automorphisms of operator algebras on $D$-dimensional uniform lattices of prime $p$-dimensional qudits (QCA), specializing in those that are translation invariant (TI) and map every prime $p$-dimensional Pauli…
We report here on the structure of reversible quantum cellular automata with the additional restriction that these are also Clifford operations. This means that tensor products of Weyl operators (projective representation of a finite…
We describe a large-scale project in applied automated deduction concerned with the following problem of considerable interest in loop theory: If $Q$ is a loop with commuting inner mappings, does it follow that $Q$ modulo its center is a…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
Taking the excess electron spin in a unit cell of semiconductor multiple quantum-dot structure as a qubit, we can implement scalable quantum computation without resorting to spin-spin interactions. The technique of single electron…
Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. For instance,…
It has been shown that certain quantum walks give rise to relativistic wave equations, such as the Dirac and Weyl equations, in their long-wavelength limits. This intriguing result raises the question of whether something similar can happen…
Quantum devices featuring mid-circuit measurement and reset capabilities, such as quantum computers and dual-species Rydberg quantum simulators, enable the realization of quantum cellular automata. These systems evolve in discrete time…
Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the r esult could actually make sense physically, as a valid quantum evolution; but…
Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer…
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…
Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins classifications…
In this work, we develop a method to use Quantum- Dot Cellular Automata (QCA) for universal quantum computing. This method is based conceptually on refocusing in NMR systems. We show how an array of QCA cells can be used for isolated single…
The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic…
The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time and space, for which an index theory has…
Group cellular automata are continuous, shift-commuting endomorphisms of $G^\mathbb{Z}$, where $G$ is a finite group. We provide an easy-to-check characterization of expansivity for group cellular automata on abelian groups and we prove…
Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in…
After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field…
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…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…