Related papers: Topological phases of unitary dynamics: Classifica…
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 provide a complete classification of Clifford quantum cellular automata (QCAs) on arbitrary metric spaces and any qudits (of prime or composite dimensions) in terms of algebraic L-theory. Building on the delooping formalism of Pedersen…
In three dimensions, there is a nontrivial quantum cellular automaton (QCA) which disentangles the three-fermion Walker--Wang model, a model whose action depends on Stiefel--Whitney classes of the spacetime manifold. Here we present a…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…
We present a general framework for constructing quantum cellular automata (QCA) from topological quantum field theories (TQFT) and invertible subalgebras (ISA) using the cup-product formalism. This approach explicitly realizes all…
We study reversible quantum cellular automata with the restriction that these are also Clifford operations. This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli operators.…
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
Clifford quantum cellular automata (CQCAs) are a special kind of quantum cellular automata (QCAs) that incorporate Clifford group operations for the time evolution. Despite being classically simulable, they can be used as basic building…
We consider the group structure of quantum cellular automata (QCA) modulo circuits and show that it is abelian even without assuming the presence of ancillas, at least for most reasonable choices of control space; this is a corollary of a…
We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth…
Clifford quantum circuits are elementary invertible transformations of quantum systems that map Pauli operators to Pauli operators. We study periodic one-parameter families of Clifford circuits, called loops of Clifford circuits, acting on…
We construct a three-dimensional quantum cellular automaton (QCA), an automorphism of the local operator algebra on a lattice of qubits, which disentangles the ground state of the Walker-Wang three fermion model. We show that if this QCA…
We investigate quantum cellular automata (QCA) on one-dimensional spin systems defined over a subalgebra of the full local operator algebra - the symmetric subalgebra under a finite Abelian group symmetry $G$. For systems where each site…
Quantum cellular automata (QCAs) are automorphisms of tensor product algebras that preserve locality, with local quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small…
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 consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary.…
Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…
This study presents a unitary quantum cellular automaton (QCA) that, in the continuum limit, converges to the (1+1)-dimensional Generalized Dirac Equation (GDE). We outline the construction of the unitary, discrete-time evolution and derive…
We consider Clifford Quantum Cellular Automata (CQCAs) and their time evolution. CQCAs are an especially simple type of Quantum Cellular Automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum…
We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution $U$. We require that this global evolution $U$ be unitary, in accordance with quantum…