Related papers: Classification of qubit cellular automata on hyper…
In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time…
We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically…
Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into…
Factorized dynamics in soliton cellular automata with quantum group symmetry is identified with a motion of particles and anti-particles exhibiting pair creation and annihilation. An embedding scheme is presented showing that the…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to…
A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations).…
We propose a scheme for quantum computation in optical lattices. The qubits are encoded in the spacial wavefunction of the atoms such that spin decoherence does not influence the computation. Quantum operations are steered by shaking the…
Classical planar vertex models afford transfer matrices with real and positive entries, which makes this class of models suitable for quantum simulations. In this work, we support this statement by building explicit quantum circuits that…
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…
We study integrable spin chains and quantum and classical cellular automata with interaction range $\ell\ge 3$. This is a family of integrable models for which there was no general theory so far. We develop an algebraic framework for such…
Here a finite-Lieb-lattice quantum computing circuit consisting of spin-1/2 quantum bits (qubits) and triplet couplers is designed. Important gradient - quantum entanglement - is analysed. This type of design could be realised in a vast…
Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using…
A scenario for realization of a quantum computer is proposed consisting of spatially distributed q-bits fabricated in a host structure where nuclear spin-spin coupling is mediated by laser pulse controlled electron-nuclear transferred…
It is shown that for the N-neighbor and K-state cellular automata, the class II, class III and class IV patterns coexist at least in the range $\frac{1}{K} \le \lambda \le 1-\frac{1}{K} $. The mechanism which determines the difference…
Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which…
We present a method for optimizing quantum circuits architecture. The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits. The method allows one to efficiently…
Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state…
We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution described by the Schr\"odinger…
An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a…