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Related papers: Quantum cellular automata without particles

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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…

Quantum Physics · Physics 2009-03-03 Pablo Arrighi , Vincent Nesme

There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…

Quantum Physics · Physics 2022-09-20 M. Freedman , M. B. Hastings

We study 1-way quantum finite automata (QFAs) and compare them with their classical counterparts. We show that 1-way QFAs can be very space efficient. We construct a 1-way QFAs that are quadratically smaller than any equivalent…

Quantum Physics · Physics 2007-05-23 Arnolds Kikusts

The Thirring Quantum Cellular Automaton (QCA) describes the discrete time dynamics of local fermionic modes that evolve according to one step of the Dirac cellular automaton followed by the most general on-site number-preserving…

Quantum Physics · Physics 2025-03-31 Alessandro Bisio , Paolo Perinotti , Andrea Pizzamiglio , Saverio Rota

The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the…

Quantum Physics · Physics 2025-01-22 Elisabeth Wagner , Federico Dell'Anna , Ramil Nigmatullin , Gavin K. Brennen

Information in a Quantum Cellular Automata architecture is encoded in the polarizazion state of a cell, i.e., in the occupation numbers of the quantum dots of which the cell is made up. Non-invasive charge detectors of single electrons in a…

Condensed Matter · Physics 2009-10-31 G. Iannaccone , C. Ungarelli , M. Macucci , E. Amirante , M. Governale

Conventional computers are ill suited to run CA models, and so discourage their development. By creating a hardware platform that makes a broad range of new CA algorithms practical for real applications, we hope to whet the appetite of…

comp-gas · Physics 2017-06-07 Norman Margolus

Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…

Cellular Automata and Lattice Gases · Physics 2025-06-02 Markus Redeker

Probabilistic cellular automata (PCA) are used to model a variety of discrete spatially extended systems undergoing parallel-updating. We propose an embedding of a number of classical nonequilibrium concepts in the PCA-world. We start from…

Statistical Mechanics · Physics 2017-01-17 Christian Maes

A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority…

Pattern Formation and Solitons · Physics 2016-05-25 Vladimir García-Morales

Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Shuichi Inokuchi , Kazumasa Honda , Hyen Yeal Lee , Tatsuro Sato , Yoshihiro Mizoguchi , Yasuo Kawahara

Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…

q-alg · Mathematics 2009-10-30 J. Wess

After the first treatments of quantum finite state automata by Moore and Crutchfield and by Kondacs and Watrous, a number of papers study the power of quantum finite state automata and their variants. This paper introduces a model of…

Computational Complexity · Computer Science 2007-05-23 Tomohiro Yamasaki , Hirotada Kobayashi , Hiroshi Imai

To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations…

Quantum Physics · Physics 2020-07-27 Terry Farrelly , Julien Streich

To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we propose quantum versions of finite-state and push-down automata, and regular and context-free…

Quantum Physics · Physics 2009-09-25 Cristopher Moore , James P. Crutchfield

We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (over 0.98), then the power of 1-way QFAs…

Quantum Physics · Physics 2007-05-23 A. Ambainis , R. Freivalds

Quantum cellular automata have been recently considered as a fundamental approach to quantum field theory, resorting to a precise automaton, linear in the field, for the Dirac equation in one dimension. In such linear case a quantum…

Quantum Physics · Physics 2015-12-21 Giacomo Mauro D'Ariano , Nicola Mosco , Paolo Perinotti , Alessandro Tosini

Our previous work dealt with the zeta function for the interacting particle system (IPS) including quantum cellular automaton (QCA) as a typical model in the study of ``IPS/Zeta Correspondence". On the other hand, the absolute zeta function…

Quantum Physics · Physics 2024-01-18 Jirô Akahori , Norio Konno , Iwao Sato

We introduce a class of noisy quantum cellular automata on a qubit lattice that includes all classical Markov chains, as well as maps where quantum coherence between sites is allowed to build up over time. We apply such a construction to…

Quantum Physics · Physics 2015-06-17 Michele Avalle , Alessio Serafini

This paper presents a simple model that mimics quantum mechanics (QM) results without using complex wavefunctions or non-localities. The proposed model only uses integer-valued quantities and arithmetic operations, in particular assuming a…

General Physics · Physics 2017-01-04 Antonio Sciarretta