Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Magnetics

Quantum Cellular Automaton for Simulating Static Magnetic Fields

T. Doi

Published May 1, 2013• 4 citations
Publisher

Abstract

This paper proposes a new quantum cellular automaton (quantum CA) for simulating macroscopic electromagnetic fields. The final target is to simulate the macroscopic electromagnetic fields on a quantum computer. In the proposal approach, Maxwell's historical model, which was explained the nature of electromagnetic fields in 1861, has been modified for a quantum CA model to simulate the electromagnetic fields. Then, a state transition rule for CA is determined by a strategy based on the quantum mechanics and the quantum computation theories. One of originalities of the proposed approach is that a system using quantum gates is superstructed to simulate magneto-static fields from currents. First, a modified Maxwell model for applying to quantum CA was shown. Second, by using the quantum computation theory, a quantum gate system to simulate the magnetic fields from currents was described. Finally, the proposed approach was applied to an example of magnetostatic field simulation.

DOI
10.1109/tmag.2013.2241273

Related papers

Quantum State Collapse as a Cellular Automaton Algorithm

Jincheng Zhang

Quantum state collapse is a fundamental process in quantum mechanics, representing the irreversible loss of information upon measurement. This paper explores the potential of utilizing a cellular automata (CA) framework to model and simulate this collapse, offering a novel approach to understanding and potentially manipulating quantum evolution. We formalize collapse as a dynamic process governed by specific rules and feedback loops, enabling the simulation of complex quantum patterns. We propose a CA-based model that incorporates the probabilistic nature of quantum mechanics, allowing for a more intuitive and potentially controllable simulation of quantum phenomena. The core mechanism focuses on systematically evolving the system's state space, mirroring the collapse process and highlighting the interplay between initial conditions and emergent behavior. This work provides a foundational step in exploring the application of CA algorithms to complex quantum systems, opening avenues for future research in quantum simulation and understanding.

•Sep 6, 2026•0 citations

Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions

Leonard D. Mlodinow, Todd A. Brun

The authors present the construction of cellular automaton models corresponding to free quantum field theories for both fermions and bosons, and demonstrate that for wavelengths long compared to the lattice spacing one recovers standard Dirac and Maxwell field theories. Correspondences such as this offer a new way of thinking about quantum field theories, and potentially a new way of simulating them on quantum computers.

arXiv:2011.05597•Physical Review A•May 7, 2021•12 citations

A Cellular Automata-Based Algorithm Design for Quantum Computation

Jincheng Zhang

This paper proposes a novel approach to quantum algorithm design by leveraging the principles of cellular automata (CA). The core idea is to utilize CA as a hardware abstraction layer for quantum computation, mimicking the evolution rules of qubits. This allows for a parallelized design and optimization of quantum algorithms. Specifically, quantum gates are mapped to CA rules, enabling the simulation of qubit superposition and entanglement through cellular interactions and information transfer. This work explores the theoretical framework and outlines a methodology for designing quantum algorithms using CA, focusing on the potential for enhanced computational efficiency and scalability. The design methodology includes defining the CA grid, encoding quantum states into cellular configurations, translating quantum gates into CA rule updates, and analyzing the resulting algorithm execution. The presented framework offers a fundamentally different perspective on quantum algorithm development, potentially bridging the gap between classical algorithmic design and the unique characteristics of quantum systems. Further research will focus on exploring specific quantum algorithms and evaluating the performance of the CA-based approach.

•Sep 5, 2026•0 citations

Cellular Automata for Quantum Algorithm Design

Jincheng Zhang

This paper explores the potential of cellular automata (CA) as a novel framework for designing and optimizing quantum algorithms. The core idea is to map quantum gates and circuits onto the rules of a CA, enabling efficient simulation and optimization through parallel exploration of the CA's state space. This approach offers a fundamentally different abstraction, potentially simplifying the mapping process from abstract quantum algorithms to physical hardware constraints. We investigate the mechanics of this mapping, focusing on how the iterative nature of CA rules can mirror the sequential execution of quantum operations. The paper presents a theoretical foundation for this concept, outlining key considerations for rule design and state space traversal, and suggests directions for future research. The primary contribution lies in demonstrating a viable pathway to reduce the complexity associated with quantum circuit design and hardware mapping.

•Sep 5, 2026•0 citations

Photonic cellular automaton simulation of relativistic quantum fields: Observation of Zitterbewegung

Alessia Suprano, Danilo Zia, Emanuele Polino +6 more

Quantum cellular automaton (QCA) is a model for universal quantum computation and a natural candidate for digital quantum simulation of relativistic quantum fields. Here we introduce the first photonic platform for implementing QCA simulation of a free relativistic Dirac quantum field in 1 + 1 dimension, through a Dirac quantum cellular automaton (DQCA). Encoding the field position degree of freedom in the orbital angular momentum (OAM) of single photons, our state-of-the-art setup experimentally realizes eight steps of a DQCA, with the possibility of having complete control over the input OAM state preparation and the output measurement making use of two spatial light modulators. Therefore, studying the distribution in the OAM space at each step, we were able to reproduce the time evolution of the free Dirac field observing the , an oscillatory movement extremely difficult to see in a real-case experimental scenario that is a signature of the interference of particle and antiparticle states. The accordance between the expected and measured oscillations certifies the simulator performances, paving the way towards the application of photonic platforms to the simulation of more complex relativistic effects. Published by the American Physical Society 2024

arXiv:2402.07672•Physical Review Research•Aug 5, 2024•2 citations

Intrinsically universal one-dimensional quantum cellular automata in two flavours

Pablo J. Arrighi, Renan Fargetton, Zizhu Wang

We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA will then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA. The encoding is linear and hence does not carry any of the cost of the computation. We do this in two flavours: a weak one which requires an infinite but periodic initial configuration and a strong one which needs only a finite initial configuration. KEYWORDS: Quantum cellular automata, Intrinsic universality, Quantum computation.

arXiv:0704.3961•Apr 30, 2007•1 citation
This paper proposes a new quantum cellular automaton (quantum CA) for simulating macroscopic electromagnetic fields. The final target is to simulate the macroscopic electromagnetic fields on a quantum computer. In the proposal approach, Maxwell's historical model, which was explained the nature of electromagnetic fields in 1861, has been modified for a quantum CA model to simulate the electromagnetic fields. Then, a state transition rule for CA is determined by a strategy based on the quantum mechanics and the quantum computation theories. One of originalities of the proposed approach is that a system using quantum gates is superstructed to simulate magneto-static fields from currents. First, a modified Maxwell model for applying to quantum CA was shown. Second, by using the quantum computation theory, a quantum gate system to simulate the magnetic fields from currents was described. Finally, the proposed approach was applied to an example of magnetostatic field simulation.
Quantum state collapse is a fundamental process in quantum mechanics, representing the irreversible loss of information upon measurement. This paper explores the potential of utilizing a cellular automata (CA) framework to model and simulate this collapse, offering a novel approach to understanding and potentially manipulating quantum evolution. We formalize collapse as a dynamic process governed by specific rules and feedback loops, enabling the simulation of complex quantum patterns. We propose a CA-based model that incorporates the probabilistic nature of quantum mechanics, allowing for a more intuitive and potentially controllable simulation of quantum phenomena. The core mechanism focuses on systematically evolving the system's state space, mirroring the collapse process and highlighting the interplay between initial conditions and emergent behavior. This work provides a foundational step in exploring the application of CA algorithms to complex quantum systems, opening avenues for future research in quantum simulation and understanding.
This paper proposes a novel approach to quantum algorithm design by leveraging the principles of cellular automata (CA). The core idea is to utilize CA as a hardware abstraction layer for quantum computation, mimicking the evolution rules of qubits. This allows for a parallelized design and optimization of quantum algorithms. Specifically, quantum gates are mapped to CA rules, enabling the simulation of qubit superposition and entanglement through cellular interactions and information transfer. This work explores the theoretical framework and outlines a methodology for designing quantum algorithms using CA, focusing on the potential for enhanced computational efficiency and scalability. The design methodology includes defining the CA grid, encoding quantum states into cellular configurations, translating quantum gates into CA rule updates, and analyzing the resulting algorithm execution. The presented framework offers a fundamentally different perspective on quantum algorithm development, potentially bridging the gap between classical algorithmic design and the unique characteristics of quantum systems. Further research will focus on exploring specific quantum algorithms and evaluating the performance of the CA-based approach.
This paper explores the potential of cellular automata (CA) as a novel framework for designing and optimizing quantum algorithms. The core idea is to map quantum gates and circuits onto the rules of a CA, enabling efficient simulation and optimization through parallel exploration of the CA's state space. This approach offers a fundamentally different abstraction, potentially simplifying the mapping process from abstract quantum algorithms to physical hardware constraints. We investigate the mechanics of this mapping, focusing on how the iterative nature of CA rules can mirror the sequential execution of quantum operations. The paper presents a theoretical foundation for this concept, outlining key considerations for rule design and state space traversal, and suggests directions for future research. The primary contribution lies in demonstrating a viable pathway to reduce the complexity associated with quantum circuit design and hardware mapping.
Quantum cellular automaton (QCA) is a model for universal quantum computation and a natural candidate for digital quantum simulation of relativistic quantum fields. Here we introduce the first photonic platform for implementing QCA simulation of a free relativistic Dirac quantum field in 1 + 1 dimension, through a Dirac quantum cellular automaton (DQCA). Encoding the field position degree of freedom in the orbital angular momentum (OAM) of single photons, our state-of-the-art setup experimentally realizes eight steps of a DQCA, with the possibility of having complete control over the input OAM state preparation and the output measurement making use of two spatial light modulators. Therefore, studying the distribution in the OAM space at each step, we were able to reproduce the time evolution of the free Dirac field observing the , an oscillatory movement extremely difficult to see in a real-case experimental scenario that is a signature of the interference of particle and antiparticle states. The accordance between the expected and measured oscillations certifies the simulator performances, paving the way towards the application of photonic platforms to the simulation of more complex relativistic effects. Published by the American Physical Society 2024
We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA will then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA. The encoding is linear and hence does not carry any of the cost of the computation. We do this in two flavours: a weak one which requires an infinite but periodic initial configuration and a strong one which needs only a finite initial configuration. KEYWORDS: Quantum cellular automata, Intrinsic universality, Quantum computation.