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

arXiv:2309.03608

Quantum cellular automata for quantum error correction and density classification

Thiago L. M. Guedes, Winter, Don, Markus Müller

Published Jan 1, 2023• 0 citations
arXivHTMLPDF

Abstract

Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant manner on all cells/qudits of a register, generating a global rule that updates cell states locally, i.e., based solely on the states of their neighbors. Although desirable features in many applications, it is generally not clear to which extent these fully automated discrete-time local updates can generate and sustain long-range order in the (noisy) systems they act upon. In special, whether and how quantum cellular automata can perform quantum error correction remain open questions. We close this conceptual gap by proposing quantum cellular automata with quantum-error-correction capabilities. We design and investigate two (quasi-)one dimensional quantum cellular automata based on known classical cellular-automata rules with density-classification capabilities, namely the local majority voting and the two-line voting. We investigate the performances of those quantum cellular automata as quantum-memory components by simulating the number of update steps required for the logical information they act upon to be afflicted by a logical bit flip. The proposed designs pave a way to further explore the potential of new types of quantum cellular automata with built-in quantum error correction capabilities.

DOI
10.18154/rwth-2024-02535

Related papers

Quantum Memory and Autonomous Computation in Two Dimensions

Gesa Dünnweber, Georgios Styliaris, Rahul Trivedi

Quantum error correction (QEC) normally requires active maintenance using measurements, classical processing and externally controlled correction schedules. Passive QEC, by contrast, was previously established only in unphysical spatial dimensions. Here, we give an explicit scheme for autonomous quantum error correction and computation in two dimensions, formulated as a dissipative quantum cellular automaton with a fixed, local and translation-invariant update rule. The construction uses hierarchical, self-simulating control elements based on ideas from the seminal classical results of Gács (1986, 1989) together with a measurement-free concatenated quantum code. We prove the existence of a nonzero noise threshold under a local noise model. Below this threshold, logical errors on encoded initial states are suppressed exponentially with increasing system size and the memory lifetime diverges in the thermodynamic limit. As an extension, we outline how this mechanism can also be implemented in continuous time by a time-independent, translation-invariant local Lindbladian. Quantum circuits can moreover be encoded in the automaton's initial state and executed fault-tolerantly with polylogarithmic overhead under the same circuit-independent rule. Our scheme thus realizes a self-correcting quantum computer capable of universal computation.

quant-pharXiv:2601.20818•Jan 29, 2026•0 citations

Quantum Cellular Automata for Quantum Error Correction and Density Classification

Thiago L. M. Guedes, D. Winter, Markus Müller

Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant manner on all cells or qudits of a register, generating a global rule that updates cell states locally, i.e., based solely on the states of their neighbors. Although desirable features in many applications, it is generally not clear to which extent these fully automated discrete-time local updates can generate and sustain long-range order in the (noisy) systems they act upon. In particular, whether and how quantum cellular automata can perform quantum error correction remain open questions. We close this conceptual gap by proposing quantum cellular automata with quantum-error-correction capabilities. We design and investigate two (quasi)one dimensional quantum cellular automata based on known classical cellular-automata rules with density-classification capabilities, namely the local majority voting and the two-line voting. We investigate the performances of those quantum cellular automata as quantum-memory components by simulating the number of update steps required for the logical information they act upon to be afflicted by a logical bit flip. The proposed designs pave a way to further explore the potential of new types of quantum cellular automata with built-in quantum-error-correction capabilities.

Physical Review Letters•Oct 7, 2024•9 citations

An overview of Quantum Cellular Automata

Pablo J. Arrighi

Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates information at a bounded speed) and translation-invariant (it acts everywhere the same). Quantum cellular automata provide a model/architecture for distributed quantum computation. More generally, they encompass most of discrete-space discrete-time quantum theory. We give an overview of their theory, with particular focus on structure results; computability and universality results; and quantum simulation results.

arXiv:1904.12956•Apr 29, 2019•2 citations

Density Classification with Non-Unitary Quantum Cellular Automata

Elisabeth Wagner, Federico Dell’Anna, Ramil Nigmatullin +1 more

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 number density and one that performs majority voting. For number-preserving DC, two QCAs are introduced that reach the fixed-point solution in a time scaling quadratically with the system size. One of the QCAs is based on a known classical probabilistic cellular automaton which has been studied in the context of DC. The second is a new quantum model that is designed to demonstrate additional quantum features and is restricted to only two-body interactions. Both can be generated by continuous-time Lindblad dynamics. A third QCA is a hybrid rule defined by both discrete-time and continuous-time three-body interactions that is shown to solve the majority voting problem within a time that scales linearly with the system size.

arXiv:2404.05461•Entropy•Dec 31, 2024•2 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-automaton decoders for topological quantum memories

Michael Herold, Earl T. Campbell, Jens Eisert +1 more

We introduce a new framework for constructing topological quantum memories, by recasting error recovery as a dynamical process on a field generating cellular automaton. We envisage quantum systems controlled by a classical hardware composed of small local memories, communicating with neighbours and repeatedly performing identical simple update rules. This approach does not require any global operations or complex decoding algorithms. Our cellular automata draw inspiration from classical field theories, with a Coulomb-like potential naturally emerging from the local dynamics. For a 3D automaton coupled to a 2D toric code, we present evidence of an error correction threshold above 6.1% for uncorrelated noise. A 2D automaton equipped with a more complex update rule yields a threshold above 8.2%. Our framework provides decisive new tools in the quest for realising a passive dissipative quantum memory. A new error correction method for quantum computing memories is based on local computing elements. Michael Herold from the Freie Universität Berlin in Germany, with colleagues in Germany, Denmark and the UK, sought to address the challenge of maintaining information stored in topological quantum memories. Without a stable memory, delicate quantum states can decay quickly, introducing errors in stored information. Error correction is an important process in stabilizing topological memories, but was previously conceived as a system-wide process. The proposed practical error correction mechanism relies on parallel cellular operations within the topological quantum memory, so that the local operations replace the need for a complex system-wide scheme. The concept has the further benefit of being compatible with classical hardware, and it is easily scalable.

arXiv:1406.2338•npj Quantum Information•Oct 26, 2015•63 citations
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant manner on all cells/qudits of a register, generating a global rule that updates cell states locally, i.e., based solely on the states of their neighbors. Although desirable features in many applications, it is generally not clear to which extent these fully automated discrete-time local updates can generate and sustain long-range order in the (noisy) systems they act upon. In special, whether and how quantum cellular automata can perform quantum error correction remain open questions. We close this conceptual gap by proposing quantum cellular automata with quantum-error-correction capabilities. We design and investigate two (quasi-)one dimensional quantum cellular automata based on known classical cellular-automata rules with density-classification capabilities, namely the local majority voting and the two-line voting. We investigate the performances of those quantum cellular automata as quantum-memory components by simulating the number of update steps required for the logical information they act upon to be afflicted by a logical bit flip. The proposed designs pave a way to further explore the potential of new types of quantum cellular automata with built-in quantum error correction capabilities.
Quantum error correction (QEC) normally requires active maintenance using measurements, classical processing and externally controlled correction schedules. Passive QEC, by contrast, was previously established only in unphysical spatial dimensions. Here, we give an explicit scheme for autonomous quantum error correction and computation in two dimensions, formulated as a dissipative quantum cellular automaton with a fixed, local and translation-invariant update rule. The construction uses hierarchical, self-simulating control elements based on ideas from the seminal classical results of Gács (1986, 1989) together with a measurement-free concatenated quantum code. We prove the existence of a nonzero noise threshold under a local noise model. Below this threshold, logical errors on encoded initial states are suppressed exponentially with increasing system size and the memory lifetime diverges in the thermodynamic limit. As an extension, we outline how this mechanism can also be implemented in continuous time by a time-independent, translation-invariant local Lindbladian. Quantum circuits can moreover be encoded in the automaton's initial state and executed fault-tolerantly with polylogarithmic overhead under the same circuit-independent rule. Our scheme thus realizes a self-correcting quantum computer capable of universal computation.
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant manner on all cells or qudits of a register, generating a global rule that updates cell states locally, i.e., based solely on the states of their neighbors. Although desirable features in many applications, it is generally not clear to which extent these fully automated discrete-time local updates can generate and sustain long-range order in the (noisy) systems they act upon. In particular, whether and how quantum cellular automata can perform quantum error correction remain open questions. We close this conceptual gap by proposing quantum cellular automata with quantum-error-correction capabilities. We design and investigate two (quasi)one dimensional quantum cellular automata based on known classical cellular-automata rules with density-classification capabilities, namely the local majority voting and the two-line voting. We investigate the performances of those quantum cellular automata as quantum-memory components by simulating the number of update steps required for the logical information they act upon to be afflicted by a logical bit flip. The proposed designs pave a way to further explore the potential of new types of quantum cellular automata with built-in quantum-error-correction capabilities.
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates information at a bounded speed) and translation-invariant (it acts everywhere the same). Quantum cellular automata provide a model/architecture for distributed quantum computation. More generally, they encompass most of discrete-space discrete-time quantum theory. We give an overview of their theory, with particular focus on structure results; computability and universality results; and quantum simulation results.
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 number density and one that performs majority voting. For number-preserving DC, two QCAs are introduced that reach the fixed-point solution in a time scaling quadratically with the system size. One of the QCAs is based on a known classical probabilistic cellular automaton which has been studied in the context of DC. The second is a new quantum model that is designed to demonstrate additional quantum features and is restricted to only two-body interactions. Both can be generated by continuous-time Lindblad dynamics. A third QCA is a hybrid rule defined by both discrete-time and continuous-time three-body interactions that is shown to solve the majority voting problem within a time that scales linearly with the system size.
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.
We introduce a new framework for constructing topological quantum memories, by recasting error recovery as a dynamical process on a field generating cellular automaton. We envisage quantum systems controlled by a classical hardware composed of small local memories, communicating with neighbours and repeatedly performing identical simple update rules. This approach does not require any global operations or complex decoding algorithms. Our cellular automata draw inspiration from classical field theories, with a Coulomb-like potential naturally emerging from the local dynamics. For a 3D automaton coupled to a 2D toric code, we present evidence of an error correction threshold above 6.1% for uncorrelated noise. A 2D automaton equipped with a more complex update rule yields a threshold above 8.2%. Our framework provides decisive new tools in the quest for realising a passive dissipative quantum memory. A new error correction method for quantum computing memories is based on local computing elements. Michael Herold from the Freie Universität Berlin in Germany, with colleagues in Germany, Denmark and the UK, sought to address the challenge of maintaining information stored in topological quantum memories. Without a stable memory, delicate quantum states can decay quickly, introducing errors in stored information. Error correction is an important process in stabilizing topological memories, but was previously conceived as a system-wide process. The proposed practical error correction mechanism relies on parallel cellular operations within the topological quantum memory, so that the local operations replace the need for a complex system-wide scheme. The concept has the further benefit of being compatible with classical hardware, and it is easily scalable.