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:2111.00167 · Nature Communications

Small-world complex network generation on a digital quantum processor

Eric B. Jones, Logan Edward Hillberry, Matthew Timothy Jones, Mina Fasihi, P. Roushan, Jiang Zhang, Alan Ho, Charles Neill, Eric P. Ostby, Peter A Graf, Eliot Kapit, Lincoln D. Carr

Published Aug 2, 2022• 20 citations
arXivHTMLPDF

Abstract

Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. The inability of classical computers to simulate large quantum systems hinders the elucidation of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here, we experimentally realize QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. We calculate calibrated and error-mitigated population dynamics and complex network measures, which indicate the formation of small-world mutual information networks. These networks decohere at fixed circuit depth independent of system size, the largest of which corresponding to 1,056 two-qubit gates. Such computations may enable the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations.

DOI
10.1038/s41467-022-32056-y

Related papers

Integrability of Goldilocks quantum cellular automata

Logan Edward Hillberry, Lorenzo Piroli, Eric Vernier +3 more

Abstract Goldilocks quantum cellular automata (QCA) have been simulated on quantum hardware and produce emergent small-world correlation networks. In Goldilocks QCA, a single-qubit unitary is applied to each qubit in a one-dimensional chain subject to a balance constraint: a qubit is updated if its neighbors are in different computational-basis states. We prove that a subclass of Goldilocks QCA, including the QCA implemented experimentally, map to free fermions and therefore can be simulated classically. We support this claim with two proofs, one involving a Jordan–Wigner transformation and one mapping the integrable six-vertex model to QCA. We compute local conserved quantities of these QCA and predict experimentally measurable expectation values. These calculations can be applied to test large digital quantum computers. In contrast, typical Goldilocks QCA have equilibration properties and quasienergy-level statistics that suggest nonintegrability. Still, each of the latter QCA conserves one quantity useful for error mitigation. Our work yields a parametric quantum circuit with tunable integrability properties useful for testing quantum hardware.

arXiv:2404.02994•Quantum Science and Technology•Mar 26, 2026•5 citations

Entangled quantum cellular automata, physical complexity, and Goldilocks rules

Logan Edward Hillberry, Matthew Timothy Jones, David L. Vargas +6 more

Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under 'Goldilocks rules' that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms—Rydberg arrays, trapped ions, and superconducting qubits—can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA.

arXiv:2005.01763•Quantum Science and Technology•Aug 10, 2021•2 citations

Quantum Cellular Automata on a Dual-Species Rydberg Processor

Ryan White, Vikram Ramesh, Alexander Impertro +6 more

As quantum devices scale to larger and larger sizes, a significant challenge emerges in scaling their coherent controls accordingly. Quantum cellular automata (QCAs) constitute a promising framework that bypasses this control problem: universal dynamics can be achieved using only a static qubit array and global control operations. Despite an extensive history of theoretical explorations and proposals, QCAs have not been experimentally explored in the context of highly-scalable globally-controlled systems. Here we realize QCAs on a dual-species Rydberg array of rubidium and cesium atoms, leveraging independent global control of each species to perform multiple quantum protocols. Seeding an automaton with different initial states, we explore many-body dynamics of quasiparticles and grow GHZ states across both species, highlighting the flexibility of our approach. We further develop a second automaton using a novel mediated entangling gate, enabling generation of 96.7(1.7)%-fidelity Bell states, 17-qubit cluster states, and high-connectivity graph states. Our results demonstrate that simple global controls enable access to a rich variety of applications through the QCA framework. The versatility and scalability of QCAs present compelling opportunities for the development of quantum information systems, as well as new perspectives on quantum many-body dynamics.

quant-pharXiv:2601.16257•Jan 26, 2026•0 citations

Entangled quantum cellular automata, physical complexity, and Goldilocks rules

Logan Edward Hillberry, Matthew Timothy Jones, David L. Vargas +6 more

Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under 'Goldilocks rules' that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms- Rydberg arrays, trapped ions, and superconducting qubits- can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA.

•Jan 1, 2021•31 citations

Quantum Cellular Automata for Simulation of Complex Systems

Jincheng Zhang

This paper explores the potential of Quantum Cellular Automata (QCA) for simulating complex systems with enhanced efficiency compared to their classical counterparts. Classical Cellular Automata (CCA) face limitations when modeling systems exhibiting quantum phenomena or requiring computational power for intricate simulations. QCA, leveraging the principles of quantum mechanics, offers a fundamentally different approach. This work details the design of a QCA where cells are represented by qubits, and the governing rules are defined by quantum gates. The core argument presented is that QCA's inherent parallelism and superposition capabilities can lead to significant speedups in simulating complex systems. This research proposes a novel methodology for applying QCA to various complex systems, highlighting its potential advantages and exploring the theoretical foundations underpinning this approach. The investigation focuses on the theoretical aspects of QCA design and simulation, without the need for experimental validation.

•Sep 6, 2026•0 citations

Coarse-grained quantum cellular automata

O. Duranthon, Giuseppe Di Molfetta

One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular automata that follow the so-called Goldilocks rules. The procedure consists in (i) space-time grouping the quantum cellular automaton (QCA) in cells of size $N$; (ii) projecting the states of a cell onto its borders, connecting them with the fine dynamics; (iii) describing the overall dynamics by the border states, that we call signals; and (iv) constructing the coarse-grained dynamics for different sizes $N$ of the cells. A by-product of this simple toy model is a general discrete analogous of the Stokes law. Moreover we prove that in the space-time limit, the automaton converges to a Dirac free Hamiltonian. The QCA we introduce here can be implemented by present-day quantum platforms, such as Rydberg arrays, trapped ions, and superconducting qubits. We hope our study can pave the way to a richer understanding of those systems with limited resolution.

arXiv:2011.04287•Physical Review A•Mar 29, 2021•9 citations
Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. The inability of classical computers to simulate large quantum systems hinders the elucidation of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here, we experimentally realize QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. We calculate calibrated and error-mitigated population dynamics and complex network measures, which indicate the formation of small-world mutual information networks. These networks decohere at fixed circuit depth independent of system size, the largest of which corresponding to 1,056 two-qubit gates. Such computations may enable the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations.
Abstract Goldilocks quantum cellular automata (QCA) have been simulated on quantum hardware and produce emergent small-world correlation networks. In Goldilocks QCA, a single-qubit unitary is applied to each qubit in a one-dimensional chain subject to a balance constraint: a qubit is updated if its neighbors are in different computational-basis states. We prove that a subclass of Goldilocks QCA, including the QCA implemented experimentally, map to free fermions and therefore can be simulated classically. We support this claim with two proofs, one involving a Jordan–Wigner transformation and one mapping the integrable six-vertex model to QCA. We compute local conserved quantities of these QCA and predict experimentally measurable expectation values. These calculations can be applied to test large digital quantum computers. In contrast, typical Goldilocks QCA have equilibration properties and quasienergy-level statistics that suggest nonintegrability. Still, each of the latter QCA conserves one quantity useful for error mitigation. Our work yields a parametric quantum circuit with tunable integrability properties useful for testing quantum hardware.
Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under 'Goldilocks rules' that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms—Rydberg arrays, trapped ions, and superconducting qubits—can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA.
As quantum devices scale to larger and larger sizes, a significant challenge emerges in scaling their coherent controls accordingly. Quantum cellular automata (QCAs) constitute a promising framework that bypasses this control problem: universal dynamics can be achieved using only a static qubit array and global control operations. Despite an extensive history of theoretical explorations and proposals, QCAs have not been experimentally explored in the context of highly-scalable globally-controlled systems. Here we realize QCAs on a dual-species Rydberg array of rubidium and cesium atoms, leveraging independent global control of each species to perform multiple quantum protocols. Seeding an automaton with different initial states, we explore many-body dynamics of quasiparticles and grow GHZ states across both species, highlighting the flexibility of our approach. We further develop a second automaton using a novel mediated entangling gate, enabling generation of 96.7(1.7)%-fidelity Bell states, 17-qubit cluster states, and high-connectivity graph states. Our results demonstrate that simple global controls enable access to a rich variety of applications through the QCA framework. The versatility and scalability of QCAs present compelling opportunities for the development of quantum information systems, as well as new perspectives on quantum many-body dynamics.
Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under 'Goldilocks rules' that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms- Rydberg arrays, trapped ions, and superconducting qubits- can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA.
This paper explores the potential of Quantum Cellular Automata (QCA) for simulating complex systems with enhanced efficiency compared to their classical counterparts. Classical Cellular Automata (CCA) face limitations when modeling systems exhibiting quantum phenomena or requiring computational power for intricate simulations. QCA, leveraging the principles of quantum mechanics, offers a fundamentally different approach. This work details the design of a QCA where cells are represented by qubits, and the governing rules are defined by quantum gates. The core argument presented is that QCA's inherent parallelism and superposition capabilities can lead to significant speedups in simulating complex systems. This research proposes a novel methodology for applying QCA to various complex systems, highlighting its potential advantages and exploring the theoretical foundations underpinning this approach. The investigation focuses on the theoretical aspects of QCA design and simulation, without the need for experimental validation.
One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular automata that follow the so-called Goldilocks rules. The procedure consists in (i) space-time grouping the quantum cellular automaton (QCA) in cells of size NNN; (ii) projecting the states of a cell onto its borders, connecting them with the fine dynamics; (iii) describing the overall dynamics by the border states, that we call signals; and (iv) constructing the coarse-grained dynamics for different sizes NNN of the cells. A by-product of this simple toy model is a general discrete analogous of the Stokes law. Moreover we prove that in the space-time limit, the automaton converges to a Dirac free Hamiltonian. The QCA we introduce here can be implemented by present-day quantum platforms, such as Rydberg arrays, trapped ions, and superconducting qubits. We hope our study can pave the way to a richer understanding of those systems with limited resolution.