An overview of quantum cellular automata

@article{Arrighi2019AnOO,
  title={An overview of quantum cellular automata},
  author={Pablo Arrighi},
  journal={Natural Computing},
  year={2019},
  volume={18},
  pages={885-899}
}
  • P. Arrighi
  • Published 29 April 2019
  • Computer Science
  • Natural Computing
Quantum cellular automata are 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… 

Information flow in one-dimensional non-unitary quantum cellular automata

The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time

A review of Quantum Cellular Automata

TLDR
This review discusses all of these applications of QCAs, including the matrix product unitary approach and higher dimensional classifications, as well as some other interesting results on the structure of quantum cellular automata.

A Quantum Cellular Automata Type Architecture with Quantum Teleportation for Quantum Computing

TLDR
An architecture based on Quantum Cellular Automata which allows the use of only one type of quantum gate per computational step, using nearest neighbor interactions is proposed, and physical implementation can be easier since at each step only one kind of input pulse needs to be applied to the apparatus.

Coarse-grained quantum cellular automata

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

Quantum fermions from classical bits

  • C. Wetterich
  • Physics
    Philosophical Transactions of the Royal Society A
  • 2021
TLDR
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions, equivalent to the classical statistical system of a generalized Ising model.

Entangled quantum cellular automata, physical complexity, and Goldilocks rules

TLDR
E entangled quantum cellular automata subject to Goldilocks rules are introduced, which underscore an emerging idea in many-body quantum physics: some systems fall outside the integrable/chaotic dichotomy.

Quantum Cellular Automata, Black Hole Thermodynamics and the Laws of Quantum Complexity

TLDR
This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators, and demonstrates that the expected exponential relationships between the quantum circuit complexity of the evolution operator, the classical entropy of the equilibrium QCA state, and the characteristic equilibration time of the QCA, all hold within this new model.

Nonequilibrium Phase Transitions in (1+1)-Dimensional Quantum Cellular Automata with Controllable Quantum Correlations.

TLDR
It is shown that projected entangled pair state tensor networks permit a natural and efficient representation of the cellular automaton, and the degree of quantumness and complexity of the dynamics is reflected in the difficulty of contracting the tensor network.

Goldilock rules, Quantum cellular automata and coarse-graining

TLDR
Inspired by classical coarse graining procedures, this work provides a simple procedures to coarse-grain color-blind quantum cellular automata, following Goldilock rules, and proves that in the spacetime limit, the automaton converge to a Dirac free Hamiltonian.

References

SHOWING 1-10 OF 135 REFERENCES

Local unitary quantum cellular automata

TLDR
A quantization of cellular automata is presented, based on a lattice of qudits and an update rule consisting of local unitary operators that commute with their own lattice translations to act as a theoretical model of quantum computation, similar to the quantum circuit model.

A decision procedure for unitary linear quantum cellular automata

  • C. DürrM. Santha
  • Computer Science
    Proceedings of 37th Conference on Foundations of Computer Science
  • 1996
TLDR
An efficient algorithm to decide if a linear quantum cellular automaton is unitary is given and the complexity of the algorithm is O(n(4r-3)/(r+1))=O(n/sup 4/) if the automaton has a continuous neighborhood of size r.

A quantum cellular automaton for one-dimensional QED

TLDR
A discrete spacetime formulation of quantum electrodynamics in one dimension in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates, is proposed, encompassing the notions of continuum limit and renormalization and providing a quantum simulation algorithm for the dynamics.

Definition and evolution of quantum cellular automata with two qubits per cell

Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate

From quantum cellular automata to quantum lattice gases

A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, we begin an investigation of exactly unitary cellular automata. After

Entanglement dynamics in one-dimensional quantum cellular automata

Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex

Quantum cellular automata without particles

Quantum cellular automata (QCA) constitute space and time homogeneous discrete models for quantum field theories (QFTs). Although QFTs are defined without reference to particles, computations are

A universal quantum cellular automaton

TLDR
It is shown that every proper qca obeys a local constraint which is comparable with the ‘inverse neighborhood’ of classical reversible cellular automata, which allows us to describe every qca as a periodic quantum gate array, which can be simulated (with a bounded error) by a universal automaton U.

Quantum state transfer through noisy quantum cellular automata

We model the transport of an unknown quantum state on one dimensional qubit lattices by means of a quantum cellular automata (QCA) evolution. We do this by first introducing a class of discrete noisy

Discrete Lorentz covariance for quantum walks and quantum cellular automata

TLDR
This work formalizes a notion of discrete Lorentz transforms for quantum walks (QW) and quantum cellular automata (QCA), in -dimensional discrete spacetime, and shows the first-order-only covariance of the Dirac QW.
...