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

  title={Quantum Cellular Automata, Black Hole Thermodynamics and the Laws of Quantum Complexity},
  author={Ruhi Shah and Jonathan Gorard},
  journal={Complex Syst.},
This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming from a formal analogy between quantum computational complexity theory and classical thermodynamics, that have arisen recently in the context of black hole physics. In particular, the apparent resonance and thermalization effects present within such QCAs are… 
Small-world complex network generation on a digital quantum processor
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
Some Relativistic and Gravitational Properties of the Wolfram Model
It is proved that causal invariance (namely, the requirement that all causal graphs be isomorphic, irrespective of the choice of hypergraph updating order) is equivalent to a discrete version of general covariance, with changes to the updating order corresponding to discrete gauge transformations, and a discrete analog of Lorentz covariance is deduced.
Algorithmic Causal Sets and the Wolfram Model
It is demonstrated that the hypergraph rewriting approach of the Wolfram model can effectively be interpreted as providing an underlying algorithmic dynamics for causal set evolution and causal invariance can be used to infer conformal invariance of the induced causal partial order.


A review of Quantum Cellular Automata
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.
Second law of quantum complexity
We give arguments for the existence of a thermodynamics of quantum complexity that includes a “second law of complexity.” To guide us, we derive a correspondence between the computational (circuit)
Reversible quantum cellular automata
The main structure theorem asserts that any quantum cellular automaton is structurally reversible, i.e., that it can be obtained by applying two blockwise unitary operations in a generalized Margolus partitioning scheme.
One-Dimensional Quantum Cellular Automata over Finite, Unbounded Configurations
It is shown that QCA always admit a two-layered block representation, and hence the inverse QCA is again a QCA, a striking result since the property does not hold for classical one-dimensional cellular automata as defined over such finite configurations.
An overview of quantum cellular automata
An overview of quantum cellular automata theory is given, with particular focus on structure results; computability and universality results; and quantum simulation results.
On one-dimensional quantum cellular automata
  • J. Watrous
  • Physics, Computer Science
    Proceedings of IEEE 36th Annual Foundations of Computer Science
  • 1995
It is demonstrated that any quantum Turing machine can be efficiently simulated by a one dimensional quantum cellular automaton with constant slowdown, and this can be accomplished by consideration of a restricted class of one dimensionalquantum cellular automata called one dimensional partitioned quantum Cellular automata.
Quantum complexity and negative curvature
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive
Introduction to UniversalQCompiler
An open source software package written in Mathematica that allows the decomposition of arbitrary quantum operations into a sequence of single-qubit rotations and controlled-NOT (C-NOT) gates, which is near optimal in terms of the number of gates required.
The unquantum quantum.
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    Scientific American
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The author's belief that the universe is an analog construction rather than a composition of discrete parts in contrast to the accepted beliefs of many physicists is discussed.
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    Proceedings of the National Academy of Sciences of the United States of America
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The quasi-ergodic hypothesis of classical Hamiltonian dynamics is generalized with the aid of the reduction of Hamiltonian systems to Hilbert space, and with the use of certain methods of the authors' closely connected with recent investigations of the algebra of linear transformations in this space.